Question

A sled is being pulled across a horizontal patch of snow. Friction is negligible. The pulling force points in the same direction as the sled's displacement, which is along the +x axis. As a result, the kinetic energy of the sled increases by 38 percent. By what percentage would the sled's kinetic energy have increased if this force had pointed 62 above the +x axis?

Answer 1

Using Work-energy theorem:

W = dKE

W = Work-done by pulling force = F.d

W = F*d*cos

Given that when pulling force is in direction of displacement, then = 0 deg, So

W = F*d*cos 0 deg = F*d

Also given that in this case kinetic energy increases by 38%, So

dKE = KEf - KEi

If KEi = K0,then KEf = 1.38*K0, So

dKE = 0.38*K0, So

F*d = 0.38*K0

Now in 2nd case, when pulling force is 62 deg above the +ve x-axis, then

W = F*d*cos 62 deg = 0.4695*F*d

So, Now from Work-energy theorem:

W = dKE

0.4695*F*d = dKE

dKE = 0.4695*0.38*K0 = 0.1784*K0

So,

KEf - KEi = 0.1784*K0

KEf = K0 + 0.1784*K0 = 1.1784*K0

So, final kinetic energy of sled will increase by 0.1784 times initial KE, In other words

kinetic energy of sled will increase by 17.84% (Approx 18%)

Let me know if you've any query.