A skateboarder with mass ms = 50 kg is standing at the top of a ramp which is hy
ID: 1429532 • Letter: A
Question
A skateboarder with mass ms = 50 kg is standing at the top of a ramp which is hy = 4.5 m above the ground. The skateboarder then jumps on his skateboard and descends down the ramp. His speed at the bottom of the ramp is vf = 6.7 m/s. Randomized Variables ms = 50 kg hy = 4.5 m vf = 6.7 m/s show answer Incorrect Answer Part (a) Write an expression for the work, Wf, done by the friction force between the ramp and the skateboarder in terms of the variables given in the problem statement. show answer Incorrect Answer Part (b) The ramp makes an angle ? with the ground, where ? = 30 degrees. Write an expression for the magnitude of the friction force, fr, between the ramp and the skateboarder.
Explanation / Answer
a) Using work energy theorem,
work done by friction + work done by normal force + work done by gravity = change in KE
Wf + 0 + mgHy = ms vf^2 /2 - 0
Wf = 0.5 ms vf^2 - mgHy
b) Wf = - f.d
and dsin@ = hy
d = hy / sin@
0.5 ms vf^2 - mgHy = - hy f / sin@
f = ( mg hy - 0.5 ms vf^2 )sin@ / hy