Question

Twin brothers, Paul and Fred, walk up a slope with an angle of 45 degrees. Paul is twice as fast as Fred. How does the force they exert with every step, the work they do to get to the top, and the power they put out compare between the two brothers?

Answer 1

Forces along the incline are:

i)Force due to gravity = mg sin 45 (down the incline) , where m is mass and g is gravitational acceleration.

ii)Upward force F.

Since they are moving at a constant speed, these forces must balance. So, F=mg sin 45.

Now, for both brothers, mass m is same as they are twins. So, force F is same.

Also, when they both reach the top , their displacements are same.

Now, work done = F*s, where F is force and s is displacement along the force. For both Paul and Fred, F and s are same. So, work done is same.

Power=work / time

Since Paul is twice as fast as Fred, he will take half the time to reach the top.

So, power for Paul would be twice as compared to Fred.

So, i)force is same ii)work done is same iii)power is twice for Paul as compared to Fred.