Question

In Fig. 7-30, a block of ice slides down a frictionless ramp at angle 50 while an ice worker pulls on the block (via a rope) with a force that has a magnitude of 50 N and is directed up the ramp. As the block slides through distance d 0.50 m along the ramp, its kinetic energy increases by 80 J. How much greater would its kinetic energy have been if the rope had not been attached to the block?

Answer 1

Answer:

It Is 25J greater.

Explanation:

Applying the Energy conservation theorem, we have:

$K_i+U_i+W_{ext}=K_f+U_f\\W_{ext}=\Delta K+\Delta U$

The Work done by the ice worker is given by:

$W_{ext}=F_w*d*cos(\theta)\\W_{ext}=50N*0.50m*cos(180)\\W_{ext}=-25J$

The angle is 180 degrees because the force exerted by the worker is opposite to the motion.

$\Delta U=\Delta K-W_{ext}\\\Delta U=80J-(-25J)\\\Delta U= 105J$

If the rope was not there, the external work is 0, so:

$\Delta U=\Delta K$

$\Delta k=105J$

The kinetic energy is 25J greater without the rope.

$\Delta K_f=105J-80J=25J$