A student designs an experiment to measure the gravitational field strength at the Earth's surface using a set of slotted masses and a calibrated newton met...
Question 1 Report
A student designs an experiment to measure the gravitational field strength at the Earth's surface using a set of slotted masses and a calibrated newton meter. She hangs increasing masses from the newton meter and records both the mass and the weight reading. Fig. 3.1 shows her apparatus. She hangs five different masses and records the values in a table. She then plots a graph of weight against mass, shown in Fig. 3.2, and measures the gradient.
(a) Using Fig. 3.2, determine the gradient of the line. Show your working. [2]
(b) State what physical quantity the gradient represents. [1]
(c) State the unit of this quantity. [1]
(d) A different student carries out the same experiment on the surface of Mars, where g = 3.7 N/kg. Describe how the graph would differ from Fig. 3.2. [1]
(e) Explain the difference between mass and weight. [2]
(f) State what would happen to the mass and the weight of an object if it were taken from the Earth to deep space, far from any planet or star. [1]
Answer Details
(a) Gradient of the line from Fig. 3.2
Pick two points on the best-fit line. The line passes through the origin (0, 0) and through (0.4, 4.0).
\(\text{gradient} = \dfrac{\Delta W}{\Delta m} = \dfrac{4.0 - 0}{0.4 - 0}\) [1]
\(\text{gradient} = 10\text{ N/kg}\) [1]
(b) Physical quantity represented by the gradient
The gradient of a weight-against-mass graph is the gravitational field strength (g). [1]
(c) Unit of this quantity
N/kg (newtons per kilogram). [1]
(d) How the graph would differ on Mars
On Mars, \(g = 3.7\text{ N/kg}\), which is less than 10 N/kg on Earth. The graph would still be a straight line through the origin, but it would have a smaller gradient (the line would be less steep). [1]
(e) Difference between mass and weight
Mass is the amount of matter in an object. It is measured in kilograms and does not change with location. [1]
Weight is the gravitational force acting on the object (\(W = mg\)). It is measured in newtons and depends on the gravitational field strength at the object's location. [1]
(f) Mass and weight in deep space
Mass stays the same (it is an intrinsic property of the object). Weight becomes approximately zero, because far from any planet or star the gravitational field strength is negligibly small. [1]
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