A crate of mass m 1 =12.4 kg is pulled by a massless rope up a 36.9 degrees ramp. The rope passes over an ideal pulley and is attached to a hanging crate of mass m 2 =16.3 kg . The crates move 1.40 m, starting from rest. Find the work done by gravity on the hanging crate.
solve
To find the work done by gravity on the hanging crate, we need to calculate the change in potential energy of the hanging crate as it moves.
The change in potential energy can be calculated using the formula:
ΔPE = mgh
where m is the mass of the hanging crate, g is the acceleration due to gravity, and h is the change in height.
In this case, the change in height is equal to the vertical displacement of the hanging crate, which is given as 1.40 m.
So,
ΔPE = (m2)(g)(h)
= (16.3 kg)(9.8 m/s^2)(1.40 m)
Now, we can calculate the work done by gravity on the hanging crate using the equation:
Work = -ΔPE
Since gravity is acting in the opposite direction of the displacement, we use the negative sign.
Therefore,
Work = -(16.3 kg)(9.8 m/s^2)(1.40 m)
Calculating this expression will give you the work done by gravity on the hanging crate.
To find the work done by gravity on the hanging crate, we need to calculate the change in potential energy of the hanging crate as it moves up the ramp.
The formula for calculating the change in potential energy is:
ΔPE = mgh
Where:
ΔPE is the change in potential energy
m is the mass of the object
g is the acceleration due to gravity
h is the change in height
In this case, the hanging crate is moving up the ramp, so the change in height (h) is the vertical displacement of the crate.
First, let's calculate the vertical displacement of the crate. We can use trigonometry to find it.
The vertical displacement (d) is given by:
d = distance moved * sin(ramp angle) = 1.40 m * sin(36.9°)
Next, let's calculate the change in potential energy:
ΔPE = m2 * g * d
Now, substitute the given values into the formula:
ΔPE = 16.3 kg * 9.8 m/s² * (1.40 m * sin(36.9°))
Finally, calculate the result:
ΔPE ≈ 16.3 kg * 9.8 m/s² * (1.40 m * 0.588)
Therefore, the work done by gravity on the hanging crate is approximately equal to the calculated value of ΔPE.