A 10.2 kg crate is pulled up a rough incline
with an initial speed of 1.5 m/s. The pulling
force is 123.0 N parallel to the incline, which
makes an angle of 14.6◦ with the horizontal.
The coe�cient of kinetic friction is 0.39 and
the crate is pulled a distance of 8.1 m.
The acceleration of gravity is 9.81 m/s2 .
a) Find the work done by Earth’s gravity
on the crate. Answer in units of J.
You don't need to worry about friction to know how much work was done by, or against, gravity. It equals the change in potential energy, which is
M g * (change in elevation).
Put a minus sign in front of it to get the work done BY gravity.
The change in elevation is
H = 8.1 sin 14.6 meters
To find the work done by Earth's gravity on the crate, we need to determine the change in gravitational potential energy.
The formula for calculating gravitational potential energy is:
Potential Energy (PE) = m * g * h
Where:
m = mass of the object (in kg)
g = acceleration due to gravity (9.81 m/s^2)
h = height (changes to 0 since we're only concerned about a horizontal distance)
In this case, since the crate is being pulled up a rough incline, the height doesn't change. Therefore, the change in gravitational potential energy will be zero.
Hence, the work done by Earth's gravity on the crate is zero J (Joules).