Understanding Force, Motion, and Momentum: Exploring Newton’s Laws
1. Motion Under Zero External Unbalanced Force
Answer: An object can travel with a non-zero velocity even when experiencing zero net external unbalanced force. This occurs when the object maintains a constant velocity in a specific direction, resulting in no net force acting upon it. To alter its state of motion, a non-zero external unbalanced force must be applied.
2. Dust Removal from a Carpet
Answer: The inertia of dust particles causes them to resist changes in their state of rest. When a carpet is beaten, it moves, but the dust particles tend to remain at rest due to inertia. As per Newton’s first law, the dust particles stay in their state of rest while the carpet moves, causing them to separate from the carpet.
3. Securing Luggage on a Bus Roof
Answer: When a bus accelerates, the luggage on its roof tends to remain at rest due to inertia. To prevent the luggage from falling off as the bus moves forward, it is recommended to secure it with a rope.
4. Detachment of Leaves from a Tree
Answer: Vigorously shaking a tree branch causes the leaves to detach due to their inertia. As the branches move, the leaves resist the motion and tend to stay at rest, leading to their separation from the tree.
5. Passenger Movement in a Bus
Answer: Due to passenger inertia:
When a moving bus brakes, passengers experience a forward force due to their inertia, which tries to maintain their state of motion. Conversely, when the bus accelerates from rest, passengers tend to fall back as their inertia opposes the forward motion.
6. Horse Pulling a Cart
Answer: A horse exerts a backward force on the ground, and in accordance with Newton’s third law, the Earth exerts an equal and opposite reaction force on the horse in the forward direction, propelling the cart forward.
7. Fireman’s Difficulty Holding a Hose
Answer: Due to the backward reaction of ejected water:
When a fireman holds a hose ejecting water at high velocity, he experiences a backward reaction force due to Newton’s third law. This force challenges his stability, making it difficult to hold the hose steady.
8. Recoil Velocity of a Rifle
Answer: Applying the law of conservation of momentum, we find that the rifle recoils backward with a velocity of 0.4375 m/s after firing a bullet.
9. Velocity After Collision
Answer 4: Using the law of conservation of momentum, we determine that the velocity of the second object after the collision is 1.165 m/s.
10. Stopping a Cricket Ball
Answer: (c) Friction force acting opposite to the ball’s motion is responsible for bringing the cricket ball to rest after it is hit.
11. Truck’s Acceleration and Force
Answer: Applying the second equation of motion, we find the truck’s acceleration to be 2 m/s². Subsequently, using Newton’s second law, the force acting on the truck is calculated as 24000 N.
12. Friction Force on a Stone
Answer: Using the third equation of motion and Newton’s second law, we determine the force of friction between the stone and ice to be – 4 N, indicating that it acts against the stone’s motion. Q
13. Train’s Acceleration and Forces
Answer:
(a) The net accelerating force is 35000 N.
(b) The acceleration of the train is 1.944 m/s².
(c) The force of wagon 1 on wagon 2 is 15552 N.
14. Stopping Force on an Automobile
Answer: Applying Newton’s second law, we find the force required to stop the automobile to be –2550 N, acting opposite to its motion.
15. Momentum and Velocity
Answer:
(d) mv
Momentum is the product of an object’s mass and velocity.
16. Friction Force on a Cabinet
Answer: Based on Newton’s third law, the frictional force exerted on the cabinet is equal and opposite to the applied force, resulting in a frictional force of 200 N.
17. Collision of Objects Moving in Opposite Directions
Answer: Applying the law of conservation of momentum, we find that the velocity of the combined object after the collision is 0 m/s.
18. Truck’s Immobility and Force Cancellation
Answer: The student’s justification is correct. The high static friction between the truck and road cancels out the applied force, preventing the truck from moving.
19. Change in Momentum of a Hockey Ball
Answer: The change in momentum of the hockey ball is calculated to be 3 kg m s-¹.
20. Bullet Penetration and Force
Answer: Using the equations of motion and Newton’s second law, we determine the distance of penetration of the bullet into the block to be 2.25 m and the force exerted by the block on the bullet to be 50 N.
21. Momentum and Velocity in a Collision
Answer: Applying the law of conservation of momentum, we find the total momentum before and after the impact to be 10 kg m s-¹. The velocity of the combined object after the collision is calculated as 5/3 m/s.
22. Momentum and Force in Uniform Acceleration
Answer:
The initial momentum of the object is 500 kg ms-¹.
The final momentum of the object is 800 kg ms-¹.
Force exerted on the object is 50 N.
23. Insect-Motorcar Collision Analysis
Answer: Kiran’s observation about the insect’s greater change in momentum is accurate. Akhtar’s conclusion regarding the car exerting a larger force on the insect is also correct due to the car’s significantly larger mass. Rahul’s explanation about equal forces is valid based on Newton’s third law, but his statement about the system’s change in momentum is incorrect as the total momentum is conserved.
24. Momentum Transfer of a Falling Dumbbell
Answer: Using the third equation of motion, we find the dumbbell’s velocity before hitting the floor to be 4 m/s. Consequently, the momentum transferred to the floor is calculated as 40 kg m s-¹.