Question

2. A block slides down a plane inclined at 35^{o} with
respect to the horizontal, with coefficient of kinetic friction
0.2. Find the ratio of the time taken to slide down the plane
starting from rest, compared to the time it would take to slide
down the plane if it were frictionless.

3. A 20 kg block slides frictionlessly down an inclined plane that is 2.8 m long and 1.2 m high. A person pushes up against the block, parallel to the incline, so that the block slides down with constant speed. How much work is done on the block by (a) the force exerted by the person, (b) the gravitational force on the block, (c) the net force on the block, and (d) the normal force exerted by the inclined plane on the block.

Answer #1

2.Without friction, the acceleration of the block down the
inclined plane
=5.62 m/s^{2}.

With friction, the acceleration of the block
=4.01 m/s^{2}.

Since
,
where t_{1} is the time to slide down the plane without
friction.

Similarly
where t_{2} is the time to slide down the plane with
friction.

Therefore =.

3.Let F be the force with which the person pushes the block up against the gravitational force. Then

.

a) The work done by the person= since the force is antiparallel to ds.

b) The work done by the gravitational force on the block=.

c) The work done by the net force=0 since there is no change in the kinetic energy of the block as it slides down the plane.

d) The work done by the normal force =0 since the force is perpendicular to the inclined plane along which the block slides so that .

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