Question #166860

A 3.50 kg block is pulled along a moving conveyor belt at a constant speed of

0.500 m/s relative to a stationary observer while the belt moves at a constant

speed of 0.200 m/s in the same direction. If the coefficient of kinetic friction is

0.400, the magnitude of the work, in J, done on the block by the force of friction

in 8.00 s is


1
Expert's answer
2021-02-28T07:26:41-0500

Let's first find the velocity of the block with respect to belt:


vblock=0.5 ms0.2 ms=0.3 ms.v_{block}=0.5\ \dfrac{m}{s}-0.2\ \dfrac{m}{s}=0.3\ \dfrac{m}{s}.

Then, we can find the distance traveled by the block in 8.0 seconds:


d=vblockt=0.3 ms8.0 s=2.4 m.d=v_{block}t=0.3\ \dfrac{m}{s}\cdot8.0\ s=2.4\ m.

Finally, we can find the work done on the block by the force of friction in 8.00 s:


Wfr=Ffrd=μkmgd,W_{fr}=F_{fr}d=\mu_kmgd,Wfr=0.43.5 kg9.8 ms22.4 m=32.9 J.W_{fr}=0.4\cdot3.5\ kg\cdot9.8\ \dfrac{m}{s^2}\cdot2.4\ m=32.9\ J.

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