Investigating Terminal Speed (WJEC GCSE Physics: Combined Science)

Aim of the Experiment

•  This experiment aims to investigate how the speed of a falling object depends upon its mass

Variables:

• Independent variable = mass, m
• Dependent variable = speed, v
• Control variables:
  • Surface area
  • Drop height
  • Air temperature / flow
  • Timing device
  • Use the same cake case for each measurement

Equipment List

Equipment	Purpose
Six paper cake cases	To drop in different amounts to give the different masses
Stopwatch	To measure the time to fall
2 metre rulers	To measure the drop height
Clamp stand, boss & clamp	To secure the pointer in place
Pointer	To indicate the drop height
Electronic Balance	To measure the mass of the paper cake cases

• Resolution of measuring equipment:
  • Ruler = ±1 mm
  • Electronic Balance = ±0.1 g
  • Stopwatch = ±0.01 s

Equipment Set Up

Set up the pointer using the clamp stand and time how long it takes the paper cake cases to fall from there to the ground

Method

1. Use the metre ruler to set up the pointer on the clamp stand at a convenient height (around 150 cm) as shown in the diagram. Record this height accurately in the table of results
2. Record the mass of a single cake case on the electronic balance
3. Drop the cake case from a height well above the pointer (about 20 cm) to give enough distance for the cake case to reach terminal velocity by the time it gets to the pointer
4. Repeat this step another four times for one cake case
5. Repeat this whole process for 2, 3, 4, and 5 cake cases in a stack

An Example Table of Results

A suitable table of results must contain all times for all trials for each number of cake cases

A Table of Expected Results

Number of cake cases	Mass of cake cases / g	Distance /m	Time taken for cake cases to fall /s						Terminal Speed / m/s
			Trial 1	Trial 2	Trial 3	Trial 4	Trial 5	Mean
1	0.40	1.50	0.71	0.73	0.70	0.72	0.71	0.71	2.12
2	0.80	1.50	0.62	0.61	0.61	0.63	0.63	0.620	2.42
3	1.20	1.50	0.55	0.56	0.54	0.53	0.55	0.546	2.75
4	1.60	1.50	0.50	0.49	0.51	0.50	0.48	0.496	3.02
5	2.20	1.50	0.46	0.46	0.47	0.45	0.45	0.458	3.28
6	2.60	1.50	0.42	0.43	0.43	0.42	0.42	0.424	3.54

Analysis of Results

• The speed of each cake stack is calculated using the equation:

• Where:
  • Distance is the height of the pointer from the ground (m)
  • Time is the time taken for the cake case to fall from the pointer to the ground (s)

1. Plot a graph of the number of cake cases against terminal speed
2. Draw a line of best fit
3. If the graph is linear (a straight line) with an increasing gradient, then the mass is proportional to the terminal speed

A Graph Showing Mass is Proportional to Terminal Speed

The graph is a straight line with an increasing gradient which shows that as the mass of the cake cases increases then so does the terminal speed

Evaluating the Experiment

Systematic Errors:

• Error in timing accuracy when the cake case passes the pointer and then hits the floor
  • The stopwatch should be pressed when both the cake case and the pointer are at eye level and again when both the cake case and floor are at eye level to avoid parallax error
  • A more accurate way to record the time to fall would be to use an electronic timing system such as light gates or sensors, so the timer starts and stops automatically
• Increasing the resolution of the measuring devices (metre ruler, electronic balance and stopwatch) increases the accuracy of the experiment

Random Errors:

• The precision of the experiment is improved by:
  • Measuring the height from which the cake case is dropped to ensure it is the same (20 cm) every time
  • Increasing the height of the pointer
  • Taking more than five readings for each number of cake cases and calculating the mean
  • Ensuring the experiment is done in a space with no draught or breeze, as this could affect the motion of the falling object
  • Using a ball bearing and an electronic data logger, like a trap door, is a good way to remove the error due to human reaction time for this experiment
• It is assumed that the cake cases reach terminal speed by the time they get to the pointer
  • An investigation should be done to determine whether this is the case

Safety Considerations

• Safety goggles should be worn because the pointer is sharp and at eye level
• Use a G clamp to secure the clamp stand to the bench so it does not topple over and cause injury
• Stand up to carry out this experiment so you do not fall over when looking level with the pointer or the ground
• Place a mat or a soft material below any falling object to cushion its fall