PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
In a classroom investigation, students study how the acceleration of a cart depends on its mass when the cart is pushed forward by an identical battery-powered fan each trial. For every trial the fan exerts the same constant horizontal force on the cart. The students add lead bricks to the cart to vary its total mass and measure the cart’s straight-line acceleration on a low-friction track. The collected data are shown in the table.
Trial | Cart mass (kg) | Measured acceleration (m/s²)
1 | 0.60 | 2.4
2 | 0.80 | 1.8
3 | 1.00 | 1.5
4 | 1.20 | 1.2
5 | 1.40 | 1.0
(a) On axes of your own choosing, sketch a graph that represents acceleration (vertical axis) versus cart mass (horizontal axis) using the data. Describe the overall trend shown by the graph.
(b) Explain how you could transform the variables so that the data would yield a straight-line graph, and identify which physical quantity would correspond to the slope of that straight line.
(c) Using an appropriate linearization of the data, calculate the numerical value and units of the constant force exerted by the fan. Show all work leading to your answer.
(d) Identify one plausible source of systematic error in this experiment and discuss qualitatively how it would affect the calculated value of the fan’s force.