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?

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krlosdark12 krlosdark12 · Answer 1 · 2019-11-05T22:10:55+01:00

Answer:

It Is 25J greater.

Explanation:

Applying the Energy conservation theorem, we have:

[tex]K_i+U_i+W_{ext}=K_f+U_f\\W_{ext}=\Delta K+\Delta U[/tex]

The Work done by the ice worker is given by:

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

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

[tex]\Delta U=\Delta K-W_{ext}\\\Delta U=80J-(-25J)\\\Delta U= 105J[/tex]

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

[tex]\Delta U=\Delta K[/tex]

[tex]\Delta k=105J[/tex]

The kinetic energy is 25J greater without the rope.

[tex]\Delta K_f=105J-80J=25J[/tex]