Acceleration of Freefall Using Electromagnets & Light Gates
Aim of the Investigations
- The overall aim of these investigations is to calculate the value of the acceleration due to gravity, g
- The first two experiments both use the method of dropping an object and either timing its fall, or finding the final velocity
- Both use the SUVAT equations to produce a straight line graph
- The third experiment, using the ramp and trolley, is based on the inclined ramp experiment done by Galileo when he proved that all objects fall at the same rate, regardless of weight
Electromagnet Method
Variables
- Independent variable = height, h
- Dependent variable = time, t
- Control variables:
- Same object being dropped
- Same electromagnet and trap door switching system
Apparatus
- Metre rule, ball bearing, electromagnet, electronic timer, trapdoor, plumb line
Apparatus used to measure g using the electromagnet method
- Resolution of measuring equipment:
- Metre ruler = 1 mm
- Timer = 0.01 s
Method
- By using the plumb line to find the vertical drop, position the trap door switch directly underneath the electromagnet.
- Check that the ball bearing triggers both the trap door switch and the timer when it is released.
- When the equipment is set up correctly;
- As the current to the magnet switches off, the ball drops and the timer starts
- When the ball hits the trapdoor, the timer stops
- The reading on the timer indicates the time it takes for the ball to fall a distance, h
- Measure the distance from the bottom of the ball bearing to the trap door switch with a metre ruler and record this distance as height, h
- Increase h (eg. by 5 cm) and repeat the experiment. At least 5 – 10 values for h should be used
- Repeat this method at least 3 times for each value of h and calculate an average t for each
Table of Results
Analysis of Results
- The acceleration is found by using one of the SUVAT equations and rearranging it to create a straight line graph (y = mx + c)
- The known quantities are
-
- Displacement s = h
- Time taken = t
- Initial velocity = u
- Acceleration a = g
- The missing SUVAT value is final velocity, v
- Therefore use
- Replace a with g and s with h and then rearrange to fit the equation of a straight line
(since initial velocity, u = 0)
- The above equation shows that if h is plotted on the y-axis and t2 on the x-axis the graph will produce a straight line with gradient = g
Evaluating the experiment
Systematic Errors:
- Residue magnetism after the electromagnet is switched off may cause t to be recorded as longer than it should be
Random Errors:
- Large uncertainty in h from using a metre rule with a precision of 1 mm
- Parallax error from reading h
- The ball may not fall accurately down the centre of the trap door
- Random errors are reduced through repeating the experiment for each value of h at least 3-5 times and finding an average time, t
Safety Considerations
- The electromagnetic requires current
- Care must be taken to not have any water near it
- To reduce the risk of electrocution, only switch on the current to the electromagnet once everything is set up
- A cushion or a soft surface must be used to catch the ball-bearing so it doesn’t roll off / damage the surface
- The tall clamp stand needs to be attached to a surface with a G clamp to keep it stable
Card and Light Gates Method
Variables
- Independent variable = height, h
- Dependent variable = final velocity, v
- Control variables:
- Same card being dropped
- All other equipment is the same
Apparatus
- Metre rule, clear tube with large enough diameter for card to fall cleanly through it, card, blu-tack, light gate, data logger, plumb line
Method
- Clamp the clear tube vertically using the plumb line as a guide
- Attach the light gate about 20 cm above the bench
- Clamp the metre ruler vertically next to the tube so that the vertical distance from the top of the tube to the light gate can be accurately measured
- Record the distance between the light gate and the top of the tube as height, h
- Cut a piece of card to approximately 10 cm, measure this length precisely and enter it into the data logger as the distance
- Weight the card slightly at one end (a large paperclip or small pieces of blu-tack can be used)
- Hold the card at the top of the tube and release it so that it falls inside the tube
- The data logger will record velocity
- Repeat this measurement from the same height two more times
- Move the light gate up by 5 cm, record the new height, h, and drop the card three more times, recording the velocity each time
- Repeat for five more values of height
Analysis of Results
- The acceleration is found by using one of the SUVAT equations and rearranging it to create a straight line graph (y = mx + c)
- The known quantities are
- Displacement s = h
- Initial velocity = u
- Final velocity = v
- Acceleration a = g
- The missing SUVAT value is time, t
- Therefore use
- Replace a with g and s with h and then rearrange to fit the equation of a straight line
(since initial velocity, u = 0)
- The above equation shows that if v2 is plotted on the y-axis and 2h on the x-axis the graph will produce a straight line with gradient = g
Evaluating the experiment
Systematic Errors:
- The metre ruler needs to be fixed vertically and close to the tube
- All height measurements are taken at eye level to avoid parallax errors
Random Errors:
- Large uncertainty in h from using a metre rule with a precision of 1 mm
- Parallax error from reading h
- The card may fall against the sides of the tube, slowing it down
- Dropping the card from the top of the tube can introduce parallax errors
- Random errors are reduced through repeating the experiment for each value of h at least 3-5 times and finding an average time, t
Safety Considerations
- The tall clamp stand needs to be attached to a surface with a G clamp to keep it stable