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1. States Newton’s third law of motion.
When two objects interact, they except equal and opposite forces on one another. For example if an object pushes on a wall, the wall would push back the object with an equal and opposite force.
2. A body is held by a a light inextensible string as shown in figure below. If the tension on the string is 2 Newton, what is the mass of the body?
As per Newton’s third law when two objects interact, they except equal and opposite forces on one another. The body is held by a string. So the tension on the string should be equal to the weight of the body.
Tension (T) = 2N
Weight = mg where m is the mass of the body.
mg = T
Mass,
m = T/g = 2/9.8 = 0.2041 kg
Mass is 0.2041 Kg
3. A body of mass 5kg lies on a smooth horizontal table. It is connected by a light inextensible string, which passes over a smooth pulley at the edge of the table, to another body of mass 3kg which is hanging freely. The system is released from rest. Find the tension in the string and the acceleration?
Consider the body B, and the forces acting on it. It is undergoing acceleration. Thus if T is the tension on the string, acceleration is a and acceleration due to gravity is g,
3a = 3g – T → [1]
Consider the body A, and the forces acting on it. It is undergoing acceleration. Thus if T is the tension on the string, acceleration is a ,
5a = T → [2]
From [1] and [2],
3a = 3g – 5a
Acceleration (a) = 3g/8 = 3.675 m/s2
From [2], Tension on the string (T) = 5a = 18.375 Newton
4. A car starting from rest has an acceleration of 5 m/s2 during the first two seconds. Calculate its velocity after 2 seconds.
Acceleration (a) = 5 m/s2.
Time taken(t) = 2 seconds.
Initial velocity (u) = 0 m/s2.
Final velocity (v) is to be found.
v= u + at
v= 0 + 5x2 = 10 m/s.
Velocity after 2 seconds = 10 meter per second.
5. A ball is being hit by a tennis racket. Suppose the ball is accelerated to a speed of 444 m/s in 1.8 seconds, then what is the acceleration and what is the distance that the ball traveled in 1.8 seconds?
When the ball is hit by a tennis racket, both the ball’s speed(v) and direction are changing. So the balls velocity is changing and it is undergoing an acceleration(a).
Acceleration is dv/dt
Acceleration = (444-0)/1.8 = 247 m/s2
Acceleration, distance travelled and time taken are related by
s = ut + 0.5at2
s = (0) x (1.80)+ 0.5x(247 )x(1.80)2 = 400 meter
6. What is inertia?
According to Newton’s first law of motion, every object continues at rest or with uniform velocity unless acted by an unbalanced force. The resistance to change of velocity is called inertia. The more the mass of the object, the harder it is to change its velocity.
7. What is momentum?
The momentum of a body is equal to its mass multiplied by its velocity. Unit of momentum is kg -1 . Momentum is a vector quantity and has the same direction as velocity.
8. State Newton’s second law of motion.
Newton’s second law states that the rate of change of momentum of an object is proportional to the resultant force which acts on the object.
9. State principle of conservation of momentum.
The principle of conservation of momentum states that for a system of interacting objects, the total momentum remains constant, provided no external resultant force acts on the system. For example when two balls collide, the momentum is conserved. The total final momentum = the total initial momentum. Or in other words, the total momentum is unchanged by the collision.
10. A ball of mass 3kg is moving to the right with velocity 3m/s and a ball of mass 1kg is moving to the left with velocity 2m/s. They collide. After the collision, the ball of mass 1kg moves away with velocity 2m/s, then determine the velocity of the other ball after the collision.
The total momentum before collision = 3x3 – 1x2 = 7 kg m/s. [towards right]
The total momentum after collision = 2x1+ Vx3
According to principle of conservation of momentum, the total final momentum = the total initial momentum.
2x1+ Vx3 = 7
V=5/3 m/s
That is the 3 kg ball moves towards right with a velocity 1.67 m/s.
11. A pellet of mass 0.001 kg is fired from an air rifle at a speed of 110 m/s into a wood block. The pellet penetrates the block to a depth of 0.05 m. Calculate the impact force.
Initial speed u = 110 m/s
Final speed v = 0
Distance s = 0.050 m
To calculate the acceleration,
v2 = u2 + 2as
0 = 1102 + 2a × 0.0
Acceleration is
Force F = ma = - 0.001 × 1.21 × 105 = - 121 N
12. What is impulse?
Impulse is the change in momentum. Impulse is defined as:
Impulse = Force × Time
13. A 0.50 kg cart (A) is pulled with a 1 N force for 1 second; another 0.50 kg cart (B) is pulled with a 2.0 N-force for 0.50 seconds. Which cart (A or B) has the greatest impulse? Explain.
Impulse is force × time
So for Cart A ,
The force = 1 N
Time = 1 second
Impact = force × time = 1Ns.
For Cart B,
The force = 2 N
Time = 0.5 second
Impact = force × time = 2 × 0.5 = 1Ns.
The impulse is the same for both the carts.
14. Define work done.
The work done by a force when it moves is the product of the force and distance moved along its line of action. The unit of work is joule, defined as the work done when a force of 1 N moves its point of application by 1 m along the line of action of the force.
W= Fs
where W = work done in joules.
F = force in Newtons
s = distance moved in metres.
15. Define Energy.
Energy is the capacity to do work. A body with no energy can do no work. Energy may exist in different forms. Example energy may be stores in a car battery in the form of chemical energy. When electricity is drawn from the battery, chemical energy is converted to electrical energy. Energy can be convert from one form to other. For example potential energy to kinetic energy when a compressed spring is released.
