Further Mechanics

Question 1

What is the derivation of the equation for the kinetic energy of a non-relativistic particle?

Answer 1

E_k = ½mv²
p = mv , v = p/m

∴ E_k = ½m(p/m)²
E_k = ½m(p²/m²)
E_k = ½(p²/m)
E_k = p²/2m

Question 2

What is the definition and equation of impulse?

Answer 2

Impulse is the rate of change of momentum on an object,
equal to the product of the force applied to the object and the time interval over which it acts

Δp = m(v - u) = FΔt
Impulse (Ns) = Force (N) x Time (s)

Question 3

What is the difference between an elastic and inelastic collision?

Answer 3

Elastic collisions:
Collisions in which kinetic energy is conserved

Inelastic collisions:
Collisions in which kinetic energy is not conserved; instead the kinetic energy is transferred into other forms e.g. heat, sound (as the total energy of a system must always be conserved)

Question 4

What must we do when applying the law of conservation of linear momentum to problems in two-dimensions?

Answer 4

Resolve the vertical and horizontal components and consider the conservation of momentum for each component separately:
The sum of the horizontal components will be equal before and after a collision
The sum of the vertical components will be equal before and after a collision

Question 5

How do you convert from degrees to radians?

Answer 5

θ° x π/180 = θ rad

Question 6

How do you convert from radians to degrees?

Answer 6

θ rad x 180/π = θ°

Question 7

What is angular displacement?

Answer 7

The angle which an object turns through when rotating
Given the symbol θ

θ = S/r, where S is the arc length (m) and r is the radius of the circle (m)

Question 8

What is angular velocity?

Answer 8

Angular velocity (ω, given in rad s^-1) is the rate of change of angular displacement
or
The angle which an object moves through per unit time

Question 9

What is instantaneous velocity?

Answer 9

The object The velocity of an object at a specific point in time