A laboratory team wishes to determine the mass of an irregularly shaped metal…

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

A laboratory team wishes to determine the mass of an irregularly shaped metal container by measuring how it responds to different known horizontal forces on a nearly friction-free air track. Five trials are performed with the same container; the applied force and resulting acceleration for each trial are listed below.

Trial	Applied Force $F$ (N)	Acceleration $a$ (m·s $^{-2}$ )
1	$0.80 \pm 0.02$	$0.168 \pm 0.005$
2	$1.20 \pm 0.02$	$0.253 \pm 0.005$
3	$1.60 \pm 0.02$	$0.335 \pm 0.006$
4	$2.00 \pm 0.03$	$0.418 \pm 0.006$
5	$2.40 \pm 0.03$	$0.501 \pm 0.007$

Assume any residual air-track friction is negligible. (1) Using an appropriate graphical or numerical method, determine the best estimate for the mass of the container from the data above. Clearly show how you arrive at your estimate. (2) Calculate the percent uncertainty in the mass obtained in part (a). State your result with an appropriate number of significant figures. (3) Discuss two distinct experimental factors, other than instrument resolution, that could contribute to the uncertainty calculated in part (b), and explain qualitatively how each would affect the mass determination. (4) If the same container were tested on a rough surface with kinetic friction present, predict qualitatively how the slope of a force-versus-acceleration graph would change. Justify your prediction based on Newton’s laws.

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