Further Mechanics

Question 1

What is Newton’s 1st law?

Answer 1

When there is no overall resultant force acting on an object, it will either remain stationary or move at a constant velocity

Question 2

What is Newton’s 2nd law?

Answer 2

There is a proportional relationship between the resultant force and acceleration, shown by ΣF = ma

Question 3

What is Newton’s 3rd law?

Answer 3

For every force A exerts on B, B exerts an equal and opposite force on A

Question 4

Show how force can be thought of as rate of change of momentum

Answer 4

F = ma 
a = (v-u)/t 
F = (mv - mu)/t = Δp/Δt

Question 5

What is the principle of conservation of momentum?

Answer 5

Within a closed system, the total momentum in any direction is the same before and after a collision

Question 6

What is an elastic collision?

Answer 6

A collision where KE is conserved

Question 7

What is an inelastic collision?

Answer 7

A collision where KE is not conserved

Question 8

How would a jet engine provide a forward thrust? (With reference to Newton’s laws)

Answer 8

• The jet engine burns fuel and ejects hot gas at high speed out the back of the engine
• The engine provides a force on the gas particles
• Newton’s 3rd law: equal and opposite reaction force of the gas particles on the engine and therefore the plane
• Newton’s 1st law: unbalanced force gives it an acceleration

Question 9

What is impulse?

Answer 9

The force multiplied by the time over which it acts

Question 10

What is a non-relativistic particle?

Answer 10

A particle travelling at a speed lower than the speed of light, so the mass stays constant

Question 11

What is the definition of a radian?

Answer 11

The angle subtended at the centre of the circle by an arc of length equal to the circle’s radius

Question 12

What is meant by centripetal acceleration?

Answer 12

The direction of velocity is constantly changing so we say the object is accelerating. An unbalanced force (weight or tension) provides an acceleration (F = ma, Newton’s 1st law). The acceleration is always directed towards the centre of the circle

Question 13

In a vertical circle, where is tension highest?

Answer 13

At the bottom, where weight acts against centripetal force

Question 14

What provides the centripetal force for a satellite orbiting the Earth?

Answer 14

The gravitational force of the Earth pulling the satellite/its weight

Question 15

What provides the centripetal force for an electron in a hydrogen atom?

Answer 15

The electrostatic attractive force of the positively charged nucleus

Question 16

What provides the centripetal force for a car cornering on a banked road?

Answer 16

The horizontal component of the reaction force of the car on the road

Question 17

What provides the centripetal force for an air craft banking?

Answer 17

The horizontal component of the lift force

Question 18

Practical to investigate the relationship between radius and velocity for a spinning bung

Answer 18

• Attach a bung to a string threaded through a plastic tube with a mass hanger with 100g hanging off the end
• Mark the string every 10cm at the point where it comes out of the tube
• Keep the 0.1m mark in line with the bottom of the tube and spin it around, measuring the time taken for 50 complete orbits
• Calculate the time taken for 1 orbit, then calculate velocity (2πR/T)
• Repeat this until R=60cm
• Plot a graph of v² against R and calculate gradient (F/m)
• Calculate the mass of the bung (v² = FR/m)
• Measure the mass of the bung and calculate % difference

Question 19

What are 2 limitations of the spinning bung practical?

Answer 19

• Human error with timing - minimise this by repeating more times and taking an average
• Friction increases value of calculated force - reduce by using a different material or lubricant

Question 20

For the conical pendulum, what provides the centripetal force?

Answer 20

The horizontal component of tension

Question 21

For the conical pendulum, what keeps the bung in a horizontal circle?

Answer 21

Vertical component of tension is balanced by weight, so it remains horizontal

Question 22

For the conical pendulum, why does tension increase as the speed increases?

Answer 22

At greater speeds, tension increases because greater centripetal force needed at higher speed (mv²/r)
At larger values of θ, vertical component is a smaller proportion of tension but is always still equal to mg (mg = Tcosθ - if θ is larger, T must be larger)

Question 23

If the lift force of a plane remains constant, what else will happen to the plane as it starts to turn in a banked circle?

Answer 23

Plane will start to lose altitude - size of vertical component will decrease so it no longer balances mg

Question 24

How can artificial gravity be created?

Answer 24

Spinning something so that centripetal acceleration is equal to g

Question 25

Why do you feel weightless when a plane spins in a circle, for example?

Answer 25

At the top of a loop, centripetal force provides weight, but there is no reaction force, so pilot would feel weightless
Generally, it is when the reaction force is zero/at the point of being zero that you feel weightless, as it is reaction force pushing against a person which makes you feel you have a weight

Question 26

What is the expression for centripetal force at the top and bottom of a vertical loop?

Answer 26

Ftop = W - Rt
Fbottom = Rb - W