Mechanics

Question 1

What does the assumption that a string is light imply?

Answer 1

The acceleration of the string and particles connected to it is constant.

Question 2

What does the assumption that a string is inextensible imply?

Answer 2

The acceleration is the same across all parts of the string i.e. if a particle connected to one end has acceleration a, a particle also connected to the string will have acceleration a.

Question 3

What does the assumption that a pulley is smooth imply?

Answer 3

The tensions in the part of the string on both sides of the pulley are the same.

Question 4

What does neglecting air resistance imply?

Answer 4

Acceleration is constant

Question 5

What is Newton’s 1st Law of Motion?

Answer 5

A body will remain at rest, or will continue to move with constant velocity, unless external forces cause it to do otherwise.

Question 6

What is Newton’s 2nd Law of Motion?

Answer 6

The force acting on an object is equal to the product of its mass and acceleration.

Question 7

What is Newton’s 3rd Law of Motion?

Answer 7

If body A exerts a force on body B, body B will exert a force of the same type and equal magnitude in the opposite direction, along the initial line of action.

Question 8

For a uniform ladder and smooth wall, what is the reaction at the wall?

Answer 8

mg/2tanθ

Question 9

What is the:

• reaction at the wall
• angle between floor and ladder

for a uniform ladder on a rough floor and wall?

Answer 9

• u_A/(u_Au_B+1) * mg
• tanθ = (1 - u_Au_B)/2u_A

Question 10

What is tangential velocity in terms of radius and angular frequency?

Answer 10

v = rω

Question 11

What are the formulae for radial acceleration?

Answer 11

a = v²/r = rω²

Question 12

What are the formulae for centripetal force?

Answer 12

T = mv²/r = mrω²

Question 13

What are the formulae for:

• max. height
• max. range
• flight time
• equation of motion

of a projectile?

Answer 13

• u²sin²θ/2g
• 2usinθ/g
• u²/g
• y = xtanθ - gx²/2u² * (1 + tan²θ)

Question 14

What is the centre of mass of an object?

Answer 14

The point inside or outside a body about which it can be balanced i.e. the point at which all its weight can be considered to act.

Question 15

What is coefficient of restitution?

Answer 15

The ratio between departing speed and arrival speed.

Question 16

How can we work out displacement, velocity and intantaneous acceleration when a body is moving with non-constant acceleration?

Answer 16

(for 2D motion, you can write the column vectors and differentiate each row separately)