Answers
Answer:
To find the density of seawater at a certain depth, we need to use the following equation:
P = P0 + ρgh
where:
P0 = pressure at the surface (given as 1 atm = 101325 Pa)
ρ = density of seawater at the depth we're interested in
g = acceleration due to gravity (9.81 m/s^2)
h = depth below the surface
We also need to use the bulk modulus equation to find the change in pressure with depth:
B = (ρ/ρ0)(P-P0)/P
where:
ρ0 = density of seawater at the surface (given as 1050 kg/m^3)
P = pressure at the depth we're interested in
Combining these two equations, we get:
B = (ρ/ρ0)((P0 + ρgh) - P0)/P
B = ρgh/P
ρ = (BP)/(gh)
Substituting the given values, we get:
ρ = (2.3 x 10^9 N/m^2)(101325 Pa)/(9.81 m/s^2)(1050 kg/m^3)(1 atm)
ρ ≈ 1031.4 kg/m^3
Therefore, the density of seawater at a depth where the pressure is 1 atm and the density at the surface is 1050 kg/m^3 is approximately 1031.4 kg/m^3.
Related Questions
Express your answer with the appropriate units. A 60.0 kg box hangs from a rope. What is the tension in the rope if:
A. The box is at rest?
B. The box moves up a steady 4.80 m/s ?
C. The box has vy = 5.00 m/s and is speeding up at 5.40 m/s^2 ? The y axis points upward.
D. The box has vy = 5.00 m/s and is slowing down at 5.40 m/s^2 ?
Answers
When the box is at rest, the tension in the rope is equal to the weight of the box. The tension in the rope is 588 N.
What is tension in physics?In physics, tension refers to the pulling force that is transmitted through a string, cable, rope, etc when it is pulled tight by forces acting at both ends. Tension is a vector quantity, and measured in units of newtons (N) or pounds (lbs).
A. When the box is at rest, the tension in the rope is equal to the weight of the box, which is given by:
Tension = Weight of the box = mg = (60.0 kg)*(9.81 m/s²) = 588 N
Thus, the tension = 588 N.
B. When the box moves up at a steady 4.80 m/s, the tension in the rope is equal to the force required to lift the box against gravity, which is given by:
Tension = Weight of the box + Force to lift the box = mg + ma = (60.0 kg)*(9.81 m/s²) + (60.0 kg)*(4.80 m/s²) = 1,167.6 N
Therefore, the tension in the rope is 1,167.6 N.
C. When the box has velocity along the y-axis = 5.00 m/s and is speeding up at 5.40 m/s², the tension in the rope is given by the equation:
Tension = Weight of the box + Force to accelerate the box = mg + ma = (60.0 kg)*(9.81 m/s²) + (60.0 kg)*(5.40 m/s²) = 1,199.4 N
Therefore, the tension in the rope is 1,199.4 N.
D. When the box has velocity along y-axis = 5.00 m/s and is slowing down at 5.40 m/s², the tension in the rope is given by the equation:
Tension = Weight of the box - Force to decelerate the box = mg - ma = (60.0 kg)(9.81 m/s²) - (60.0 kg)(5.40 m/s²) = 981.6 N
Therefore, the tension in the rope is 981.6 N.
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Which has more kinetic energy:
a. A compact car going 70 MPH or a tractor trailer going 15 MPH?
b. An SUV going 30 MPH or a pickup truck going 30 MPH?
c. A school bus going 15 MPH, an SUV going 35 MPH, or a
compact car going 45 MPH?
Answers
Answer:
Explanation:
a. The compact car going 70 MPH has more kinetic energy than the tractor trailer going 15 MPH. Kinetic energy is proportional to the square of the velocity, so even though the tractor trailer may have more mass, the higher velocity of the compact car results in greater kinetic energy.
b. The SUV and the pickup truck have the same kinetic energy since they have the same mass and velocity.
c. The compact car going 45 MPH has the most kinetic energy since it has the highest velocity out of the three vehicles. The SUV going 35 MPH has less kinetic energy, and the school bus going 15 MPH has the least kinetic energy.
A uniformly charged insulating sphere with radius r and charge +Q
lies at the center of a thin-walled hollow cylinder with radius R>r
and length L>2r. The cylinder is non-conducting and carries no net charge.
1:Determine the outward electric flux through the rounded "side" of the cylinder, excluding the circular end caps. (Hint: Choose a cylindrical coordinate system with the axis of the cylinder as its z -axis and the center of the charged sphere as its origin. Note that an area element on the cylinder has magnitude dA=2πRdz
2:Determine the electric flux upward through the circular cap at the top of the cylinder.
3:Determine the electric flux downward through the circular cap at the bottom of the cylinder.
4:Add the results from parts A - C to determine the outward electric flux through the closed cylinder.
5:What result is expected according to Gauss's law?
Note:Express your answers in terms of electric constant ϵ0
and some or all of the variables r, R , L , Q .
Answers
According to Gauss' equation, the total flux of an electric field in a confined surface is directly proportional to the charge enclosed.
State Gauss’s law.1)To determine the outward electric flux through the rounded "side" of the cylinder, we can use Gauss's law. We choose a cylindrical Gaussian surface with radius r and length L, centered at the origin (where the charged sphere is located). The electric field due to the sphere is spherically symmetric, so the electric field lines are parallel to the cylinder's axis and perpendicular to its sides.
E = (1/4πϵ0) (Q/r^2)
where r is the distance from the origin (center of the sphere) to the point on the Gaussian surface.
The area element of the Gaussian surface is dA = 2πRdz, where dz is an element of length along the cylinder's axis. The electric flux through the top and bottom surfaces of the Gaussian surface is then given by:
Φ = ∫E⋅dA = E ∫dA = E(2πR)L
Substituting the expression for the electric field, we have:
Φ = (Q/2ϵ0r^2)(2πRL)
Therefore, the outward electric flux through the rounded "side" of the cylinder is:
Φ = (Q/ϵ0)(R/Lr^2)
2)To determine the electric flux upward through the circular cap at the top of the cylinder, we use a flat Gaussian surface with radius R and height r, centered at the top of the cylinder. The electric field due to the charged sphere is perpendicular to the Gaussian surface, so the electric flux through the top cap is simply the flux through the flat Gaussian surface. The electric field at any point on the Gaussian surface is given by Coulomb's law as:
E = (1/4πϵ0) (Q/R^2)
The area element of the Gaussian surface is dA = πR^2, so the electric flux through the top cap is given by:
Φ = ∫E⋅dA = E ∫dA = EπR^2
Substituting the expression for the electric field, we have:
Φ = (Q/ϵ0)(R/r^2)
3)To determine the electric flux downward through the circular cap at the bottom of the cylinder, we use a similar flat Gaussian surface with radius R and height r, centered at the bottom of the cylinder. The electric flux through the bottom cap is also given by:
Φ = (Q/ϵ0)(R/r^2)
4)Adding the results from parts 1-3, we have the total outward electric flux through the closed cylinder as:
Φ_total = Φ_side + Φ_top + Φ_bottom
= (Q/ϵ0)(R/Lr^2) + 2(Q/ϵ0)(R/r^2)
Simplifying this expression, we have:
Φ_total = (Q/ϵ0) [(2R/r^2) + (R/Lr^2)]
5)According to Gauss's law, the total outward electric flux through a closed surface is proportional to the total charge enclosed within that surface. In this case, the closed surface is the cylindrical Gaussian surface with radius r and length L, centered at the origin (where the charged sphere is located). The charge enclosed within this surface is simply the charge of the sphere, which is +Q. Therefore, we expect the total outward electric flux through the closed cylinder to be:
Φ_total = Q/
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6. An 8000.0 kg truck starts off from rest and reaches a velocity of 18.0 m/s in 6.00 seconds. What is the truck’s acceleration and how much momentum does it have after it has reached this final velocity?
Answers
The truck's acceleration is 3.0m/s² and the momentum of the truck is 144000 kg m/s.
What is acceleration?It is the rate at which the speed and direction of a moving object vary over time.
We can use the following equation to calculate the acceleration of the truck:
a = (v - u) / t
where
a = acceleration
v = final velocity = 18.0 m/s
u = initial velocity = 0 m/s (the truck starts from rest)
t = time taken = 6.00 s
Substituting the values, we get:
a = (18.0 m/s - 0 m/s) / 6.00 s
a = 3.00 m/s²
Therefore, the acceleration of the truck is 3.00 m/s².
We can use the following equation to calculate the momentum of the truck:
p = m * v
where
p = momentum
m = mass of the truck = 8000.0 kg
v = final velocity = 18.0 m/s
Substituting the values, we get:
p = 8000.0 kg * 18.0 m/s
p = 144000 kg m/s
Therefore, the momentum of the truck after it has reached its final velocity is 144000 kg m/s.
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an object is launched at a velocity of 40m/s in a direction making an angle of 50°upward with the horizontal
a)what is the maximum height reached by the object
b) what is the object total flight time between launch and touching the ground
c) what's the object horizontal range(maximum ×above ground)
Answers
an electron of hydrogen is present in the 3.4eV energy state find angular momentum of electron
Answers
To find the angular momentum of an electron in the hydrogen atom, we can use the formula:
L = n * h / (2 * π)
where L is the angular momentum, n is the principal quantum number, h is Planck's constant, and π is a mathematical constant approximately equal to 3.14159.
First, we need to determine the value of n for the electron in the 3.4 eV energy state. We can use the formula for the energy of an electron in a hydrogen atom:
E = -13.6 eV / n^2
where E is the energy of the electron and -13.6 eV is the energy of the electron in the ground state of the hydrogen atom.
Solving for n, we get:
n^2 = (-13.6 eV) / E
n^2 = (-13.6 eV) / (3.4 eV)
n^2 = 4
n = 2
Therefore, the electron is in the second energy level of the hydrogen atom.
Now, we can calculate the angular momentum using the formula above. Substituting the values, we get:
L = 2 * h / (2 * π)
L = h / π
We can approximate π as 3.14159 and use the value of Planck's constant as h = 6.626 x 10^-34 J s. Substituting these values, we get:
L = (6.626 x 10^-34 J s) / (3.14159)
L = 2.104 x 10^-34 J s
Therefore, the angular momentum of the electron in the second energy level of the hydrogen atom is 2.104 x 10^-34 J s.
A soccer player kicks a ball of mass 0.500 kg toward the goal.The ball hits the crossbar at a height of 2.6 m with a speed of 15.0m/s. Suppose the ball was at rest on the ground before it was kicked. Use g = 9.80 m/s.
Answers
Answer:
The speed of the ball just before it hits the crossbar is 7.22 m/s.
Explanation:
We can use the conservation of energy to solve this problem.
At the moment the player kicks the ball, the ball has only kinetic energy, since it was at rest on the ground before being kicked. When the ball hits the crossbar, it has both kinetic energy and potential energy, since it is at a height above the ground. We can set the initial kinetic energy equal to the sum of the final kinetic and potential energy:
(1/2)mv^2 = mgh
where:
m = mass of the ball (0.500 kg)
v = initial speed of the ball (15.0 m/s)
g = acceleration due to gravity (9.80 m/s^2)
h = height of the crossbar above the ground (2.6 m)
We want to solve for the speed of the ball just before it hits the crossbar, which we can do by rearranging the equation:
v = sqrt(2gh)
v = sqrt(29.802.6) = 7.22 m/s (rounded to two decimal places
Which material would you choose to make the handrails of the playhouse? Use the data to explain your reasoning.
Answers
Answer:
Explanation:
To choose a material for the handrails of the playhouse, we need to consider its strength and durability. One option could be stainless steel, which has a high tensile strength and is resistant to corrosion and weathering. Another option could be treated wood, which is also strong and can be treated to resist moisture and insects. Ultimately, the choice would depend on factors such as cost, aesthetics, and availability of materials.
A 2.1 x 103 kg car starts from rest in a driveway. An average force of 4.0 x 103 N act on the car so that the car’s speed at the end of the driveway is 3.8 m/s. What was the length of the driveway?
Answers
Answer:
Explanation:
We can use the kinematic equation v^2 = u^2 + 2as to solve for the length of the driveway. Here, u = 0 (since the car starts from rest), v = 3.8 m/s, a = F/m = 4.0 x 10^3 N / 2.1 x 10^3 kg = 1.9 m/s^2. Solving for s, we get:
s = (v^2 - u^2) / 2a = (3.8^2) / (2 x 1.9) = 3.8 m
So the length of the driveway is 3.8 meters.
A power plant involves thermodynamic cycles to generate electrical power. In the first stage, water is pumped under saturated conditions from a pressure of 0.7 bar to 30 bar. Water then goes to the boiler at constant pressure and leaves the boiler at 500°C. In this condition, the steam is then expanded isentropically in a steam turbine so that the pressure returns to 0.7 bar and is cooled in a condenser. Determine:
a) Pump work
b) The incoming heat is given to the boiler
c) Turbine work
d) The heat removed by the condenser
e) Cycle thermal efficiency
Answers
To solve this problem, we can use the first law of thermodynamics, which states that the change in internal energy of a closed system is equal to the heat added minus the work done:
ΔU = Q - W
where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system.
We can apply this equation to each stage of the power plant cycle:
a) Pump work:
Since water is pumped under saturated conditions, its specific volume can be assumed to be constant. Therefore, the work done by the pump is given by:
W_pump = m * v * (P_2 - P_1)
where m is the mass of water pumped, v is the specific volume of water, and P_1 and P_2 are the initial and final pressures, respectively. From the given data, we have:
P_1 = 0.7 bar
P_2 = 30 bar
v = v_f = 0.00106 m^3/kg (from saturated water table)
m = 1 kg (Assumed)
Plugging in these values, we get:
W_pump = 1 kg * 0.00106 m^3/kg * (30 bar - 0.7 bar) = 0.0307 kJ
Therefore, the work done by the pump is 0.0307 kJ.
b) Heat added to the boiler:
At constant pressure, the heat added to the water is given by:
Q_boiler = m * cp * (T_2 - T_1)
where m is the mass of water, cp is the specific heat of water, and T_1 and T_2 are the initial and final temperatures, respectively. From the given data, we have:
T_1 = T_sat = 100°C (from saturated water table)
T_2 = 500°C
cp = 4.18 kJ/kg·K
Plugging in these values, we get:
Q_boiler = 1 kg * 4.18 kJ/kg·K * (500°C - 100°C) = 1672 kJ
Therefore, the heat added to the boiler is 1672 kJ.
c) Turbine work:
Since the steam is expanded isentropically in the turbine, its specific entropy remains constant. Therefore, the work done by the turbine is given by:
W_turbine = m * (h_1 - h_2)
where m is the mass of steam, h_1 is the specific enthalpy of steam at the inlet to the turbine, and h_2 is the specific enthalpy of steam at the outlet of the turbine. From the given data, we have:
h_1 = h_sat + cp * (T_2 - T_sat) = 2882 kJ/kg (from steam tables)
h_2 = h_sat + cp * (T_3 - T_sat) = 1952 kJ/kg (from steam tables)
T_3 = T_sat = 100°C (from saturated water table)
m = 1 kg (Assumed)
Plugging in these values, we get:
W_turbine = 1 kg * (2882 kJ/kg - 1952 kJ/kg) = 930 kJ
Therefore, the work done by the turbine is 930 kJ.
d) Heat removed by the condenser:
The steam is condensed at constant pressure, and the heat removed by the condenser is given by:
Q_condenser = m * (h_2 - h_3)
where h_3 is the specific enthalpy of water at the outlet of the condenser, which is the same as the specific enthalpy of water at the inlet to the pump. From the given data, we have:
h_3 = h_f = 419 kJ/kg (from saturated water table)
Plugging in the values, we get:
Q_condenser = 1 kg * (1952 kJ/kg - 419 kJ/kg) = 1533 kJ
Therefore, the heat removed by the condenser is 1533 kJ.
e) Cycle thermal efficiency:
The cycle thermal efficiency is the ratio of the net work output to the heat input. The net work output is the difference between the turbine work and the pump work, i.e.,
W_net = W_turbine - W_pump = 930 kJ - 0.0307 kJ = 929.97 kJ
The heat input is the heat added to the boiler, i.e.,
Q_in = Q_boiler = 1672 kJ
Therefore, the cycle thermal efficiency is:
η = W_net / Q_in = 929.97 kJ / 1672 kJ = 0.555 or 55.5%
Therefore, the cycle thermal efficiency of the power plant is 55.5%.
A harp string has a length of 30.5 cm and vibrates with a node at each end and an antinode inthe center. If its frequency is 440 Hz, find (a) the wavelength and (b) the speed of the waves on the string.
Answers
Answer:
In this problem, the harp string is fixed at both ends, so it is a standing wave with nodes at both ends and an antinode in the center. The frequency of the wave is given as 440 Hz, and the length of the string is 30.5 cm.
(a) To find the wavelength of the wave, we can use the formula:
λ = 2L/n
where λ is the wavelength, L is the length of the string, and n is the number of nodes. In this case, n = 2 (since there are nodes at both ends) and L = 30.5 cm, so we have:
λ = 2(30.5 cm)/2 = 30.5 cm
Therefore, the wavelength of the wave is 30.5 cm.
(b) To find the speed of the wave on the string, we can use the formula:
v = fλ
where v is the speed of the wave, f is the frequency of the wave, and λ is the wavelength. In this case, f = 440 Hz and λ = 30.5 cm, so we have:
v = (440 Hz)(30.5 cm) = 13420 cm/s
Therefore, the speed of the wave on the string is 13420 cm/s
Explanation:
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a mass of 20kg is held stationary by a rope passing over a frictionless pally. what is the tension T in the rope?
Answers
The tension in the rope is 196.2 N. The rope is exerting a force of 196.2 N on the object to keep it stationary.
Assuming that the mass is not accelerating, the tension in the rope must be equal to the weight of the mass. The weight of the mass can be found using the formula:
weight = mass x acceleration due to gravity
where acceleration due to gravity is approximately 9.81 m/s².
Therefore, the weight of the mass is:
weight = 20 kg x 9.81 m/s² = 196.2 N
Since the mass is held stationary, the tension in the rope must be equal to the weight of the mass, which is 196.2 N. So the tension T in the rope is 196.2 N.
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State each of Newton's Laws of Motion and explain how each can be observed during the flight of a space craft, from liftoff until the craft enters space.
Answers
newton 3th law of motion and newton's law of universal gravitation
Answer: 1. Newton's First Law of Motion (Law of Inertia): An object at rest will remain at rest, and an object in motion will remain in motion with a constant velocity unless acted upon by an external force.
During liftoff, the spacecraft is initially at rest. However, the rocket engines generate a force that propels the spacecraft forward and overcomes its initial state of rest. Once the spacecraft is in motion, it will continue to move forward with a constant velocity unless acted upon by other external forces, such as air resistance or gravity.
2. Newton's Second Law of Motion: The acceleration of an object is directly proportional to the force applied to it, and inversely proportional to its mass.
As the rocket engines burn fuel, they generate a force that propels the spacecraft forward. The acceleration of the spacecraft is directly proportional to the force generated by the engines, and inversely proportional to the mass of the spacecraft. As fuel is consumed and the spacecraft becomes lighter, its acceleration will increase, allowing it to reach escape velocity and enter space.
3. Newton's Third Law of Motion: For every action, there is an equal and opposite reaction.
During liftoff, the rocket engines generate a powerful force that propels the spacecraft forward. However, the engines also generate an equal and opposite reaction force, pushing back against the rocket and causing it to shake and vibrate. This force is also responsible for the loud noise and exhaust plumes that are visible during liftoff.
These are the three laws of motion developed by Sir Isaac Newton, and they explain how objects move and interact with one another. They can be observed in the launch and flight of a spacecraft, from the initial state of rest to the forces that drive it forward, to the equal and opposite forces that shake the rocket during liftoff.
What is the electric potential energy of the group of charges in the figure? (Figure 1)
Answers
that the relative placements of the charges as well as their multiples affect a set of ions' potential energy. When the specific charge have the same sign or have equal signs, the energy is positive. Or else, it is negative.
How is potential energy calculated?The force acting just on two objects affects the potential energy formula. The formula for gravitational force is P.E. (= mgh, where g seems to be the acceleration caused by gravity (9.8 m/s2 at the earth's surface) while h represents the elevation in metres.
What is a system with two charges' potential energy?As a result, the system's potential energy equals the sum of a work that was done to set up the entire system of two counts. The potential energy that exists in the combination of two charges in such an external field can be stated as follows: q1V(r1) = q2V(r2) + (q1q2/4or12).
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waves are generated in a rope of length 6m. What is the speed of the wave if its period is 25.m
Answers
The speed of the wave would be0.48 m/s.
Speed of a waveThe speed of a wave is given by the formula:
v = λ/T
where v is the wave speed, λ (lambda) is the wavelength, and T is the period.
To solve this problem, we need to know the wavelength of the wave. We can find the wavelength using the formula:
λ = 2L
where L is the length of the rope. Substituting L = 6 m, we get:
λ = 2 × 6 m = 12 m
Now we can use the formula for wave speed:
v = λ/T
Substituting λ = 12 m and T = 25 s, we get:
v = 12 m/25 s = 0.48 m/s
Therefore, the speed of the wave is 0.48 m/s.
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Answers
If F₁ has a greater magnitude than F₂, the box will accelerate backward because the net force is in the backward direction (1st option)
How do i know which direction the box will move to?To obtain the direction in which the box will move, we shall determine the net force acting on the box. This is illustrated below:
Assumption:
Magnitude of force 1 (F₁) = 40 NMagnitude of force 2 (F₂) = 25 NNet force (F) =?Net force = Magnitude of force 1 (F₁) - Magnitude of force 2 (F₂)
Net force = F₁ - F₂
Net force = 40 - 25
Net force = 15 N backward
From the above illustration, we can see that the net force is 15 N backward.
Thus, we can conclude from the box will accelerate backward (1st option)
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Gas pressure is defined as
Select one:
O a. mass per unit area
O b.
O c. force per unit area
O d. force per unit volume
acceleration per unit volume
Answers
Answer: b. force per unit area.
Explanation:
Owen hits a baseball with a velocity of 55 m/s. The ballpark fence is 120 m away.
Does the ball reach the fence if it leaves the bat traveling upward at an angle of 30°
to the horizontal?
Answers
Answer:
Explanation:
We can solve this problem using kinematic equations. We know that the initial velocity of the ball is 55 m/s at an angle of 30° to the horizontal. We can break this velocity into its horizontal and vertical components:
vx = v0 cos θ = 55 cos 30° = 47.6 m/s
vy = v0 sin θ = 55 sin 30° = 27.5 m/s
We can now use the vertical motion equation to find the time it takes for the ball to reach its maximum height:
Δy = vy t + 0.5 a t^2
At the maximum height, the vertical velocity of the ball is 0, so we have:
0 = vy + a t_max
Solving for t_max, we get:
t_max = -vy / a = -27.5 / (-9.8) = 2.81 s
The ball will take twice this time to reach the fence, since it needs to come back down to the ground:
t_total = 2 t_max = 5.62 s
The horizontal distance the ball travels during this time is:
Δx = vx t_total = 47.6 × 5.62 = 267.7 m
Since this distance is greater than the distance to the fence (120 m), the ball will reach the fence if it leaves the bat traveling upward at an angle of 30° to the horizontal.
A firefighting crew uses a water cannon that shoots water at 29.0 m/s
at a fixed angle of 53.0 ∘
above the horizontal. The firefighters want to direct the water at a blaze that is 10.0 m
above ground level. How far from the building should they position their cannon? There are two possibilities ( d1
); can you get them both? (Hint: Start with a sketch showing the trajectory of the water.)
Express your answer in meters.
d1 and d2
Answers
The second possibility is that the firefighters can position their cannon anywhere within a range of 60.2 m from the building to hit the blaze at 10.0 m above ground level.
What is Horizontal Velocity?
Horizontal velocity is the component of velocity in the horizontal direction, perpendicular to the vertical direction. It describes the speed and direction of motion of an object in the horizontal plane. In the absence of external forces, the horizontal velocity of an object moving through the air remains constant, as there is no force acting on the object in the horizontal direction.
Let's first find the time it takes for the water to reach the maximum height:
The vertical component of the initial velocity is:
vy = v * sin(θ) = 29.0 m/s * sin(53.0°) = 22.7 m/s
Using the kinematic equation:
where Δy = 10.0 m, vyi = 22.7 m/s, and a = -9.81 m/[tex]s^{2}[/tex] (the negative sign indicates that acceleration is in the opposite direction to the initial velocity).
We get:
10.0 m = 22.7 m/s * t - 1/2 * 9.81 m/[tex]s^{2}[/tex] * [tex]t^{2}[/tex]
Simplifying and solving for t, we get:
t = 1.61 s
Now, let's find the horizontal displacement of the water:
The horizontal component of the initial velocity is:
vx = v * cos(θ) = 29.0 m/s * cos(53.0°) = 18.7 m/s
Using the equation:
Δx = vx * t
where Δx is the horizontal displacement, vx is the horizontal component of the initial velocity, and t is the time we found above.
We get:
Δx = 18.7 m/s * 1.61 s = 30.1 m
So the firefighters should position their cannon 30.1 m away from the building.
To find the second possibility, we need to find the range of the water cannon, which is the horizontal distance traveled by the water before it hits the ground. The range can be calculated using the formula:
where R is the range, v is the initial velocity, θ is the angle above the horizontal, and g is the acceleration due to gravity.
Plugging in the values we get:
R = [tex]29.0^{2}[/tex] * sin(2 * 53.0°) / (2 * 9.81) = 60.2 m
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Two asteroids are suspended in space 50 meters apart. The masses of the asteroids are 2000000 kg and
3000000 kg.
Answers
Answer:
Explanation:
What is the gravitational force between them?
To calculate the gravitational force between two objects, we can use the formula:
F = G * (m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant (6.6743 x 10^-11 N * m^2 / kg^2), m1 and m2 are the masses of the two objects, and r is the distance between them.
Plugging in the given values, we get:
F = (6.6743 x 10^-11 N * m^2 / kg^2) * (2000000 kg) * (3000000 kg) / (50 m)^2
F = 0.8046 N
Therefore, the gravitational force between the two asteroids is approximately 0.8046 N.
A rock with a mass of 10.0 kg is balanced on top of a large boulder. Describe the forces acting on the rock, and use the concept of forces to explain why it stays on top of the boulder.
Answers
There are two forces acting on the rock: the force of gravity pulling it downward and the force of the boulder supporting it from underneath.
What is the force of gravity?The force of gravity is the gravitational attraction between the rock and the Earth. It pulls the rock downward with a force equal to its weight, which is given by the equation Fg = mg, where Fg is the force of gravity, m is the mass of the rock, and g is the acceleration due to gravity (approximately 9.81 m/s^2).
Why do boulder stays on top?The concept of forces explains why the rock stays on top of the boulder because the forces are balanced. The force of gravity pulling the rock downward is equal and opposite to the force of the boulder supporting it from underneath. As a result, the rock remains in equilibrium, or a state of balance, on top of the boulder. If either force were to change, the equilibrium would be disrupted, and the rock would either fall to the ground or be pushed off the boulder.
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An empty cylindrical barrel is open at one end and rolls without slipping straight down a hill. The barrel has a mass of 21.0 kg, a radius of 0.260 m, and a length of 0.650 m.
The mass of the end of the barrel equals a fifth of the mass of its side, and the thickness of the barrel is negligible. The acceleration due to gravity is =9.80 m/s2.
What is the translational speed f of the barrel at the bottom of the hill if released from rest at a height of 31.0 m above the bottom?
Answers
The translational speed of the barrel at the bottom of the hill is 28.1 m/s.
What is translational speed?Translational speed is the speed of an object in a straight line. It is different from rotational speed, which is the speed of an object’s rotation. Translational speed is a measure of how quickly an object is moving in a specific direction. It is calculated by dividing the distance traveled by the time it took to travel that distance.
The barrel's initial potential energy can be calculated using the equation U = mgh, with m being the mass of the barrel (21.0 kg),
g being the acceleration due to gravity (9.80 m/s2),
and h being the height of the barrel above the bottom of the hill (31.0 m). Therefore, the barrel's initial potential energy is U = 21.0 kg × 9.80 m/s2 × 31.0 m = 6259.8 J.
At the bottom of the hill, the barrel's potential energy is zero, since it is at the lowest point.
Therefore, the barrel's total mechanical energy is equal to its kinetic energy.
Since the kinetic energy of an object is given by K = ½mv2,
where m is the mass of the barrel and v is its velocity,
we can calculate the barrel's velocity at the bottom of the hill by rearranging the equation to v = √(2K/m).
Substituting in the values for the barrel's mass (21.0 kg) and its total mechanical energy (6259.8 J) gives us v = √(2 × 6259.8 J / 21.0 kg) = 28.1 m/s.
Therefore, the translational speed of the barrel at the bottom of the hill is 28.1 m/s.
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Two hot air balloons with the same mass and amount of helium put inside of them if one is a rigid material and the other expands which one would be the highest?
Answers
Answer:
One is that atmospheric pressure is dramatically reduced at high altitudes, so a helium balloon expands as it rises and eventually explodes. If you inflate a balloon beyond its limits at room temperature, it will break into small pieces up to about ten centimetres long
Explanation:
A gas is contained in a cylinder with a frictionless moveable piston at a pressure of 2.7 * 105 pascals and a volume of 0.04 cubic meters. What is the work done by the gaseous system if the volume is increased to 0.12 cubic meters ?
Answers
The work done by the gaseous system if the volume is increased to 0.12 cubic meters is given as 21,600 joules
How to solve for the workdoneTo find the work done by the gas, we can use the formula:
W = PΔV
where W is the work done, P is the pressure of the gas, and ΔV is the change in volume.
At the initial state, the pressure is P = 2.7 × 10^5 Pa and the volume is V1 = 0.04 m^3. At the final state, the volume is V2 = 0.12 m^3.
The change in volume is ΔV = V2 - V1 = 0.12 m^3 - 0.04 m^3 = 0.08 m^3.
Substituting these values into the formula, we get:
W = PΔV = (2.7 × 10^5 Pa) × (0.08 m^3) = 21,600 J
Therefore, the work done by the gaseous system is 21,600 joules (J).
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Answer:
4.6x10^4 joules
Explanation:
A contractor is pushing a stove across a kitchen floor with a constant velocity of 18 cm/s [fwd]. The contractor is exerting a constant horizontal force of 85 N [fwd]. The force of gravity on the stove is 447 N [down].
Determine the normal force (FN ) and the force of friction (Ff ) acting on the stove.
Determine the total force applied by the floor (Ffloor) on the stove.
Answers
Answer:
Explanation:
Since the stove is moving with a constant velocity, we know that the net force on the stove is zero. Therefore, the force of friction acting on the stove must be equal in magnitude and opposite in direction to the horizontal force being applied by the contractor. We can use Newton's second law to solve for the normal force and force of friction:
ΣF = ma
where ΣF is the net force, m is the mass of the stove, and a is the acceleration of the stove (which is zero in this case).
First, we need to convert the velocity to m/s and the forces to Newtons (N):
18 cm/s = 0.18 m/s
85 N [fwd] - force applied by contractor
447 N [down] - force of gravity on the stove
Now we can solve for the normal force:
ΣFy = 0 (since the stove is not accelerating in the y-direction)
FN - 447 N = 0
FN = 447 N
Therefore, the normal force acting on the stove is 447 N.
Next, we can solve for the force of friction:
ΣFx = 0 (since the stove is moving at a constant velocity)
Ff - 85 N = 0
Ff = 85 N [bkwd]
Therefore, the force of friction acting on the stove is 85 N [bkwd].
Finally, we can solve for the total force applied by the floor:
ΣF = ma = 0 (since the stove is not accelerating)
Ffloor - 85 N - 447 N = 0
Ffloor = 532 N [up]
Therefore, the total force applied by the floor on the stove is 532 N [up].
help me
Write your answer on the lines below.
4. Are the light waves reflecting off a red stop sign longer or shorter than the waves reflecting off a violet-colored jacket? Explain how you know.
Answers
The light waves reflecting off a red stop sign would be longer than the light waves reflecting off a violet-colored jacket. This is because red light has a longer wavelength than violet light.
Light waves and reflectionLight waves, like all waves, are characterized by their wavelength. The wavelength of a wave determines its color, with shorter wavelengths appearing as blue and violet, and longer wavelengths appearing as red and orange.
Because the wavelength of red light is longer than the wavelength of violet light, the light waves reflecting off the red stop sign would be longer than the light waves reflecting off the violet-colored jacket.
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Before a collision, a 200-kg Honda is driving 30 m/s towards a
600-kg Toyota that is not moving. After the crash, the two cars
are stuck together. What is their velocity?
m/s
Answers
As a result, the combined Honda-Toyota system's post-collision speed is 7.5 m/s.
How can you calculate the entire momentum prior to a collision?The system's center of mass was v/2 before to the collision since one automobile had a velocity of v and the other zero. The total momentum is equal to the entire mass times the velocity of the center of mass, or (2m)(v/2) = mv before and after.
Initial momentum of Honda = m1 * v1
= 200 kg * 30 m/s
= 6000 kg·m/s
Final momentum of combined system = (m1 + m2) * v_final
Setting the two momenta equal to each other, we get:
6000 kg·m/s = 800 kg * v_final
Solving for v_final, we get:
v_final = 6000 kg·m/s / 800 kg
= 7.5 m/s
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When a ball is thrown into the air, its kinetic energy is lowest
A at its highest point.
B. at the moment it is released.
C. as it begins to fall back to the ground.
Answers
A uniform electric field makes an angle of 60.0∘ with a flat surface. The area of the surface is 6.66×10−4m2. The resulting electric flux through the surface is 4.44 N⋅m2/C.
Calculate the magnitude of the electric field.(Express your answer with the appropriate units.)
Answers
Answer:
Explanation:
The electric flux through a surface is given by the equation:
Φ = EAcos(θ)
where Φ is the electric flux, E is the electric field, A is the area of the surface, and θ is the angle between the electric field and the surface normal.
We are given Φ = 4.44 N⋅m2/C, A = 6.66×10−4 m2, and θ = 60.0∘. Substituting these values into the equation above and solving for E, we get:
E = Φ / (Acos(θ))
= 4.44 N⋅m2/C / (6.66×10−4 m2cos(60.0∘))
= 1.62×10^4 N/C
Therefore, the magnitude of the electric field is 1.62×10^4 N/C.
The magnitude of the electric field is 13,320 N/C.
What is electric flux?The electric flux through a surface is defined as the product of the electric field and the area of the surface projected perpendicular to the electric field. Mathematically, we can write:
Φ = EAcos(θ)
where Φ is the electric flux, E is the electric field, A is the area of the surface, and θ is the angle between the electric field and the surface normal.
Here in the Question,
We are given the electric flux Φ = 4.44 N·m^2/C, the area A = 6.66×10^-4 m^2, and the angle θ = 60.0°. We can solve for the magnitude of the electric field E by rearranging the equation as follows:
E = Φ / (A*cos(θ))
Substituting the given values, we get:
E = 4.44 N·m^2/C / (6.66×10^-4 m^2*cos(60.0°))
Simplifying the denominator, we get:
E = 4.44 N·m^2/C / (6.66×10^-4 m^2*0.5)
E = 13,320 N/C
Therefore, 13,320 N/C is the magnitude of the electric field.
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What is the defining property of an mechanical wave?
A. It travels by compressing particles.
B. It travels up and down.
C. It does not need a medium to travel.
D. It needs a medium to travel.
Answers
Answer: D. It needs a medium to travel.
Explanation:
One way to categorize waves is on the basis of the direction of movement of the individual particles of the medium relative to the direction that the waves travel. Categorizing waves on this basis leads to three notable categories: transverse waves, longitudinal waves, and surface waves.