Chp 3: Dynamics

Question 1

state n1L

Answer 1

every body continues in its state of rest or uniform motion in a straight line unless acted upon by a net external force

Question 2

state n2L

Answer 2

The rate of change of momentum of a body is directly proportional to the resultant force acting on it and occurs in the direction of the force

Question 3

state n3L

Answer 3

If a body A exerts a force on body B, then body B exerts an equal but opposite force of the same type on body A. (action and reaction pairs)

Question 4

define inertia

Answer 4

The inertia of a body can be described as its reluctance to start moving or to change its
motion once it has started. The mass of a body is a measure of its inertia.

Question 5

define weight

Answer 5

is a measure of the gravitational force that the Earth exerts on the object.

Question 6

define momentum

Answer 6

The momentum of a body is defined as the product of its mass, m and its velocity, v. It
acts in the same direction as the velocity

Question 7

define impulse

Answer 7

Impulse is defined as the product of a force F acting on an object and the time ∆t for which the force acts

Question 8

state the principle of conservation of momentum

Answer 8

The total momentum of a system remains constant before, during and after the interaction, provided that there are no net external force acting on the system.

Question 9

what is an elastic collision?

Answer 9

Collision in which both total momentum and total kinetic energy are conserved

Question 10

what is an inelastic collision?

Answer 10

Collision in which total momentum is conserved but total kinetic energy is not conserved

Question 11

what is a perfectly inelastic collision?

Answer 11

Collision in which total kinetic energy is not conserved and the particles stick together
after collision so that their final velocities are the same. Total momentum is conserved.

Question 12

In equilibrium:

Answer 12

resultant force in all directions is zero.

resultant torque about any axes is zero.

Question 13

describe the subsequent motion of the 2 bodies knowing that the collision is head-on

Answer 13

the final and initial velocity of both spheres are aligned joining the centre of gravity of both spheres

Question 14

describe in words the motion of the bodies after the collision ( when body A of mass m is moving with initial velocity u makes an elastic head-on collision with an identical body B which is initially at rest)

Answer 14

after collision, A will be stationary while B will be moving with velocity U in the same direction

Question 15

explain why the bodies have the same velocity at max compression

Answer 15

If Va > Vb, the spheres are in the midst of compression. If Vb > Va, the spheres are in the midst of separation. Hence, at the max compression, they must have the same velocity

Question 16

Why ke is NOT CONSERVED DURING COLLISION?

Answer 16

Usually, when the balls collide, a portion of the KE is converted to EPE to compress the balls. After collision, EPE stored in balls would be converted back to KE of balls.

Question 17

why actual acceleration is greater than the value calculated when the rocket is going further from earth

Answer 17

Since g ∝ 1/r^2, as rocket flies away from earth, g decreases. Since ma = Thrust - mg, a is larger

Question 18

A box is placed on a weighing machine in a moving lift. Describe the motion of the lift such that its apparent weight is

its real weight

Answer 18

moving at constant velocity

Question 19

A box is placed on a weighing machine in a moving lift. Describe the motion of the lift such that its apparent weight is

less than its real weight

Answer 19

moving downwards at constant acceleration

Question 20

A box is placed on a weighing machine in a moving lift. Describe the motion of the lift such that its apparent weight is

zero

Answer 20

FREE FALLING, a=g

Question 21

When F is constant (horizontal line) in a F-t graph, impulse is

Answer 21

F△t(also area under F-t graph, just that it is a rectangle)

Question 22

When F is varibale(line with a gradient) in a F-t graph, impulse is

Answer 22

Area under the F-t graph

Question 23

Explain how your answer to bi) is consistent with the principle of conservation of momentum

bi) shows a graph that already has a mountain (F by A on B) on F-t graph and you drew the mountain’s reflection (reflection on the x-axis)

Answer 23

1. Force A on B is equal in magnitude to the force B on A
2. Time of contact over force is acting is the same for both bodies
3. change in linear momentum found under area of F-t graph
4. Since area under A has same magnitude as area under B but both has opposite signs, total change in momentum = 0

Question 24

A ball is thrown upwards towards a brick wall. The ball bounces back with the same speed.

State and explain if momentum is conserved in this collision

Answer 24

No, ball is not a closed system/got external force (F by wall on ball) acting on ball

Question 25

Head-on Collision:

Answer 25

Collision in which the centre of mass of the objects are collinear before and after the
collision.

Question 26

What is mean by an inelastic collision between 2 objects by reference to:

Speed:

Energy:

Answer 26

Speed: the relative speed of approach more than to the relative speed of separation.

Energy: the final total kinetic energy after the collision is lower than the total initial kinetic
energy before the collision.

Question 27

State if the 2 spheres can be stationary at the same time if the total initial momentum is
non-zero:

Answer 27

Since the total initial momentum is non-zero, by the principle of conservation of momentum, at any point in time, the total momentum of the system cannot be zero. However, if both spheres are simultaneously stationary, the total momentum of the system will be zero which violates the principle of conservation of momentum.

Question 28

By reference to the direction of impulse, explain why for the spheres to move horizontally after collision, the centres of the spheres must be on the same horizontal level.

Answer 28

The direction of the impulses on each sphere are rightwards and leftwards horizontally. For the final velocities to be horizontal, the spheres must undergo a head-on collision in which their centres of mass are collinear.

Question 29

Does the principle of conservation of momentum apply in cases where two colliding
bodies lose kinetic energy as a result of sticking to one another at the point of collision?
Explain your answer with reference to Newton’s third law.

Answer 29

Yes. According to Newton’s Third Law, the two bodies exert equal and opposite forces on each other. Hence the impulse (or change in momentum) of body A will be equal but opposite to that of body B. Taken as a whole system, the total momentum of the colliding bodies remains unchanged, and the principle applies.

Question 30

State if 2 spheres can be stationary at the same time if their total initial momentum is zero but their total initial kinetic energy is not, when they undergo an elastic collision.

Answer 30

Since the total initial momentum is zero, by the principle of conservation of momentum, total momentum of the system during collision can be zero. At the instant of collision when both objects undergo maximum compression, their velocities will be the same and zero. Kinetic energy for an elastic collision is only conserved before and after a collision, not during, as some of the kinetic energy gets converted to elastic potential energy to compress the objects momentarily.

Question 31

A toy rocket is fired vertically into the air. Its mass decreases at a constant rate as the fuel
burns and is ejected out as exhaust gas. The rocket rises to a height such that, during the
flight, the gravitational field strength of the Earth may be considered to have the constant
value of 9.81 Nkg-1

Use appropriate physics law(s) to explain how the toy rocket works.

Answer 31

The rocket exerts a downward force on the gas to eject the exhaust gas by N2L as the gas changes momentum. By Newton’s Third Law, the exhaust gas exerts a force that is equal in magnitude and opposite in direction on the rocket upwards, hence the rocket can be propelled upwards (when this force exceeds weight of rocket).

Question 32

In qualitative terms, what can be stated about the subsequent motion as a result of
knowing that
(i) the collision is elastic
(ii) the collision is head-on

Answer 32

(i) The relative speed of approach is equal to the speed velocity of separation.
(ii) The subsequent motion of the two bodies is collinear.

Question 33

An astronaut in a spacecraft orbiting the Earth may be described as weightless. Explain
why this is so.

Answer 33

The astronaut and spacecraft are both accelerating at the same value towards the Earth as they are both undergoing circular motion. Gravitational force acting on the astronaut just sufficiently provides for the centripetal force on the astronaut. Therefore, no normal contact force is experienced by the astronaut and is experiencing weightlessness.

Question 34

Discuss how seat belts and airbags in a car ensure greater safety.

Answer 34

Seat belts and air bags increase the time for which the same change in momentum of the person occurs, thus reducing the decelerating force acting on him. Air bags also reduce the pressure on the driver as a result of the larger area over which the force acts.

Question 35

A stone is dropped from a point a few meters above the Earth’s surface. Considering the
system of the stone and the Earth, discuss briefly how the principle of conservation of
momentum applies before the impact of the stone with the Earth.

Answer 35

The initial total momentum of the system of stone and Earth as it is released is zero. As the stone falls and accelerates towards the Earth, its downward momentum increases. However, since there is no net external force acting on the system of stone and Earth, by the principle of conservation of momentum, the total momentum of the stone-Earth system is unchanged and thus remains as zero. Therefore, the Earth must accelerate upwards towards the falling stone, with the magnitude of upward momentum of Earth equals downward momentum of stone throughout the motion. (However, as Earth is much larger in mass than the stone, its velocity is negligible and hence, its movement is not noticeable.)

Question 36

When a man falls from a height and undergoes free fall, his momentum increases. Explain if principle of conservation of momentum is violated.

Answer 36

If the system consists of only the man, the gravitational force on the man by the Earth will be an external force. Since there is a net external force acting on the system, momentum is not conserved. If the system consists of the man and the Earth, gravitational force on the man by the Earth and the gravitational force exerted on Earth by man are internal forces. Since there is no net external net force, momentum is conserved.

Question 37

Two strong magnets are held stationary with the north pole of one pushed against the north pole of the other. On letting go, the magnets spring apart. It is apparent that the kinetic energy of the magnets has Increased. Explain how the law of conservation of momentum and law of conservation of energy apply in this case.

Answer 37

Law of conservation of momentum: No net external force acts on the system of 2 magnets. By the principle of conservation of momentum, since initial total momentum of magnets is zero, when released, magnets move of in opposite directions with momentum of the same magnitude such that final total momentum of the system is also zero.

Law of conservation of energy: Potential energy is stored when the magnets are pushed together and is converted into kinetic energies of the magnets when they are released.

Question 38

If a car now travels down a slope with the same speed and average resistive force as on
the flat road, explain why the distance the car travels before coming to rest is greater than
on the flat road.

Answer 38

Net decelerating force on the flat road was the average resistive force. Net decelerating force on the slope is the (average resistive force - component of weight of car). Hence, it is reduced, and the distance traveled must be larger before the car comes to a stop.

Question 39

A cyclist travels at constant speed along horizontal ground. Frictional forces oppose the motion of the cyclist. Use Newton’s first law of motion to explain why the cyclist travels at constant speed.

Answer 39

If a car now travels dThe forward force by the ground on the cyclist is equal to the backward frictional forces on the cyclist. Hence there is no net external force acting on the cyclist. By Newton’s first law, the cyclist is moving at constant speed.wn a slope with the same speed and average resistive force as on the flat road, explain why the distance the car travels before coming to rest is greater than on the flat road.