The following is the distance-time table of an object in motion:
| Time in seconds | Distance in meters |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 8 |
| 3 | 27 |
| 4 | 64 |
| 5 | 125 |
| 6 | 216 |
| 7 | 343 |
(a) What conclusion can you draw about the acceleration? Is it constant, increasing, decreasing, or zero?
(b) What do you infer about the forces acting on the object?
(a) Since the distance travelled in in equal intervals of time is not equal rather it is increasing. It means the object is moving with a non-uniform velocity. It is accelerating.
By looking at the table we find distance (S) ∝ t3 ...(I)
Let us check if acceleration is constant. We know that for fixed 'a', equation S = ut + ½at2 is valid.
In this case, u = 0, (since at t = 0, S = 0), ⇒ S = ½at2 or (S) ∝ t2 ... (II)
But from the table, we get S ∝ t3, we conclude, that 'a' is increasing.
(b) Since the object is in accelerated condition, According to Newton's Second Law, F ∝ a.
We can say, unbalanced force is acting on the object.
While driving on a highway, an insect strikes on the car windshield and splatters. Which experiences greater impact (force): an insect or the windshield?
An object of mass 1 kg travelling in a straight line with a velocity of 10 m/s collides with, and sticks to, a stationary wooden block of mass 5 kg. Then they both move off together in the
same straight line. Calculate the total momentum just before the impact and just after the impact. Also, calculate the velocity of the combined object.
It is difficult to balance our body when we accidentally slip on a peel of banana. Explain why?
A man pushes a box of mass 50 kg with a force of 80 N. What will be the acceleration of the box due to this force? What would be the acceleration if the mass were doubled ?
A TV set is lying on a table. The TV set experiences a gravitational force (pull) downwards (FW) by the Earth. It also experiences a force on it due to table in contact i.e. (FTable-TV) in upward direction. Do these forces form an action-reaction pair? Do these forces follow Newton's third Law of motion?
A hammer of mass 500 g, moving at 50 m/s, strikes a nail. The nail stops the hammer in a very short time of 0.01 s. What is the force of the nail on the hammer ?
Identify the action and reaction forces in the following cases:
(a) A television (TV) lying on a table
(b) Pushing a wall with your hand
(c) Firing a bullet from a gun.
(d) Walking of a person on a ground.
| Time(s) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|---|
| Distance (m) | 0 | 1 | 8 | 27 | 64 | 125 | 216 | 343 |
A stone of 1 kg is thrown with a velocity of 20 m s-1 across the frozen surface of a lake and comes to rest after travelling a distance of 50 m. What is the force of friction between the stone and the ice? (Calculate time taken and acceleration also).
From a rifle of mass 4 kg, a bullet of mass 50 g is fired with an initial velocity of 35 m/s. Calculate the initial recoil velocity of the rifle.
A hockey ball of mass 200 g travelling at 10 m s-1 is struck by a hockey stick so as to return it along its original path with a velocity at 5 m s-1. Calculate the change of momentum occurred in the motion of the hockey ball by the force applied by the hockey stick.
An object experiences a net zero external unbalanced force. Is it possible for the object to be travelling with a non-zero velocity? If yes, state the conditions that must be placed on the magnitude and direction of the velocity. If no, provide a reason.
A motorcar of mass 1200 kg is moving along a straight line with a uniform velocity of 90 km/h. Its velocity is slowed down to 18 km/h in 4 s by an unbalanced external force. Calculate the acceleration and change in momentum. Also calculate the magnitude of the force required.