Solved Problems on Laws of Motion - Science

SOLVED PROBLEMS

Problem-1

Calculate the velocity of a moving body of mass 5 kg whose linear momentum is 2.5 kg m s^–1.

Solution:

Linear momentum = mass × velocity

Velocity = linear momentum / mass. V = 2.5 / 5 = 0.5 m s^–1

Problem 2

A door is pushed, at a point whose distance from the hinges is 90 cm, with a force of 40 N. Calculate the moment of the force about the hinges.

Solution:

Formula: The moment of a force M = F × d

Given: F = 40 N and d = 90 cm = 0.9 m.

Hence, moment of the force = 40 × 0.9 = 36 N m.

Problem 3

At what height from the centre of the Earth the acceleration due to gravity will be 1/4^th of its value as at the Earth.

Solution:

Data: Height from the centre of the Earth, Rʹ = R + h

The acceleration due to gravity at that height, gʹ = g/4

From the centre of the Earth, the object is placed at twice the radius of the earth.

Understanding the Principle of Conservation of Linear Momentum

Principle of Conservation of Linear Momentum

PRINCIPLE OF CONSERVATION OF LINEAR MOMENTUM

There is no change in the linear momentum of a system of bodies as long as no net external force acts on them.

Let us prove the law of conservation of linear momentum with the following illustration:

Figure 1.7 Conservation of linear momentum

Proof:

Let two bodies A and B having masses m₁ and m₂ move with initial velocity u₁ and u₂ in a straight line. Let the velocity of the first body be higher than that of the second body. i.e., u₁>u₂ . During an interval of time t second, they tend to have a collision. After the impact, both of them move along the same straight line with a velocity v₁ and v₂ respectively.

Force on body B due to A,

F_B= m₂ (v₂–u₂)/t

Force on body A due to B,

F_A = m₁ (v₁–u₁)/t

By Newton’s III law of motion,

Action force = Reaction force

F_A    =         –F_B

m₁ (v₁-u₁)/t  =       –m₂ (v₂-u₂)/t

m₁v₁ + m₂v₂ = m₁u₁ + m₂u₂ ------ (1.9)

The above equation confirms in the absence of an external force, the algebraic sum of the momentum after collision is numerically equal to the algebraic sum of the momentum before collision.

Hence the law of conservation linear momentum is proved.

Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail. 10th Science : Chapter 1 : Laws of Motion : Principle of Conservation of Linear Momentum.

Linear Momentum: Definition, Formula, and Units | 10th Science Laws of Motion

10th Science : Chapter 1 : Laws of Motion : Introduction

Linear Momentum

LINEAR MOMENTUM

The impact of a force is more if the velocity and the mass of the body is more. To quantify the impact of a force exactly, a new physical quantity known as linear momentum is defined. The linear momentum measures the impact of a force on a body.

The product of mass and velocity of a moving body gives the magnitude of linear momentum. It acts in the direction of the velocity of the object. Linear momentum is a vector quantity.

Linear Momentum = mass × velocity

p = m v

It helps to measure the magnitude of a force. Unit of momentum in SI system is kg m s^–1 and in C.G.S system its unit is g cm s^-1.

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Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail for 10th Science : Chapter 1 : Laws of Motion.