# Problems Based on Newton’s Second Law of Motion

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NEWTON’S LAWS OF MOTION

• Newton’s First Law of Motion – Any object remains in the state of rest or in uniform motion along a straight line, until it is compelled to change the state by applying external force.
• Newton’s Second Law of Motion – The rate of change of momentum is directly proportional to the force applied in the direction of force.
• Newton’s Third Law of Motion – For every action there is an equal and opposite reaction.

NEWTON’S SECOND LAW OF MOTION

Newton’s second Law of Motion states that The rate of change of momentum is directly proportional to the force applied in the direction of force.

For example; when acceleration is applied on a moving vehicle, the momentum of the vehicle increases and the increase is in the direction of motion because the force is being applied in the direction of motion. On the other hand, when brake is applied on the moving vehicle, the momentum of the vehicle decreases and the decrease is in the opposite direction of motion because the force is being applied in the opposite direction of motion.

Force = mass × acceleration

Newton’s Second Law of Motion gives the relation between force, mass and acceleration of an object.

According to the relation obtained above, Newton’s Second Law can be modified as follows:
The product of mass and acceleration is the force acting on the object.
The SI unit of Force: Newton (N)

From the above relation it is clear that
Acceleration increases with increase in force and vice versa.
Acceleration decreases with increase in mass and vice versa.
That’s why a small vehicle requires less force to attain more acceleration while a heavy vehicle requires more force to get the same acceleration

Problems Based on Newton’s Second Law of Motion

Q.1. What is acceleration produced by a force of 12 Newton exerted on an object of mass 3 kg?

Q.2. What force would be needed to produce an acceleration of 4m/s2 on a ball of mass 6 kg?

Q.3. A force of 4 N acts on a body of mass 2 kg for 4 s. Assuming that the body to be initially at rest, find (i) its velocity when the force stops acting (ii) the distance covered in 10 s after the force starts acting.

Q.4. A feather of mass 10 g is dropped from a height. It is found to fall down with a constant velocity. What is the net force acting on it?

Q.5. A force of 5 N gives a mass m1, an acceleration of 8 m/s2, and a mass m2, an acceleration of 24 m/s2. What acceleration would give if both the masses are tied together?

Q.6. Calculate the force required to impart a car a velocity of 30m/s in 10 seconds. The mass of the car is 1500 kg.

Q.7. A force of 5 N gives a mass m1, an acceleration of 10 m/s2, and a mass m2, an acceleration of 20 m/s2. What acceleration would it give if both the masses were tied together?

Q.8. A 150 g ball traveling at 30m/s strikes the palm of a players hand and is stopped in 0.06 sec. Calculate the force exerted by the ball on the hand.

Q.9. A motorcycle is moving with a velocity of 90km/h and it takes 5 seconds to stop after the brakes are applied. Calculate the force exerted by the brakes on the motorcycle if its mass along with the rider is 200kg.

Q.10. What is the momentum of a man of mass 75kg when he walks with a velocity of 2m/s?

Q.11. What would be the force required to produce an acceleration of 2m/s2 in a body of mass 12 kg ?What would be the acceleration it the force were doubled?

Q.12. A man pushes a box of mass 50 kg with a force of 80N. What will be the acceleration of the box? What would be the acceleration if the mass were doubled?

Q.13. A certain force exerted for 1.2 second raises the speed of an object from 1.8m/s to 4.2 m/s. Later, the same force is applied for 2 second. How much does the speed change in 2 second?

Q.14. A constant force acts on an object of mass 5 kg for duration of 2 second. It increases the object’s velocity from 3cm/s to 7m/s. Find the magnitude of the applied force. Now if the force were applied for a duration of 5 seconds, what would be the final velocity of the object?

Q.15. A motorcar is moving with a velocity of 108km/h and it takes 4 seconds to stop after the brakes are applied. Calculate the force exerted by the brakes on the motorcar it its mass along with the passengers is 1000 kg.

Q.16. A hockey ball of mass 200g traveling from west to east at 10m/s is struck by a hockey stick. As a result, then ball gets turned back and now has a speed of 5m/s. If the ball and hockey stick were in contact for 0.2 s, calculate (i) initial and final momentum of the ball (ii) rate of change of momentum of the ball (iii) the force exerted by hockey stick on the ball.

Q.17. A stone of mass 500 g is thrown with a velocity of 20m/s across the frozen surface of a lake. It comes to rest after traveling a distance of 0.1 km. Calculate force of friction between the stone and frozen surface of lake.

Q.18. A body starts from rest and rolls down a hill with a constant acceleration. If its travels 400 m in 20 seconds, calculate the force acting on the body if its mass is 10kg.

Q.19. For how long should a force of 100 N act on a body of mass 20 kg so that it acquires a velocity of 100 m/s?

Q.20. A body of mass 1 kg is kept at rest. A constant force of 6.0 N starts acting on it . Find the time taken by the body to move through a distance of 12m.

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