Force And Laws Of Motion

The quantity of motion of a moving body, measured as a product of its mass and velocity is called as momentum. It is also defined as the impetus gained by a moving object.

Mass of the object = m

Let, the Velocity of the object be 'v'

Since, Momentum = Mass ×Velocity

Hence, Momentum = mv

Momentum is considered to be a measure of the quantity of motion of a body. It is the product of the mass and velocity of an object, quantified in kilogram-meters per second. It is dimensionally equivalent to impulse, the product of force and time, quantified in Newton - seconds.

The SI unit of momentum is kilogram meter per second and it is symbolized as kg m/s

Momentum is a vector quantity. For a particle with mass, the momentum equals mass times velocity, and velocity is a vector quantity while mass is a scalar quantity. A scalar multiplied by a vector is a vector.

When we fire a bullet from a gun, its veleocity is zero before firing, hence momentum is also zero.

Momentum is defined to be ‘mass x velocity’, so it is a vector, in the same direction as the velocity.

Mass is measured in kilograms, kg, and velocity is measured in metres per second, m/s. These are the standard SI units of these quantities. Hence, the SI unit of momentum is kg m/s.

Balanced Forces cannot produce motion, but can change the shape of the body.

.It is frictional force which slows down the bicycle and gradually stops the cycle when we stop pedaling it.

False: Balanced forces acting on a body change its shape.

When a ball is thrown towards the ground from the height h then, acceleration due to gravity acts on the body in the same direction of the motion of the body.

Hence acceleration of the body increases.

The intrinsic property of material body which resists a change in its state of rest or of uniform motion along a straight line is called inertia. Inertia is a natural tendency of the body.

Newton's first law of motion is also called as the law of inertia. An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

Since, mass is directly proportional to inertia. Hence, Ball B, which is heavier than Ball A and thus having a greater mass, will also have a greater inertia.

Sir Issac Newton gave laws of motion which constitute three physical laws that, together, laid the foundation for classical mechanics.

Force is defined as the product of mass and acceleration. We know, that mass is a scalar quantity while acceleration is a vector quantity whose direction and magnitude both can be specified. The product of a scalar and vector always yield a vector quantity. Hence, force is a vector quantity.

Since momentum is equal to the product of mass and velocity. Hence, mass of bull should be multiplied to its speed in order to find its Momentum.

(a) Mass

(b) Forward

(c) Backward

(d) Inertia

(e) Friction; Air

When a car is moving with a high velocity, its momentum is also high and the people in the vehicle are also in the same momentum. We know that momentum is inversely proportional to time. So if the momentum is bought to 0 at a short time then force acting on a body is very large. So when a car meets with an accident, the person falling front with the presence of stretchable seat belt as these elastic seat belt reduce the momentum in more time to reduce the force.

When you hit the ground, the ground exerts a force up on you to stop you. The force which it exerts depends on how long the collision lasts. You have no control over your mass or the speed you hit the ground, but you can increase the time and reduce the rate of change in momentum and rolling is one such trick. Hence, we would get less hurt.

An aircraft needs air due to following reasons:

(i) Air moving under the wings of aircraft is strong enough to hold it up, and

(ii) Air burns the fuel in aircraft engines.

Since there is no air on moon, an aircraft cannot fly on the moon.

The amount of downward force on a falling object depends on its weight. The greater the mass, the greater the force will be, and, therefore, the greater the terminal velocity. It is important to understand, that acceleration due to gravity is the same for all objects; it is the drag factor that causes the variations with weight and shape.

A large person will fall faster than a small person due to the greater weight of the large person in relation to the cross-sectional area as compared to the small person.For a very light person, the drag will eventually become equal to the weight of the person and therefore very small animals such as mice when dropped from large height will escape un hurt.

Using conservation of momentum

MV + mv = (M + m) v'

Where:

M - Mass of the boy - 50kg

m - Mass of the trolley - 20kg

V- Velocity of the boy - 5m/s

v - Velocity of the trolley - 1.5m/s

v' - common velocity - x

(50+20) x = (50x5 +20x1.5)

x= 4m/s.

Hence, the common velocity is 4m/s.

Mass of girl, m₁= 50kg

Mass of the boat, m₂= 300kg

Velocity of the girl, v₁= 3m/s

v₂=? we have to find it

We know,

According to Law of conservation of momentum,

= m₁v₁ + m₂v₂= 0 (As no initial velocity is applied)

⇒50 × 3+ 300 × v₂ =0

v₂ = - 150/300

= (- 0.5m/s)

Since, the boat is moving in backward direction the velocity (v₂) will be 0.5m/s in the backward direction.

Let

m1=500,

m2=1500

u1=4m/s

u2=2m/s

v1=v2 (since after collision they stuck together)

According to law of conservation of momentum,

m1u1 + m2u2 = m1v1 + m2v2

500 x 4 + 1500 x 2 = (500 + 1500) v

5000 = 2000v

v = 5000/2000

v = 2.5m/s

Mass of ball X, m1 = 1 kg

Mass of ball Y, m² = 1kg

According to conservation of momentum,

m1u1 + m2u2 = m1v1 + m2v2

1*2 + 1*0 = 1*0 + 1*v2

2 + 0 = 0 + v2

v2 = 2 m/s

Applying conservation of momentum,

P1 = P2

Mass of car A be 2000kg

Mass of car B be 500kg

Velocity of car A before impact = Va = 10m/s

Velocity of car B before impact = Vb=?

Velocity of car A after impact = 0

Velocity of Car B after impact = 0

2000 Va + 500Vb = 2000×0 + 500×0

2000 × 10 + 500Vb = 0

Vb = - 20000/500 = - 40m/s

Negative sign shows that direction of Va and Vb are opposite.

m - Mass of bullet

= 0.02 kg

M - Mass of man

= 80 kg

u - Initial velocity of bullet

= 400 m/s

U - Initial velocity of man

= 0 m/s

v - Final velocity of bullet

= 0 m/s

V - Final velocity of man

Using conservation of momentum

Initial momentum = Final momentum

M * u + M * U = m * v + M * V

0.02 * 400 + 80 * 0 = 0.02 * 0 + 80 * V

8 = 80 * V

V = 0.1 m/s

Therefore, the man moves with a velocity of 0.1 m/s

We know that

Momentum, p = mv

As from question, balls have same speed.

p α m

Since cricket ball has more mass than the tennis ball.

So, cricket ball has more momentum than the tennis ball.

That is why it is easier to stop a tennis ball than a cricket ball moving with the same speed.

.P = mv, shows the method to calculate the momentum of an object. Where, p represents momentum

m, mass of object and v, velocity of the object.

It shows that the momentum of an object is the product of its mass and velocity.

In doing so, the entire momentum of the hand is reduced to zero in very short interval of time. As a result, very large force is delivered to the pile of tiles which breaks it in a single blow.

Given: Mass of car, m =200g

Velocity of car, v =5 m/s

Now, 1 kg = 1000 g

Thus, mass of car, m = 0.2kg

Momentum of the car, p= mass × velocity

= 0.2kg × 5 m/s

= 1 kg-m/s

The formula of change in momentum= mv - mu,

Where m = mass i.e. 1500kg,

v = final velocity i.e. 72 km/hr,

u = initial velocity i.e. 36 km/hr.

We will change the v and u to m/s

i.e. 72 X 5/18=20 m/s and 36 X 5/18=10 m/s.

Hence, change in Momentum= mv - mu

= 1500X20 - 1500X10

=1500[20 - 10]

= 1500 X 10

= 15000 kg m/s

Given: mass of the body, m =25 kg

Let the velocity of the body be v m/s

125 = 25(v)

Hence, the velocity of the body is 5 m/s

As we know,

Momentum, p = mv

Where, m is the mass of the body

V is the velocity of the body,

(a) m = 2000 kg

v = 5 m/s

p = (2000) × (5)

= 10000 kg m/s

(b) m = 0.2 kg

v = 400 m/s

p = (0.2) × (400)

= 80 kg m/s

Balanced forces can change the shape of the object.

Example: Squeeze a rubber ball between the palms of your hands. What do you observe? The shape of the rubber ball changes. The force applied on the ball is equal and opposite, so, the resultant of this force does not move the object, this is balanced force.

Inertia can easily be described as the reluctance or resistance of a body to change its state of motion i.e. if a body is at rest, it will continue to remain at rest if an external force is not applied to change its state of rest whereas if a body is in motion, it will continue to remain in motion if an external force is not applied to change its state of motion.

Newton's first law of motion, also referred to as the law of inertia states that an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

For example,

(i) When a bus suddenly starts, the passengers sitting or standing in the bus tend to fall backward. This is due to inertia of rest and can be explained as follows: when the bus suddenly starts, the lower part of the body of the passenger which is in contact with the bus moves along with the bus while the upper part of the body tends to retain its state of rest due to inertia. As a result, the passenger falls backward.

(ii)A rider on a running horse is thrown forward when the horse stops suddenly due to inertia of motion.

Inertia of a body depends on its mass. A cricket ball has more mass than a rubber ball, hence it has more inertia.

When a bus suddenly starts, the passengers sitting or standing in the bus tend to fall backward. This is due to inertia of rest and can be explained as follows: when the bus suddenly starts, the lower part of the body of the passenger which is in contact with the bus moves along with the bus while the upper part of the body tends to retain its state of rest due to inertia. As a result, the passenger falls backward.

When moving bus suddenly stops, the passengers sitting or standing in the bus are thrown forward. This is due to inertia of motion and can be explained as follows: when the moving bus suddenly stops, the lower part of the body of the passenger contact with the bus suddenly comes to rest while the upper part of the body tends to retain its state of motion due to inertia. As a result, the passenger is thrown forward.

When a blanket is given a sudden jerk, the dust particles in it fall off due to inertia at rest. Dust particles were at rest on the carpet. However when you beat the carpet, you are forcing the dust to move along with the carpet. Due to the dust having inertia, it doesn't move, or rather, it resists motion. This is why dust comes out of a carpet when it is beaten with a stick.

When a branch of a tree is vigorously shaken the fruits and seeds in It fall down due to inertia of rest. The tree was at rest (at first), when the tree is shaken the branches of the tree gains motion but the fruits and leaves tends to be in rest due to inertia of rest and hence they fall down.

The man jumping out from a moving bus possesses the inertia of motion. As the man lands on the ground, feet come to rest immediately while the upper part of body continue to move due to inertia of motion and hence the person may fall forward. Hence, it is dangerous to jump out of a moving bus.

As we know,

Momentum, p = m × v

Where, m is the mass of the body

v is the velocity of the body,

Here, m = 10 kg

(a) v = 5 m/s

p = (10) × (5)

= 50 kg m/s

(b) v = 20 cm/s = 0.2 m/s

p = (10) × (0.2)

= 2 kg m/s

(c) v = 36 km/h = 10 m/s

p= (10) × (10)

= 100 kg m/s

Momentum is defined as amount of motion a body contains. Mathematically it is defined as the product of mass and velocity. So the factors on which momentum of a body depends are its mass and velocity.

The formula of change in momentum= mv - mu,

Where m=mass i.e. 5kg

v=final velocity i.e. 0.2 m/s

u=initial velocity i.e. 20m/s

Hence, change in Momentum= mv - mu

= 5 (0.2 - 20)

= 5(-19.8)

= -99 kg m/s

99 kg m/s decreases

A push or pull is a force. Or in other words we can say that force is the capacity to do work or cause any physical change.

The Effects of Forces are - force acting on an object may cause the object to change shape, to start moving, to stop moving, to accelerate or decelerate.

When two objects interact with each other they exert a force on each other, the forces are equal in size but opposite in direction.

The required examples of forces are:

(a) While pushing a table, a stationary object is moved through force.

(b) When brakes are applied in order to stop the bicycle.

(c) While hitting a moving football changes its direction, here the force changes the direction of a moving object.

(d) When we push a slowly moving bicycle its speed increases gradually.

(e) Applying force on a rubber ball changes its shape. Here a force tends to change the shape of an object.

Forces that are equal in size but opposite in direction are called balanced forces. Balanced forces do not cause a change in motion. When balanced forces act on an object at rest, the object will not move. For example- If you push against a wall, the wall pushes back with an equal but opposite force. Neither you nor the wall will move.

Forces that cause a change in the motion of an object are unbalanced forces. Unbalanced forces are not equal and opposite. For example- Suppose that one of the teams in tug of war pulls harder than the other team. The forces would no longer be equal. One team would be able to pull the other team in the direction of the larger force.

When we press the rubber ball between our hands an equal and opposite force acts and only the shape of the ball is changed, hence we can conclude that the balanced forces acts on it. As an effect of force the shape of the ball changes, it gets a little compressed.

When the bus takes a sharp turn the passengers travelling in a bus tends to fall due to the Inertia of direction. While the bus is moving the passengers exist the Inertia of motion in the direction the bus is moving but when it takes sharp turn the body of the passengers opposes the change, hence they tends to fall.

This is because of the momentum. When a car or a vehicle moves in a slow speed its momentum is less due to which the damage due to the accident is less but when a car or vehicle moves at a high speed then damage due to accident is very large so it is advised to drive cars at slow speeds to be in control and prevent damage and if the damage occurs then the damage will be less.

Since, balanced forces are forces that produce no change in motion but can change its shape.

Since, Inertia is the resistance of any physical object to any change in its state of motion; this includes changes to its speed, direction, or state of rest.

Since, Forces that cause a change in the motion of an object are unbalanced forces.

Since, when the coin is tossed the train accelerates forward whereas coin due to inertia tends to move with the same velocity when tossed.

Since, due to inertia of rest the dust particles come out of the carpet when beaten with stick.

This happens due to the Inertia of motion that water exist at that moment.

Since, unbalanced forces are the forces that cause a change in the motion of an object.

Since, The heavier the body more the Inertia it exists.

As the balanced forces cause the change in shape of an object without bringing a change to its motion.

Since, only the balanced forces can cause the change in shape of the body.

The amount of momentum that an object has depends on two physical quantities: the mass and the velocity of the moving object in the frame of reference.

We know,

p = m × v

where p is the momentum, m is the mass and v is the velocity.

Since, in the above case both the mass and velocity of clay ball and plastic ball are same and they are travelling in the same frame of reference their momentum will be equal.

Thus, the wall will receive equal momentum from both plastic and clay ball.

There is an external force of friction between the tyres and the road and in the axles of the bicycle acting which resists the motion and hence tends to stop the cycle.

(i) The momentum, p = mv.

The values of mass and velocity are given as

Mass, m =500g = 0.5 kg

Initial velocity, u = 10 m / s

Initial Momentum = mu

= 0.5 ×10 = 5 kg m/s

(ii) At the highest point, the velocity of the ball will be zero. So, its momentum is zero.

These forces would be the air friction and the friction between the tires and the road which would tend to bring the car at rest. Frictional force would contribute more in stopping the car.

(a) Unbalanced forces as these forces are not opposite in direction and equal in size always cause a change in motion.

(b) Balanced forces as balanced forces can cause an object to stay at rest or at constant velocity but don't change the motion of the object rather may change the shape.

Force is the rate of change of momentum. The SI unit of force is the Newton and it's symbol is 'N'.

Consider a body of mass m, initial velocity of magnitude u, a force F acts on the body to a final velocity of magnitude v. We have from Newton's second law F= m(v-u)/t or F = (mv-mu)/t. mu is the initial momentum of the body and mv is the final momentum of the body.

Force = rate of change of momentum.

F = DP/Dt or Dp = F x Dt

The FDt is called the impulse of the force F.

The change in momentum can be calculated by the area under the graph of force against time.

F = D (mv)/Dt

= m/Dt x Dv.

The SI unit of force is the Newton and it's symbol is 'N'.

The force which when applied on a body of mass of 1 kg provides the acceleration of 1 m/s² is known as 1 Newton force.

1 Newton force = 1 kg m/s²

Newton's second law of motion describes the relationship between force and acceleration.

The force is defined as the rate of change of momentum of a body

OR in mathematical terms,

F= dP/dt

where P is momentum that is equal to m*v, where m is mass of the body and v is its velocity.

Putting this value, we get

F= d (mv)/dt

If the mass of the body is constant not variable then m is constant and can be taken out

F= m (dv/dt)

Now rate of change of velocity with respect to time is acceleration, a

So, F = ma

The acceleration would remain the same. It can be explained as-

We know, F=ma a=F/m

When both Force and Mass are doubled it means

A = 2F/2m

= F/m

Hence, acceleration remains constant.

'Newton' is the unit of force which can be defined as the rate of change in Momentum.

Simply by Newton's third law I.e. conservation of momentum. The jet engine exerts force rearwards by throwing high velocity jet of air and as a reaction the plane moves forward.

It relates with the principle of Newton's 3rd law of motion stated as "for every action there is a equal and opposite reaction". When the force on with holds the rocket then, the rocket pushes itself through the ground and hence, this is the principle on which a rocket works and flies into space.

True: Rockets and engines in space behave according to Isaac Newton's third law of motion: Every action produces an equal and opposite reaction. When a rocket shoots fuel out one end, this propels the rocket forward — no air is required.

Newton produces an acceleration of 1 m/s² in a body of mass 1 kg.

1 Newton force = 1 kg m/s²

Force, F= 5N

Mass, m=10 kg

Let, the acceleration be 'a'

We know,

F =ma

a= F/m

=5/10

= 0.5 m/s²

250N (Due to the 3rd law of motion)

Mass of the car would make it easier to accelerate a small car than a large car. Since, mass is inversely proportional to acceleration. Hence, lesser the mass more the acceleration it would have.

(a) equal; opposite (As per Newton’s third law)

(b) Vector; kg m/s (As momentum is the product of mass and velocity and velocity is a vector quantity)

(c) Acceleration; rate; momentum

(d) Magnitude; directions (Conservation of momentum)

(e) Momentum; force; (Explained in conservation of momentum)

F is the net force applied,

m is the mass of the body,

And a is the body's acceleration. Thus, the net force applied to a body produces a proportional acceleration. This states that the rate of change of momentum of a body, is directly proportional to the force applied and this change in momentum takes place in the direction of the applied force.

Pushing of the river bank is an action, the river thus pushes back the boat in the forward direction as a reaction in accordance with the Newton's third law of motion which states that every action has a equal and opposite reaction.

This is because when the bullet is fired from the gun, it moves forwards and exerts a force on the gun; an equal amount of force is exerted on the bullet by the gun. This is because according to third law of motion, when a force is applied on a body, the body exerts an equal and opposite force on another body.

When horse is moving forward it applies a backward effort towards the ground, meaning that when the horse push the ground backwards from his feet then the ground also exerts a forward push on the horse. That is why the horse moves and so the cart along with it.

Rockets are great examples of how forces make things move. ... This can be explained by the force what's often called "action and reaction" (another name for Newton's third law of motion). During the launching of rocket the hot exhaust gas firing down act as the action force creating an equal and opposite force as the reaction that speeds the rocket up.

Action and reaction always acts on two different bodies.

For example: A boatman jumps out of the boat and then boat goes backwards. Here jumping of boatman is action and backward motion of boat is reaction.

They are equal in magnitude and opposite in direction. And yes they are simultaneous.

This can be explained by Newton's Third law: The mutual forces of action and reaction between two bodies are equal, opposite and collinear.

Jumping off the boat is the action, and as a result the boat moves backward is the reaction. This is the reason why boat moves backward when the man jumps out of the boat.

You push backward with your feet. Newton's third law: the ground pushes you forward. But that interaction is friction. Reduce friction and it doesn't matter how strong your legs are, the surface is incapable of pushing you accordingly. The coefficient of static friction is very low so it is easy to slide your foot rather than push. Accordingly, the ground doesn't push back.

According to Newton's third law of motion to every action there is an equal and opposite reaction. When runners push the ground the ground also push the runner with an equal and opposite force which he utilizes to run fast. Runners push the ground so he can gain more reaction force from ground. The harder the runner pushes the ground, the more force he can gain to move forward.

Mass of bullet, m1 = 0.06 kg,

Speed of bullet, v1 = 500m/s

Mass of gun, m2 = 5kg,

Velocity of recoil of gun, v2 = ?

By using the law of conservation of momentum,

0.06×500 = 5×v2

v2 = 0.06*500/5

= 6m/s

Hence, the gun recoils with the velocity of 6m/s.

Mass of bullet, m = 10 g

= 0.01 kg

Speed of bullet, v = 200 m/s

Mass of target, M = 2 kg

Combine speed after hitting target = V

Before collision, momentum of the system is = mv = 2

After collision, the bullet and target move together. Their combined mass is (m+M) = 2.01 kg

So, the momentum of the system after collision is = 2.01V

Applying conservation of momentum,

Momentum of the system before collision = momentum of the system after collision

2 = 2.01 V

V = 0.99 m/s

This is the combined velocity of the target and bullet after the collision.

Given:

Mass of Body, m = 2 kg

Initial velocity, u = 0 m/s

Final velocity, v = 30 m/s

Time, t = 1 s

We know,

F = ma

from, First equation of motion


We get,

F = m × a = 2 × 30 =60 N

According to the question we have:-

Mass of body, m = 5kg

Initial velocity, u=10m/s

Final velocity, v=35m/s

Time taken, t=25s

We know that,

v = u + at

Putting the values we get,
⇒ 35m/sec = 10 m/sec + a×25 sec
⇒ (35 - 10 ) m/sec = a×25 sec
⇒ 25 m/sec = a×25 sec
⇒ a = 1m/sec²

Now, using Newton's Second law of motion, we get,

F= ma

F = 5kg×1m/sec²

F = 5kg-m/sec²

^{F = 5 Newton}

Mass, m = 2400 kg

Initial velocity, u = 20 m/s

Time, t = 10 s

Final velocity, v = 0 m/s

We know that,

a = v-u/t

=-20/10

=-2 m/s²

Now,

Force, F = ma

=2400 (-2)

= 4800 N

Force F = m (v-u)/t ........equation 1

u is initial velocity = 0

v is final velocity = 100m/s

F = 100N

m = 20kg

Putting these values in equation 1 we can find time t

100 = 20(100-0)/t

t = 20 seconds

Force applied (F) = -10 N (since the force is acting in the opposite direction of motion or opposing the motion)

Mass of body (m) = 2.5kg

Initial velocity of body (u) = 20m/s

Final velocity of body (v) = 0m/s

According to Newton's second law of motion

F = ma

-10 = 2.5×a

-10/2.5 = v-u/t (since a = v-u/t)

-4t = 0 - 20

t = -20/-4

t = 5 sec

Mass of the body, m = 10 kg

Initial velocity, u = 4 m/s

Final velocity, v = 8 m/s

Time, t = 2s

(a) Initial Momentum, p1 = mu

= 10 × 4 = 40 kg m/s

(b) Final Momentum, p2 = mv

= 10× 8= 80 kg m/s

(c) Gain in momentum for 2s = p2 – p1 = 40kg m/s

Gain in momentum per second = = 20kg m/s

(d) Acceleration, a = = = 2 m/s²

Force = m * a = 10 * 2 = 20N

(i) For gun,

M₁ =3 kg(Given)

V₁ =?

For bullet,

V₂ = 100m/s

By law of conservation of momentum

3 × V₁ = 0.03 × 100

Hence, the velocity of recoil of gun is 1m/s

(ii) Acceleration of bullet, a = v-u/t

100-0/0.003 = 33333.33m/s²

We know that:-

Force, F = ma

= 0.03 × 33333.33

= 1000 N

Rocket works on the principle of Newton’s third law of motion.

Every action there is equal and opposite reaction.

When exhausted gas moves downward, they provide equal amount of force on the rocket in upward direction, therefore rocket gets the thrust in upward direction.

(a) The name of the corresponding law is law of conservation of momentum. It can be derived from Newton's laws of motion.

(b) The name of corresponding law is Newton's second law of motion which proves that the acceleration of the body is inversely proportional to its mass.

(c) In this Newton's third law of motion is involved which says that every action has a equal and opposite reaction.

(d) This involves Newton's first law of motion or the law of inertia which states that n object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

The second law states that the rate of change of momentum of a body is directly proportional to the force applied and this change in momentum takes place in the direction of the applied force.

Acceleration is produced when a force acts on a mass. The greater the mass (of the object being accelerated) the greater the amount of force needed (to accelerate the object).

Vehicle Mass = 1000 kg

Initial Velocity (that is speed) let it be u = 20 ms-1

Final Velocity let it be v= 0ms-1

Distance travelled = 50 m

Let the acceleration be "a"

From equation = v2 = u2 + 2as

Putting all value

0= 20 + 2*a*50

0= 400+ 100a

0- 400= 100a (Side changing)

-400 = 100a

-400/ 100 = a (Side changing)

-4= a

a = -4 m/s²

This shows that the acceleration is in opposite direction that means it is retardation.

Retardation = 4m/s²

A cricketer moves his hand backwards because by doing this he increases the time due to which the rate of change of momentum decreases. That means that the ball comes to rest gently and does not hurt the fielder. But, if does not move his hand backwards, then the ball would come to rest in a fraction of a second with a high rate of change of momentum. The ball will exert a lot of force on the hands of the fielder which will hurt him.

Mass of ball = 150g = 0.15kg

Initial velocity, u = 30 m/s

Final velocity, v = 0m/s (as player stops the ball)

Time, t = 0.05s (as player stops ball in 0.05s)

Force, F = m x a

F = m x v-u/t

F = 0.15 x 0-30/0.05

F = 3 x -30

F = -90 N

The third law states that all forces between two objects exist in equal magnitude and opposite direction: if one object A exerts a force FA on a second object B, then B simultaneously exerts a force FB on A, and the two forces are equal in magnitude and opposite in direction: FA = −FB

The water from the house pipe rushes out with great speed in forward direction (action of house pipe on water).Then due to Newton's 3rd law of motion the house pipe moves in backward direction as a reaction.

The law of conservation of momentum states that for any two objects colliding in an isolated system, the total momentum before and after the collision is equal. This is because the momentum lost by one object is equal to the momentum gained by the other.

(i) Before launch, the total momentum of a rocket and its fuel is zero. During launch, the downward momentum of the expanding exhaust gases just equals in magnitude the upward momentum of the rising rocket, so that the total momentum of the system remains constant—in this case, at zero value. In a collision of two particles, the sum of the two momentum before collision is equal to their sum after collision.

(ii) In airplane, the turbine works the compressor and drives the gas through tail piece of engine at larger speed. This results in forward momentum and jet moves forward. The forward momentum is equal to backward momentum of gases. The rates of burning and ejection of gases in the fuel burning chamber is adjusted to get desired increase momentum in the forward direction.

It moves in the upwards direction because according to Newton's third law of motion EVERY ACTION HAS IT'S OPPOSITE AND EQUAL REACTION and therefore when the air starts coming out from the mouth of the balloon(ACTION) in the downward direction, as a reaction the balloon moves upward .

For unloaded truck,

Mass, m = 2000 kg

a = 0.5 m/s²

Now, using F = ma

F = 2000 x 0.5

= 1000 N

For loaded truck,

m = 2000 + 2000 = 4000 kg

F = 1000 N (remains unchanged)

Again,

F = ma

a = F/m

= 1000/4000

= 0.25 m/s²

When exhausted gas moves downward, they provide equal amount of force on the rocket in upward direction, therefore rocket gets the thrust in upward direction.

As according to the law of inertia the object will keep moving with the same velocity if no external force is applied.

As it's the unit of mass.

That is the reason why Momentum remains conserved.

Since, Momentum is the product of mass and velocity.

As per 3rd law of motion which states that every action has equal and opposite reaction.

Since the speed of all the vehicles are same, hence the accelaration will depend on the the mass of the object.

Since, Accelaration is inversely proportional to the mass of the object.

Hence, the maximum accelaration will be of Tata Nano.

As per Newton's 2nd law of motion where F = ma

As the second law states that the rate of change of momentum of a body, is directly proportional to the force applied and this change in momentum takes place in the direction of the applied force.

As it increases the time taken to bring the momentum to zero.