A 31.00 kg block starts from rest at the top of a 24.0 m long 30.0° incline. Its kinetic energy at the bottom of the incline is 3645.6 J. How much work is done by friction?
work done by friction= mgh - finalKE
M*g = 31 * 9.8 = 303.8 N. = Wt. of block.
h = 24 * sin30 = 12 m.
KE + F*d = PE.
3645.6 + F*d = 303.8 * 12 = 3645.6,
F*d = 0. Therefore, there is no friction and no work done by friction.
To find the work done by friction, we first need to calculate the gravitational potential energy at the top of the incline and the kinetic energy at the bottom of the incline.
Step 1: Calculate the gravitational potential energy at the top of the incline.
The formula for gravitational potential energy is:
Potential Energy = m * g * h
Where:
m = mass of the block (31.00 kg)
g = acceleration due to gravity (approximately 9.8 m/s^2)
h = height of the incline (24 m * sin(30°))
First, we calculate the height of the incline:
h = 24 m * sin(30°) = 12 m
Now, we can calculate the gravitational potential energy at the top:
Potential Energy = 31.00 kg * 9.8 m/s^2 * 12 m = 3628.8 J
Step 2: Calculate the work done by friction.
The work done by friction is the difference between the initial potential energy and the final kinetic energy (due to the work-energy principle), which is the energy lost to friction.
Work done by friction = Potential Energy at the top - Kinetic Energy at the bottom
Work done by friction = 3628.8 J - 3645.6 J = -16.8 J
The negative sign indicates that work is done on the block, causing it to lose energy to friction.
Therefore, the work done by friction is approximately -16.8 J.