Question

A small smooth object slides from rest down a smooth inclined plane inclined at 30° to the horizontal. What is (i) the acceleration down the plane, (ii) the time to reach the bottom if the plane is 5 m long? The object is now thrown up the plane with an initial velocity of 15 m/s. (iii) How long does the object take to come to rest? (iv) How far up the plane has the object then travelled? ​

Answer 1

Answer:

The time it takes for the object to come to rest depends on the amount of friction that is between the object and the plane.

Question : A small smooth object slides from rest down a smooth inclined plane inclined at 30° to the horizontal.

Explanation:

From the above question,

They have given :

A small smooth object slides from rest down a smooth inclined plane inclined at 30° to the horizontal.

Assuming no air resistance, the object will accelerate down the inclined plane at an acceleration of 9.81 m/$s^{2}$ sin(30°) = 4.91 m/$s^{2}$.

The acceleration is in the direction of the inclined plane and not in the horizontal direction.

(i) The acceleration down the plane

       Assuming no air resistance, the object will continue to accelerate down the inclined plane until it reaches terminal velocity, which is the maximum velocity an object can reach in a given medium when the force of air resistance is equal to the force of gravity.

(ii) The time to reach the bottom if the plane is 5 m long

     The time to reach the bottom if the plane is 5 m long is approximately 1.02 seconds.

The object is now thrown up the plane with an initial velocity of 15 m/s.

(iii) How long does the object take to come to rest? (iv) How far up the plane has the object then travelled

         

Assuming no friction, the object will take approximately 0.5 seconds to come to rest. In this time, it would have traveled approximately 2.5 meters up the plane.

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