Further Mechanics

Question 1

What is the law of conservation of linear momentum?

Answer 1

The total momentum of two objects before they collide/explode equals the total momentum of the two objects after they collide/explode providing no external forces act.

Question 2

Distinguish between a collision and an explosion.

Answer 2

Collisions – two objects colliding together (they could stick together or rebound).

Explosion – two objects moving apart.

Question 3

How would you need to modify the calculation of momentum before and after a collision if it is in 2 dimension?

Answer 3

Momentum would need to be resolved either horizontally/vertically or parallel/perpendicular to the line of impact - whatever is easiest.

Then, the parallel components of momentum before = parallel components of momentum afterwards etc

Question 4

Rewrite Newton’s 2nd law in terms of momentum,

Answer 4

The size of the resultant force is proportional to the rate of change of momentum, F = Δp / Δt

Question 5

What is impulse? What would a large/small value of impulse tell you?

Answer 5

Impulse is a vector quantity defined as the product of the force acting on a body and the time that the force acts.

Impulse is also the change of momentum (Δp)

Impulse is directly proportional to force, so a high impulse means a high force is exerted.

Question 6

What are the possible units for impulse?

Answer 6

Ns (from F x t)

kg ms^-1 (from Δp)

Question 7

What could you find from a force-time graph for a collision?

Answer 7

Area under the graph, would give the impulse of the collision/explosion (ie Ft or change of momentum).

Question 8

What is the difference between an elastic and an inelastic collision?

Answer 8

Elastic: both momentum and kinetic energy are conserved

Inelastic: only momentum is conserved; the kinetic energy is not conserved as it is usually converted into thermal energy somewhere

Question 9

Derive the kinetic energy equation in terms of momentum.

Answer 9

Ek = ½mmv2 and p = mv

Ek = ½pv

v = p/m Ek = p^2/2m

Question 10

How can you convert between radians and degrees?

Answer 10

90 = 1/2π
180 = π
270 = 3/2π
360 = 2π

Question 11

How can linear speed/linear velocity by calculated?

Answer 11

v = s / t

v = 2πr / T

v = 2πfr

Question 12

How can angular speed/angular velocity be calculated?

Answer 12

ω = θ / t

ω = 2π / T

ω = 2π

Question 13

How are linear and angular speed/velocity linked?

Answer 13

v = ωr

Question 14

Why is no work done when something is moving in a circle?

Answer 14

W = Fd (where the direction of the force is the same as the direction of movement).

The resultant force is towards the centre of the circle. There is no movement in the direction of the resultant force, therefore no work is done.

Question 15

What direction does the centripetal force at?

Answer 15

Towards the centre of a circle.

Question 16

Why is “centripetal force” not drawn on free-body force diagrams?

Answer 16

It is not a new type of a force. Centripetal force is produced by the usual named forces that act on objects.

Question 17

What causes the centripetal force that keeps a planet in orbit?

Answer 17

Gravitational force (of attraction).

Question 18

What causes the centripetal force that keeps an electron moving around a nucleus?

Answer 18

Electrostatic force (of attraction).

Question 19

What causes the centripetal force for a car going round a circular track, or an ice skater skating in a circle, or a mass stuck on a turntable?

Answer 19

Friction.

Question 20

When something is moving in a vertical circle, what are the forces at 0, 90, 180 and 270 degrees?

Answer 20

At 0 and 180, the vertical component of force is “mg” down. The horizontal component of force is “T = mv^2 / r”.

At 90, there are only vertical components of forces, “mg” down and “T = mv^2 / r - mg” down.

At 270, there are only vertical components of forces too, “mg” down and “T = mv^2 / r + mg” up.

Question 21

What happens if the string being swung in a vertical circle breaks?

Answer 21

The bung will move off at a tangent.

Question 22

What other areas of physics can circular motion be linked to?

Answer 22

Magnetic, electric, gravitational forces (equating mv2/r with any of these). Simple harmonic motion. Particle accelerators.

Question 23

Explain the “CPAC 9: Investigate the relationship between the force exerted on an object and the change of momentum.” experiment.

Answer 23

1) Set up an air track onto a desk and at the end of the desk at the end of the air track, clamp a pulley. Place a trolley onto the air track, attached to a string that hangs over the pulley and is connected to a hanging mass. Put two light gates over the air track at a set distance with enough height that the trolly can pass through and be detected. Connect these light gates to a data logger and computer.

2) Make sure the total mass stays constant. The total mass of the system is equal to the sum of the mass on the trolley and the hanging mass.

3) Hold the trolley at one end of the air track and then release it. The hanging mass will fall, pulling the trolley along the air track.

4) Use the data logger and computer to find the velocity of the trolley at each light gate. From this, calculate the change in momentum of the system “Δp(system) = m(system)Δv” where Δv is the change in velocity between the light gates and since the change of velocity of the trolley is equal to the change in velocity of the hanging mass because the string doesn’t stretch. So the change in the velocity of the system = Δv.

5) You can also use the data logger to find the time taken for the trolley to travel between the two light gates, Δt. Using Δt and your value for the change of momentum of the system, you can find the rate of change of momentum of the system, “Δp(system) / Δt”.

6) Repeat this three times to find an average value of “Δp(system) / Δt”.

7) The force acting on the system is equal to the weight of the handing mass, F = Mg.

8) Repeat each experiment for varying masses on the end of the string, each time you remove a mass from the handing mass, place it on the trolley, so that the mass of the system remains constant. Make sure you measure the hanging mass each time to find the value of F.

9) Plot a graph of the force acting on the system, F, against rate of change of momentum of the system.

10) The graph will be a straight line, showing that “F = Δp(system) / Δt”.

Question 24

Explain the “CPAC 10: Use ICT to analyse collisions between small spheres, e.g. ball bearings on a table top.” experiment.

Answer 24

1) Weigh the two ball bearings, with a mass balance, and note down their masses.

2) On a level table top, position two metre rulers at right angles to each other. Put one of the ball bearings on the table and position a video camera above the table.

3) Start the video camera recording, then roll the second ball bearing towards the stationary ball bearing so that they collide.

4) When both ball bearings have come to rest, stop the video recording and use video analysis software to study the collision.

5) If you know the time between each frame of the video, you can work out how many frames there are in each 0.1s.

6) Go through frame by frame and use the rulers to find the distance travelled by each ball bearing in the horizontal and vertical directions every 0.1s. Then you can use Pythagoras to find the magnitude of each ball’s velocity immediately before and immediately after the collision, and trigonometry to find the directions of the velocity.

7) You can show that momentum is conserved by calculating the total momentum before the collision and the total momentum after the collision.