Answers to Problems on (Newton's Laws of Motion) HC Verma's Questions for Short Answer (9-17)

 Q#9

The acceleration of a particle is zero as measured from an inertial frame of reference. Can we conclude that no force acts on the particle?

Answer:
It can not be concluded that no force acts on the particle. We can only say that net force or the resultant of all forces acting on the particle is zero.

Q#10
Suppose that you are running fast in a field when you suddenly find a snake in front of you. You stop quickly. Which force is responsible for your deceleration?

Answer:
It is the force of friction in backward direction between our feet and the ground that decelerates.

Q#11
If you jump barefooted on a hard surface, your legs get injured. But they are not injured if you jump on a soft surface like sand or pillow. Explain.

Answer:
On a hard surface our downward velocity quickly comes to zero, means the rate of change of velocity that is acceleration (in the upward direction) is high. It is due to the stronger force exerted by the hard surface on our legs so they get injured. On the other hand, if we jump on the soft surfaces like sand or pillow it takes more time to achieve zero velocity as our legs plunge to a distance. So the rate of change of velocity ie deceleration is lower because the soft surface exert lesser force on our legs and they are not injured.

Q#12
According to Newton's third law, each team pulls the opposite team with equal force in a tug of war. Why then one team wins and other team loses?

Answer:
Newton's third law connects the forces exerted by two bodies on one another but these two forces act on two different bodies and they never appear together on one body when it is considered as a system. So these forces will not cancel each other. In a tug of war when we consider a team as a system, the forces acting on it will be pull in the rope, the weight of the team, Normal force by the floor and force of friction between floor and feet. The net of these forces for each team may not be equal that is why one team wins and the other team loses. 

Q#13
A spy jumps from an airplane with his parachute. The spy accelerates downward for some time when the parachute opens. The acceleration is suddenly checked and the spy slowly falls on the ground. Explain the action of a parachute in checking the acceleration.

Answer:
When the spy jumps the forces acting on him is - 1. His weight in the downward direction and 2. resistance of the air in the upward direction. The magnitude of resistance of air depends upon the area of the object available perpendicular to the direction of motion and velocity of the object. Before opening the parachute, this area is due to his body which is very small, so the air resistance is also very small. So the net downward force is hardly reduced and the spy accelerates downwards. But as the parachute opens, air begins to fill in it and its area gradually increases. In this period air resistance starts to increase and net downward force begins to reduce but it is still not zero that is why for some time he accelerates. But as the parachute opens fully, due to the wide area of the parachute and high velocity, the air resistance in upward direction gets greater than the weight of the spy and not only the acceleration is checked the high velocity achieved begins to decrease (deceleration) due to net upward force. But as the velocity reduces so does the air resistance. And both the forces adjust to become equal and opposite at some slower velocity at which he falls on the ground.

Q#14
Consider a book lying on a table. The weight of the book and the normal force by the table on the book are equal in magnitude and opposite in direction. Is it an example of Newton's third law?

Answer: Yes.

Q#15
Two blocks of unequal masses are tied by a spring. The blocks are pulled stretching the spring slightly and the system is released on a friction-less horizontal platform. Are the forces due to the spring on the two blocks equal and opposite? If yes, is it an example of Newton's third law?

Answer:
The forces due to the spring on the two blocks are equal and opposite. Yes, it is an example of Newton's third law.

Q#16
When a train starts, the head of a standing passenger seems to be pushed backward. Analyze the situation from the ground frame. Does it really go backward? Coming back to to the train frame, how do you explain the backward movement of the head on the basis of Newton's law? 

Answer: 

From the ground frame the head of the passenger in the train will look static while his lower part of the body will be moving forward with the train. Because according to the first law of motion, the head does not want to change the state of rest due to inertia.  

From the train's frame, the lower part of the passenger moves forward with the frame because it is in contact with the seat and it will look at rest. Since the accelerating frame of the train is a non-inertial frame, so to explain it by Newton's laws of motion a pseudo force opposite to the direction of movement equal to 'ma' will have to be applied on the passenger. The upper part of the passenger not with contact with the seat moves backward due to this pseudo force.

Q#17
A plumb bob is hung from the ceiling of a train compartment. If the train moves with an acceleration 'a' along a straight horizontal track, the string supporting the bob makes an angle tan^-1(a/g) with the normal to the ceiling. Suppose the train moves on an inclined straight track with uniform velocity. If the angle of incline is tan^-1(a/g), the string still makes the same angle with the normal to the ceiling. Can a person sitting inside the compartment tell by looking at the plumb line whether the train is accelerated on a horizontal straight track or it is going on an incline? If yes, how? If no, suggest a method to do so.

Answer:
ince in both of the cases the angle that string makes with normal to the ceiling is same, a person sitting inside the compartment can not tell by looking at the plumb line whether the train is accelerated on a horizontal track or it is going on an incline.

To determine this he should know the weight of the bob and measure the tension in the string with a spring balance. If the tension and the weight of the bob are the same then the train is going with uniform velocity on an incline. If the tension in the string is more than the weight of the bob, the train is moving on a horizontal track with an acceleration.