further mechanics spec points

Question 1

Deriving impulse

Answer 1

F = ma
F = m x v/t
F △t = △p

F is a constant force
t is the impact time
p is momentum

Question 2

What is impulse

Answer 2

F △t
Change in momentum

Question 3

CP09: investigate the relationship between the force exerted on an object and its change of momentum

Aims and variables

Answer 3

Determine the change in momentum of a trolley due to a force acting on it (this is known as impulse)

IV - accelerating mass, m
DV - time taken to pass between two light gates, t
CV - overall mass of system (trolley and accelerating masses)
- tilt angle of ramp
- trolley and ramp used
- size of interrupter card

Question 4

CP09: investigate the relationship between the force exerted on an object and its change of momentum
Equipment list

Answer 4

Dynamics trolley
Ramp, slightly tilted
Bench pulley
String
5 slotted masses (10g) and hanger
Light gates and computer or datalogger
Balance
Interrupt card

Question 5

CP09: investigate the relationship between the force exerted on an object and its change of momentum
Method

Answer 5

1. Measure the total mass, M, of the trolley and the five 10g masses using the balance
2. Set up equipment, secure the bench pulley to one end of the runway allowing one end to project over the end of the bench.
   Tilt the ramp slightly. This is to compensate for friction.
   Place mass hanger (without the masses on them) on the floor and move the trolley backwards until the string becomes tight, with the mass on the floor.
   Place the light gates at either end of the ramp. There should be enough space on the ramp to allow the trolley to clear the light gate at the bottom before hitting the pulley
3. Set the start position for the experiment
   Move the trolley further backwards until the mass hanger is closer to the pulley
   Put the five 10g masses on the trolley so that they will not slide off
4. Record the total hanging mass, m, in the results table
5. Release the trolley and start the timing software
   The computer will record the velocity through each gate, and then the time taken for the trolley to travel between them
6. Repeat the readings and calculate the mean time and velocity for this value of m
7. Move one 10g mass from the trolley to the hanger and repeat.
   Repeat until all masses are on hanger

Question 6

CP09: investigate the relationship between the force exerted on an object and its change of momentum
Analysis

Answer 6

p = M(v2-v1)
p = mgt

Combine two equations
M(v2-v1) = mgt

y = mx + c
mt = M/g x (v2-v1) + 0
Plot straight line graph and get gradient

Question 7

CP09: investigate the relationship between the force exerted on an object and its change of momentum
Errors

Answer 7

The interrupt card may be a different width to that recorded in the data logger
Interrupt card may not be of sufficient height to trigger the light gate
Mass of system may not be measured correctly
Trolley may not travel in a straight line
Trolley may hit one of the light gates when passing through

Question 8

CP09: investigate the relationship between the force exerted on an object and its change of momentum
Safety considerations

Answer 8

• stand well away from masses in case they fall on the floor
• soft surface to cushion their fall
• keep liquids away from data logger

Question 9

CP10: use ICT to analyse collisions between small spheres e.g. ball bearings on a table top
Analysis

Answer 9

Use tracker to analyse video clips
Input the mass and diameter of each sphere when prompted
Use the ‘velocity overlay’ feature so that the software can analyse velocities
The tracker software allows for frame-by-frame analysis of the movement of the spheres
Orientate the axes to make the velocity of the moving ball along one of the axes
Record the momentum of each ball as indicated in tracker

Question 10

Elastic collisions

Answer 10

Where both momentum and kinetic energy are conserved

Question 11

Inelastic collisions

Answer 11

Where only momentum is conserved, while some of the KE is converted into other forms and may be larger or smaller after a collision.

If the objects which collide stick together after the collision, then this is an inelastic collision.
An explosion is inelastic as the KE after the explosion is greater than before.

Question 12

Deriving Ek formula

Answer 12

Ek = 1/2 mv^2
p = mv

Ek = 1/2m x p^2/m^2
Ek = p^2/2m

Question 13

Converting from degrees to radians

Answer 13

Multiply by pi/180

Question 14

Converting from radians to degrees

Answer 14

Multiply by 180/pi

Question 15

Angular velocity (w)

Answer 15

Is the angle an object moves through per unit time.

w = v / r

v - linear velocity
r - radius of the circular path its travelling