NCERT Class 9 Science Solutions: Chapter 9 – Force and Laws of Motion Part 5 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Q_14_Image_Showing_Bullet_And_Wooden_Block

Question 14

Q. A bullet of mass 10g travelling horizontally with a velocity of 150 strikes a stationary wooden block and comes to rest in 0.03s. Calculate the distance of penetration of the bullet into the block. Also calculate the magnitude of the force exerted by the wooden block on the bullet.

Answer:

Now, it is given that the bullet is travelling with a velocity of 150 m/s.

Thus, when the bullet enters the block, its velocity Initial velocity,

Final velocity, (Since the bullet finally comes to rest)

Time taken to comes to rest,

According to the first equation of motion,

Acceleration of the bullet, a

(Negative sign indicates that the velocity of the bullet is decreasing.)

According to the third equation of motion:

Hence, the distance of penetration of the bullet in to the blocks 2.25 m.

From Newton՚s second law of motion:

Force, F

Mass of the bullet,

Acceleration of the bullet,

Hence, the magnitude of force exerted by the wooden block on the bullet is 50 N.

Question 15

An object of mass 1 kg travelling in a straight line with a velocity of 10 collides with, and sticks to, a stationary wooden clock 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.

Answer:

Mass of the object,

Velocity of the object before collision,

Mass of the stationary wooden block,

Velocity of the wooden block before collision,

Total momentum before collision

It is given that after collision, the object and the wooden block stick together.

Total mass of the combined system

Velocity of the combined object v

According to the law of conservation of momentum:

Total momentum before collision Total momentum after collision

The total momentum after collision is also 10 kg

Total momentum just before the impact kg

Total momentum just after the impact

Hence, velocity of the combined object after collision

Question 16

Q. An object of mass 100 kg is accelerated uniformly from a velocity of 5 to 8 in 6 s. Calculate the initial and final momentum of the object. Also, find the magnitude of the force exerted on the object.

Answer:

Initial velocity of the object,

Final velocity of the object,

Mass of the object,

Time take by the object to accelerate,

Initial momentum

Final momentum

Force exerted on the object,

Initial momentum of the object is 500 kg

Final momentum of the object is 800 kg

Force exerted on the object is 50 N.

Question 17

Q. Akhtar, Kiran and Rahul were riding in a motorcar that was moving with a high velocity on an expressway when an insect hit the windshield and got stuck on the windscreen. Akhtar and Kiran started pondering over the situation. Kiran suggested that the insect suffered a greater change in momentum as compared to the change in momentum of the motorcar (because the change in the velocity of the insect was much more than that of the motorcar) . Akhtar said that since the motorcar was moving with a larger velocity, it exerted d larger force on the insect. And as a result the insect died. Rahul while putting an entirely new explanation said that both the motorcar and the insect experienced the same force and a change in their momentum. Comment on these suggestions.

Answer:

According to the law of conservation of momentum:

Momentum of the car and insect system before collision = Momentum of the car and insect system after collision

Hence, the change in momentum of the car and insect system is zero.

The insect gets stuck on the windscreen. This means that the direction of the insect is reversed. As a result, the velocity of the insect changes to a great amount. On the other hand, the car continues moving with a constant velocity. Hence, Kiran՚s suggestion that the insect suffers a greater change in momentum as compared to the car is correct. The momentum of the insect after collision becomes very high because the car is moving at a high speed. Therefore, the momentum gained by the insect is equal to the momentum lost by the car.

Akhtar made a correct conclusion because the mass of the car is very large as compared to the mass of the insect.

Rahul gave a correct explanation as both the car and the insect experienced equal forces caused by the Newton՚s action-reaction law. But, he made an incorrect statement as the system suffers a change in momentum because the momentum before the collision is equal to the momentum after the collision.

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