Minus sign indicates in the direction opposite to that of bullet.
Q. Which of the following has more inertia:
(a) a rubber ball and a stone of the same size?
(b) a bicycle and a train?
(c) a five rupees coin and a one-rupee coin?
Ans:
(a) a rubber ball and a stone of the same size?
Ans: Stone has more mass than a rubber ball. Therefore, stone has more inertia.
(b) a bicycle and a train?
Ans: Train has more mass than a bicycle. Therefore, Train has more inertia.
(c) a five rupees coin and a one-rupee coin?
Ans: A five-rupee coin has more mass than a one-rupee coin. Therefore, Five rupee coin has more inertia.
Q. In the following example, try to identify the number of times the velocity of the ball changes:
“A football player kicks a football to another player of his team who kicks the football towards the goal. The goalkeeper of the opposite team collects the football and kicks it towards a player of his own team”.
Also identify the agent supplying the force in each case.
Ans: The Velocity of the football in the above case changes four times. The agent supplying the force in each case are as follows:
Case I: Football player when he kicks the ball towards his team mate.
Case II: The team mate when he kicks the ball towards goalkeeper.
Case III: Goal keeper when he stops the ball
Case IV: Goal keeper when he kicks the ball towards the player of his own team.
Q. An object experiences a net zero external unbalanced force. Is it possible for the object to be travelling with a non-zero velocity? If yes, state the conditions that must be placed on
Ans: A body continues in the state of rest or of uniform motion according to Newton's first law of motion unless an outside force acts upon it. As a result, the body will maintain its initial velocity if it has some initial velocity even when there is no net force acting on it.
Q. A batsman hits a cricket ball which then rolls on a level ground. After covering a short distance, the ball comes to rest. The ball slows to a stop because
(a) the batsman did not hit the ball hard enough.
(b) velocity is proportional to the force exerted on the ball.
(c) there is a force on the ball opposing the motion.
(d) there is no unbalanced force on the ball, so the ball would want to come to rest.
Ans: (c) there is a force on the ball opposing the motion.
Hint: This force is the force of Friction which opposes the motion of the body.
Q. A 8000 kg engine pulls a train of 5 wagons, each of 2000 kg, along a horizontal track. If the engine exerts a force of 40000 N and the track offers a friction force of 5000 N, then calculate:
(a) the net accelerating force and
(b) the acceleration of the train.
Ans: Given,
Mass of Engine = 8000 kg
Mass of Wagon = 2000 kg
Number of Wagons = 5
Force exerted by engine = 40000 N
Friction force = 5000 N
Now, a) Net accelerating force = Force exerted by the engine – Frictional force
Net accelerating force = 40000 – 5000
Net Accelerating force = 35000 N
b) To calculate Acceleration of the Train, we know
F = MA (Where F is the net force, M is the total mass of the train)
35000 = 18000 x A
A = 35000/18000
A = 1.94 m/s2
Q. An automobile vehicle has a mass of 1500 kg. What must be the
force between the vehicle and road if the vehicle is to be stopped with a
negative acceleration of 1.7 m/s2?
Ans: Given,
Mass = 1500 kg
Acceleration = - 1.7 m/s2
Therefore,
Force required to stop the vehicle (F) = MA
F = 1500 x -1.7
F = -2550 N
Q. What is the momentum of an object of mass m, moving with a
velocity v?
(a) (mv) 2 (b) mv2 (c) ½ mv2 (d) mv
Ans: (d) mv
Q. Using a horizontal force of 200 N, we intend to move a wooden
cabinet across a floor at a constant velocity. What is the friction force that
will be exerted on the cabinet?
Ans: To move a wooden cabinet across a floor at a constant
velocity, the frictional force should balance the horizontal force.
Therefore, frictional force of 200 N shall be exerted on the
cabinet.
Q. According to the third law of motion when we push on an object,
the object pushes back on us with an equal and opposite force. If the object is
a massive truck parked along the roadside, it will probably not move. A student
justifies this by answering that the two opposite and equal forces cancel each
other. Comment on this logic and explain why the truck does not move.
Ans: When the student pushes a massive truck, it does not move. The
student justifies it by answering that two opposite and equal forces cancel
each other.
The justification is not true. The truck does not move because the
push applied is far less than the force of friction between the truck and the
road. The force applied by the student is lost as heat.
Q. A hockey ball of mass 200 g travelling at 10 m/s is struck by a
hockey stick so as to return it along its original path with a velocity at 5 m/s.
Calculate the magnitude of change of momentum occurred in the motion of the
hockey ball by the force applied by the hockey stick.
Ans: Given,
Mass (M) = 200 g i.e. 0.2 kg
Initial velocity (U) = 10 m/s
Final Velocity (V) = - 5 m/s (Minus sign indicates that the
direction of motion is opposite to the Initial motion)
Therefore Change in momentum = Final Momentum – Initial Momentum
Change in Momentum = 0.2 x - 5 - 0.2 x 10
Change in Momentum = - 1 - 2
Change in Momentum = - 3 kg.m/s
Q. A bullet of mass 10 g travelling horizontally with a velocity
of 150 m/s strikes a stationary wooden block and comes to rest in 0.03 s.
Calculate the distance of penetration of the bullet into the block. Also
calculate the magnitude of the force exerted by the wooden block on the bullet.
Ans: Given,
Mass, m = 10 g i.e 0.01 Kg
Initial Velocity, u = 150 m/s
Final Velocity = 0 m/s
Time = 0.03 s
A) To Find Distance of Penetration (S), We should first know the acceleration
of bullet,
Acceleration of Bullet = V – U/T
A = 0 – 150/0.03
A = - 5000 m/s2 (Minus sign indicates the velocity is reducing)
Now, Distance of Penetration =
V2 – U2 = 2AS
0 - (150)^2 = 2 x -5000 x S
S = - 150 x 150/-10000
S = 2.25 m/s2
B) To find the magnitude of force exerted by the wooden block on
the bullet, We Know
F = M A
F = 0.01 x -5000
F = - 50 N (Minus sign indicates that the force is applied in the
opposite direction of the motion of bullet)
Q. An object of mass 1 kg travelling in a straight line with a
velocity of 10 m/s collides with, and sticks to, a stationary wooden block of
mass 5 kg. Then they both move off together in the same straight line.
Calculate the total momentum just before the impact and just after the impact.
Also, calculate the velocity of the combined object.
Ans: Given,
Mass of object, m1 =1kg
Mass of wooden block, m2= 5kg
Velocity of Object, u1=10 m/s
Velocity of Wooden block, u2= 0 m/s
Mass of the combined object, M=
m1+ m2 = 6kg
Let velocity of combined object = ?
Now,
Momentum of the system just before collision, P1=m1u1
+ m2u2
P1 = 1 × 10 + 5 ×0
P1 =10 kg. m/s
Now,
According to law of conservation of momentum, momentum before and
after the collision remains the same. i.e Final Momentum = Initial Momentum
Therefore, Final
momentum =10 kg. m/s
Now,
To find the velocity of combined object, We know
P = MV
10 = 6 x V
V = 10/6
V = 1.67 m/s
Q. An object of mass 100 kg is accelerated uniformly from a
velocity of 5 m/s to 8 m/s in 6 s. Calculate the initial and final momentum of
the object. Also, find the magnitude of the force exerted on the object.
Ans: Given,
Mass of Object, m = 100 kg
Initial Velocity, u = 5 m/s
Final Velocity, v = 8 m/s
Time, t = 6 s
Initial Momentum, P1 = M.U
P1 = 100 x 5 = 500 Kg.m/s
Final Momentum, P2 = M.V
P2 = 100 x 8 = 800 Kg.m/s
To Find the magnitude of the force exerted on the object, we should
know the acceleration of the object,
A = V – U/T
A = 8 – 5/6
A = 3/6
A = 0.5 m/s^2
Now, Force = Mass x Acceleration
F = 100 x 0.5
F = 50 Newton
Q. How much momentum will a dumb-bell of mass 10 kg
transfer to the floor if it falls from a height of 80 cm? Take its downward
acceleration to be 10 m s–2 .
Ans: Given,
Mass, m = 10 kg
Height, S = 80 cm i.e. 0.8 m
Acceleration = 10 m/s^2
Now, To find the momentum of the dumb bell we need to find the
Initial velocity of the dumbbell first,
We Know,
V^2 – U^2 = 2 AS
V^2 – 0 = 2 x 10 x 0.8
V^2 = 16
V = √16
V = 4 m/s
Thus, Momentum of Dumb bell, P = M x V
P = 10 x 4
P = 40 Kg.m/s
Q. Akhtar, Kiran and Rahul were riding in a motorcar that was moving with a high velocity on an expressway when an insect hit the windshield and got stuck on the windscreen. Akhtar and Kiran started pondering over the situation. Kiran suggested that the insect suffered a greater change in momentum as compared to the change in momentum of the motorcar (because the change in the velocity of the insect was much more than that of the motorcar). Akhtar said that since the motorcar was moving with a larger velocity, it exerted a larger force on the insect. And as a result the insect died. Rahul while putting an entirely new explanation. He said that both the motorcar and the insect experienced the same force and a change in their momentum. Comment on these suggestions.
Ans: (Caveat: The below answer is generated using AI as I myself felt confusion regarding the question)
Let's analyze each suggestion:
1. Kiran's Suggestion: Kiran is correct in stating that the insect suffered a greater change in momentum compared to the motorcar, assuming the insect came to a complete stop upon impact. This is because the insect's initial velocity was likely much lower than that of the motorcar, so its change in velocity (and therefore momentum) would be greater. However, this does not necessarily mean the insect experienced a greater force.
2. Akhtar's Suggestion: Akhtar is correct that the motorcar exerted a larger force on the insect due to its greater mass and velocity. The force exerted by the motorcar on the insect is equal and opposite to the force exerted by the insect on the motorcar, according to Newton's third law of motion. The greater force exerted by the motorcar likely resulted in the insect's demise.
3. Rahul's Suggestion: Rahul is correct in stating that both the motorcar and the insect experienced the same force and a change in their momentum, but his explanation is incomplete. While it's true that both objects experienced the same force (but in opposite directions), the change in momentum depends on the mass and velocity of each object. Since the motorcar has much greater mass than the insect, its change in velocity (and momentum) would be much smaller compared to the insect.
In summary, all three suggestions have some merit, but Akhtar's and Kiran's explanations provide a more complete picture of the situation.
