Force And Laws Of Motion

● When we apply pressure on a spring, it get compressed.

● When we squeeze a rubber ball by apllying force with our hands, it get compressed.

According to Newton’s third law, to every action there is an equal and opposite reaction. So when we kick a stone with much force, an equal and opposite reaction from the stone is applied on our legs which hurt our legs.

Force is any interaction that will change the motion of an object when unopposed. A force can cause an object with mass to change its velocity which includes to begin moving from a state of rest, i.e., to accelerate. Force is a vector quantity as it has both magnitude and direction. Mathematically, Force = mass acceleration. Its S.I. unit is Newton.

One Newton is the force required to accelerate one kilogram of mass at the rate of one metre per Second Square in the direction of the applied force.

Dyne is the CGS unit of force One dyne is equal to the force needed to accelerate one gram of mass at the rate of one centimeter per second square.

According to Newton’s law, an object which is at rest or in motion will continue its state of rest or motion unless and until an external force is applied on it. This property is known as inertia. Dust particles are at rest with respect to the carpet. When the carpet is beaten, the dust due to inertia tends to remain at rest while the carpet moves due to external force applied. So the dust comes out of the carpet.

According to Newton’s third law, to every action there is equal and opposite reaction. In the horse and cart system, the horse is applying force on the cart and instantaneously the cart exerts an equal and opposite force on the horse. But these two forces are acting on two different objects and not on the same object and therefore the force will not get cancelled. Thus the horse is able to pull the cart.

We are able to walk due to force of friction. Friction is a contact force and arises when two objects are in direct contact with each other. While walking our feet exerts force on the ground pushing it backwards and the ground exerts equal and opposite reaction to our feet helping us to move forward. When we step on banana peel, the friction force between the feet and the peel decreases and we are not able to move forward and slip.

The leaves are at rest with respect to the tree. According to law of inertia, it has a tendency to remain at rest and is resistant to change its state. When we apply external force on the branches, the branches are in motion but the leaves remain at rest due to which it falls off.

Luggage is in contact with the roof of the bus. When the bus is moving the luggage is also in the state of motion and had a tendency to remain in motion due to law of inertia. When the driver apply the brakes, the bus stops suddenly but the luggage is in motion and thus fall from the roof. It is therefore advised to tie the luggage.

Let an object of mass ‘m’ is moving along a straight line with initial velocity ‘u’. A constant force ‘F’ is applied in time ‘t’ to accelerate it and its final velocity becomes ‘v’.

Initial momentum, p₁ = mu
Final momentum, p₂ = mv
Change in momentum p₂ - p₁
mv – mu
m(v – u)
The rate of change of momentum =

Rate of change of momentum = force applied
Force
Force = k where k = proportionality constant

Force = kma where a = acceleration =

Law of conservation of momentum states that total momentum of the system remains conserved in the absence of external force.

Proof: Consider two bodies of mass m₁ and m₂ moving with initial velocity u₁ and u₂ respectively. The two bodies collide with each other for a time interval ‘t’ . The velocity after collision be v₁ & v₂ respectively. Let F₁₂ be the force applied by m₁ on m₂ and F₂₁ be the force applied by m₂ on m_1.

Momentum of mass m₁ before collision = m₁ u₁
Momentum of mass m₂ before collision = m₂ u₂
Momentum of mass m₁ after collision = m₁ v₁
Momentum of mass m₂ after collision = m₂ v₂

Impulse = force time = change in momentum

For mass m₁ :

F₁₂ t = m₁ v₁ - m₁ u₁ …………….(1)

For mass m₂ :

F₂₁t = m₂ v₂ – m₂ u₂ ……………..(2)

Adding equation (1) & (2)

F₁₂ t + F₂₁t = (m₁ v₁ - m₁ u₁) + (m₂ v₂ – m₂ u₂)

(F₁₂ + F₂₁ )t = (m₁ v₁ + m₂ v₂) - (m₁ u₁ + m₂ u₂)

According to Newton’s third law:
F₁₂ = - F₂₁
F₁₂ + F₂₁ = 0

(m₁ v₁ + m₂ v₂) = (m₁ u₁ + m₂ u₂)

Final momentum = Initial momentum

Hence momentum is conserved.

Force = 40 N

Acceleration = 5 m s^-2

force = mass acceleration

mass = = = 8 kg

Mass = 80 kg
Initial velocity, u = 5 m s^-1
final velocity, v = 25 m s^-1
Time, t = 2 sec

Rate of change of momentum = force applied

Force = = = = 800N

Let the mass of first block = m₁
acceleration of block of mass m₁ = a
Let the mass of second block = m₂
acceleration of block of mass m₂ = 5a

Force = mass acceleration

Since forces are equal,

m₁ a = m₂5a

= = 5

=

Acceleration = 8 m s^-2

Time = 1 sec

Distance travelled, s = ?

Initial velocity, u = 0

Using the equation, s = ut + at²

s = 01 + ² = 4 metres

Force = 10^-2 N = 0.01 N initial velocity, u = 0
mass, m = 500 g = 0.5 kg distance travelled, s =?
time, t = 10 sec
Force = mass acceleration
acceleration, a = = = 0.02 m/s²

Using the equation, s = ut + at²

s = 010 + ² = 1 metre

We are able to walk due to force of friction. Friction is a contact force and arises when two objects are in direct contact with each other. While walking our feet exerts force on the ground pushing it backwards and the ground exerts equal and opposite reaction to our feet helping us to move forward. When we walk on ice, the friction force between the feet and the ice decreases and it causes slipping. Therefore we take small steps on ice.

When the tyre of the cycle is inflated, the pressure inside the tyre is reducing the normal force between tyre and the ground, and thus reducing the friction between the tyre and the road. When the tyre gets punctured, it gets deformed during the rotation of the tyre, the energy supplied is used up in changing the shape and not overcoming the friction, and due to deformation, friction increases. Therefore we have to apply more force in order to move the cycle.

According to Newton’s third law, to every action there is equal and opposite reaction. When we jump on the shore from the boat, we are applying force on the boat in the opposite direction in order to move forward and hence the boat moves in the opposite direction.

It is difficult for a fireman to hold a hose which ejects large amount of water at high velocity because according to third law of Newton which states that for every action there is an equal and opposite reaction.

As the hose ejects a large amount of water in the forward direction has great force. So an equal and opposite reaction is applied on the fireman. That is why he finds it difficult to hold the hose. Also according to law of conservation of momentum, the amount (mass) of water coming out (velocity) produces recoil on the hose. To stop the hose from moving, the fireman has to supply his own force on the hose, and must exert a large quantity of force to counter the hose's recoil.

Luggage is in contact with the roof of the bus. When the bus is moving the luggage is also in the state of motion and had a tendency to remain in motion due to law of inertia. When the driver apply the brakes, the bus stops suddenly but the luggage is in motion and thus fall from the roof. It is therefore advised to tie the luggage.

An athlete runs before jumping to gain momentum because it helps in jumping higher and longer because of inertia of motion gained due to the motion. When the athletes jump they already have a forward motion that would be greater than that of a jump made from standing in one spot. While running, the athlete cannot gain energy or apply larger force because initially he would be rest and while running he will lose energy.

Dust particles are at rest with respect to the carpet. When the carpet is beaten, the dust due to inertia tends to remain at rest while the carpet moves due to external force applied. So the dust comes out of the carpet. Inertia of motion is not involved here as the dust particles are at rest and inertia is involved in this case. So option B. & C. are not the correct option.

When the man pushes the ice backward the ice will give an equal reaction in the forward direction and thus helps him to reach the shore. This action reaction law is explained in third law. First law is also known as law of inertia & second law is known as law of force and acceleration.

According to Newton’s law, an object which is at rest or in motion will continue its state of rest or motion unless and until an external force is applied on it. This property is known as inertia.

Force is a vector quantity which can only be explained by both magnitude and its direction.

One Newton is the force required to accelerate one kilogram of mass at the rate of one metre per Second Square in the direction of the applied force. Newton per second is S.I. unit of impulse. Newton-metre is the unit of torque. Newton per square metre is S.I. unit of pressure.

School bag has the mass greater than the pin, pen and book. So, it offers greater resistance and hence had higher inertia.

The rate of change of momentum =

Rate of change of momentum = force applied
Force
Velocity is rate of change of displacement and acceleration is rate of change of velocity. Impulse is change in momentum.

The combustion of fuel generates a large amount of gas which escapes from backward direction. Due to very high velocity, the backward rushing gases have large momentum. They impart equal and opposite reaction to the jet engine due to which it moves forward with great velocity. First law is law of inertia & second law is law of force and acceleration.

According to Newton’s third law, to every action there is equal and opposite reaction. But these two forces are acting on two different objects and not on the same object. If the forces act on same object the forces will get cancelled and the object will not move.

Force acceleration. So if acceleration is doubled, force will also increase by a factor of two.

The property or tendency of a moving object to continue moving is called momentum. For an object moving in a line, the momentum is the mass of the object multiplied by its velocity. Volume, density and shape does not determine the momentum.

Newton’s 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. First law gives measure of inertia.

Force acceleration. Acceleration is rate of change of velocity. Mass is a constant quantity. Inertia is a tendency to resist the state of rest or motion.

According to Newton’s third law, to every action there is equal and opposite reaction. But these two forces are acting on two different objects and not on the same object. If the forces act on same object the forces will get cancelled and the object will not move.

According to law of conservation of momentum, initial momentum is equal to the final momentum. So in order to conserve momentum, the gun recoils. Velocity, force and speed are not conserved.

Newton’s 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. Newton’s first law gives the law of inertia and third law the action & reaction law. Law of conservation of momentum states that initial momentum is equal to final momentum.

Rate of change of momentum = force applied
Force
Force = k where k = proportionality constant

Force = kma where a = acceleration =

Newton’s first law states that an object at rest will stay at rest and an object in motion will stay in motion with the same speed and direction unless and until an external force is applied on the object. Newton’s third law the action & reaction law. Law of conservation of momentum states that initial momentum is equal to final momentum.

Balanced forces acts on an object in opposite directions and are equal in strength. They do not cause a change in the speed of a moving object. For all the other options unbalanced forces are required.

Zero unbalanced force means the body is not accelerating but it moves with a constant velocity.

True

A balanced force does not produce any motion but unbalanced force does.

False

According to Newton’s third law, to every action there is equal and opposite reaction. But these two forces are acting on two different objects and not on the same object. If the forces act on same object the forces will get cancelled and the object will not move.

False

Impulse = force time = change in momentum
Rate of change of momentum is force applied and not momentum.

False

One Newton is the force required to accelerate one kilogram of mass at the rate of one metre per Second Square in the direction of the applied force.

True

According to Newton’s third law to every action, there is equal and opposite reaction and thus two forces comes into play.

False

Force of friction is greater in solids than in liquids because solids have greater surface area than liquids. More the surface area more is the friction. Moreover, liquids are smooth in comparison to solids and therefore their friction is less.

True

Newton’s first law states that an object at rest will stay at rest and an object in motion will stay in motion with the same speed and direction unless and until an external force is applied on the object. This tendency to resist its state of motion is called inertia.