Question:
Using second law of motion, derive the relation between force and acceleration.
Answer:
Let an object of mass, m is moving along a straight line with an initial velocity, u.
Let the final velocity = v m/s
Acceleration = a ms-2
Time taken = t s
and Force applied = F.
Initial momentum (before the force applied) = P1 = mu
Final momentum (after the force applied) = P2 = mv
Change in momentum ∝ P2 - P1
and Rate of Change in momentum ∝ (P2 - P1)/t
⇒ ∝ (mv - mu)/t ∝ m(v - u)/t
According to Newton's second law, Rate of Change in momentum = F
⇒ F ∝ m(v - u)/t
⇒ F ∝ ma (∵ v = u + at)
⇒ F = kma (where k is a constant of proportionality).
The SI units for m is 1 kg, a is ms-2 , thus k = 1
⇒ F = ma
SI unit of force is Newton (N) = kg-ms-2
Force and Laws of Motion
Q 1.
Are action-reaction forces simultaneous ?
Q 2.
Do action-reaction forces produce the same magnitude of acceleration ?
Q 3.
On what factor does inertia of a body depend ?
Q 4.
What is the unit of force in c.g.s system?
Q 5.
Can every force produce motion in every object?
Q 6.
It is difficult to balance our body when we accidentally slip on a peel of banana. Explain why?
Q 7.
Explain why a player lowers his hands while catching a cricket ball.
Q 8.
What is the SI unit of impulse.
Q 9.
The masses of two objects are 2 kg and 20 kg. Which has greater inertia ?
Q 10.
Fill in the blanks :
The study of motion of a body under the action of a force is called ______.
Q 11.
While driving on a highway, an insect strikes on the car windshield and splatters. Which experiences greater impact (force): an insect or the windshield?
Q 12.
A body of mass 25 kg has momentum of 125 kg m/s. What is the velocity of the body?
Q 13.
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.
Q 14.
A man pushes a box of mass 50 kg with a force of 80 N. What will be the acceleration of the box due to this force? What would be the acceleration if the mass were doubled ?
Q 15.
When a branch of a tree is shaken, some of the fruits may fall down.Why ?
Q 16.
A car weighs 1500 kg.Its speed time graph is shown in Fig. Calculate the force required at the end of 5 seconds to bring the car to a stop within one second.
Q 17.
Can balanced forces change the shape and size of an object?
Q 18.
A TV set is lying on a table. The TV set experiences a gravitational force (pull) downwards (FW) by the Earth. It also experiences a force on it due to table in contact i.e. (FTable-TV) in upward direction. Do these forces form an action-reaction pair? Do these forces follow Newton's third Law of motion?
Q 19.
Fill in the blanks :
When a bus starts suddenly, the bus passengers standing in the bus tend to fall backwards. It is due to _______________.
Q 20.
A certain force exerted for 1 -2 s raises the speed of an object from 1.8 m/s to 4.2 m/s. Later,the same force is applied for 2 second. How much does the speed change in 2 s ?
Q 21.
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 the magnitude and direction of the velocity.If no,provide a reason.
Q 22.
What is the net momentum of gun and bullet system before firing?
Q 23.
In the above question, which body is damaged more ?
Q 24.
For how long should a force of 100 N act on a body of mass 20 kg so that it acquires a velocity of 100 m/s ?
Q 25.
State Newton’s second law of motion and establish that F = ma where symbols have their usual meanings.
Q 26.
Using second law of motion, derive the relation between force and acceleration.
Q 27.
When a force acts on a body, what are the two essential effects it can produce?
Q 28.
Which principle is involved in the working of a jet plane?
Q 29.
Why is the person hurt less when he falls on a spongy surface?
Q 30.
Two objects of masses 100 g and 200 g are moving along the same line in the same direction with velocities of 2 m/s and 1 m/s,respectively.They collide and after the collision, the first object moves at a velocity of 1.67 m/s in the same direction.Determine the velocity of the second object
Q 31.
A bullet of mass 10 g travelling horizontally with a velocity of 150
strikes a 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.
Q 32.
An unloaded truck weighing 2000 kg has a maximum acceleration of 0.4
.What is the maximum acceleration, when it carries a load of 2000 kg ?
Q 33.
Derive the relation F = ma,where the symbols have their usual meanings.
Q 34.
Discuss briefly Galileo's ideas about motion.
Q 35.
State Newton's First Law of motion.
Q 36.
Fill in the blanks :
When a car enters a curved path, the person sitting in it is thrown outwards. This is because of the property of ______________.
Q 37.
Fill in the blanks :
________ is the tendency of an object to resist a change in motion.
Q 38.
What is formula of impulse?
Q 39.
A force of 5 N gives a mass
an acceleration of 10
,and a mass
,an acceleration of 20
.What acceleration would it give if both the masses were tied together ?
Q 40.
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 of 5 m/s.Calculate the change in momentum of the hockey ball by the force applied by the hockey stick.
Q 41.
Derive the unit of force using the second law of motion. A force of 5 N produces an acceleration of
on a mass
and an acceleration of 24
on a mass
.What acceleration would the same force provide if both the masses are tied together ?
Q 42.
Can balanced forces move a body at rest ?
Q 43.
Define momentum of a body.
Q 44.
What is one newton force ?
Q 45.
Give atleast four applications of Newton’s second law of motion.
Q 46.
Honey and Sunny are two friends.Both are financially well off.Honey is fond of driving an SUV while Sunny enjoys driving Tata Nano.Honey explains to Sunny the risks of driving a light vehicle and Sunny explains to Honey the cost factor.
Read the above passage and answer the following questions :
(i) With whom do you agree,with Honey or with Sunny?
(ii) Explain, why?
(iii) Which values of life do you learn from this discussion?
Q 48.
What a force can do?
Q 49.
Why do you fall in the forward direction when a moving bus brakes to a stop and fall backwards when it accelerates from rest?
Q 50.
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 the magnitude and direction of the velocity. If no, provide a reason.
