Mod 5 Advanced Mechanics

Question 1

What is non-unifrom circular motion

Answer 1

Circular motion where the speed of the object changes as it moves around a fixed path

Question 2

What cause non-uniform circular motion

Answer 2

The net force is chaging in magnitude and in direction and hence does not provide required centripetal force (radial force)

Question 3

What two components form net force in non-uniform circular motion

Answer 3

• Centripetal force
• Tangential force

Question 4

Is net force constant in unifrom circular motion

Answer 4

Yes, since net force is centripetal force towards centre of circle

Question 5

When a rocket is launched into a LEO how does its energy change during the journey

Answer 5

The rockets total mechanical energy (E= U + K) increases since work is done on rocket through use of thrusters to burn fuel

Question 6

What 2 equations are equated to find orbital velocity

Answer 6

• F = mv^2/r
• F = GMm/r^2

Question 7

Why don’t AC induction motors need brushes or slip rings

Answer 7

Current in the squirrel cage rotor is induced through three phase AC power supply not directly supplied

Question 8

How do you prove that projectile motion is parabolic

Answer 8

• Through showing that equations of motion are in the form:
• y = ax^2+bx+c

Question 9

What is the general process for solving projectile motion questions

Answer 9

1. What is the value of g (are we on Earth)
2. Do we have u(y)
3. No –> find u(y) first
4. Yes –> Try to solve by analysing vertical motion and use equations of motion
5. if No find time using s(x) = u(x)t

Question 10

What are the forces acting on an object on a banked track

Answer 10

• Normal force to track
• weight force mg directly down
• Acceration towards centre

Question 11

Why are objects able to travel around banked tracks without any sideway force on the wheels by the track

Answer 11

• The normal force is tilted as a result of the banking
• Therefore a component of the normal force towards the centre of rotation exists and acts as a centripetal force required to execute a circular motion hence sideway force is not required

Question 12

How is energy required to transfer to a new orbit calculated

Answer 12

• W = E(orbit)f-E(orbit)i

Question 13

How is total mechanical energy of a satellite in orbit calculated

Answer 13

• E = U + K
• E = -GMm/r + 1/2(mv^2)
• E = -GMm/r + 1/2 m(GM/r)
• E = - 1/2 (GMm/r)

Question 14

What impact does a chnage in mass of a space probe have on its motion

Answer 14

• r^3/T^2 = constant
• independent of mass of orbiting probe
• Any change in mass will not affect ratio hence if altitude remains the same then orbital period remains the same
• Speed is given by v = 2(pi)r/T since r and T do not change orbital velocity remains constant

Question 15

How is escape velocity calculated

Answer 15

• When E = U + K = 0
• Hence 1/2mv^2 - GMm/r = 0
• 1/2v^2 = GM/r
• Vesc = sqrt(2GM/r)

Question 16

What is Kepler’s second law

Answer 16

• Equal time equal areas
• v(A)/v(B) = r(B)/r(A)

Question 17

What is total energy of an orbit when v = v(escape)

Answer 17

0

Question 18

How is weightlessness calculated

Answer 18

• When apparent weight = 0
• or normal force = 0

Question 19

What is coefficient of friction

Answer 19

muN

Question 20

What is process for solving uniform circular motion questions

Answer 20

• Identify forces –> N is perpendicular to object, weight is vertically down, Tension is pulling force along wire, friction is towards centre
• Determine acceleration acceleration always towards centre
• Decompose the forces
• Apply F = ma to find unknowns

Question 21

What is centripetal force acting on a rigid body

Answer 21

• F = mv^2/ r = mrw^2

Question 22

What are the two ways we can take advantage of Earth’s rotation to launch satellites into orbits

Answer 22

• Launch vertically at the equator velocity from axial rotation is greatest
• Launch towards East tangential velocity from Earths rotation is added