[Figure 9.1] shows an astronaut in space near to a space station in orbit above the Earth. The total mass of the astronaut and all his equipment is 160 kg. The astronaut is initially at rest relative to the space station but he is then pulled towards the space station by the rope. His acceleration towards the space station is 0.35m/s² for 1.2s.
- (a)(i)Calculate the resultant force that causes a mass of 160kg to accelerate at 0.35 m/s²,[2]
- (a)(ii)the speed at which the astronaut is travelling after 1.2s.[2]
- (b)(i)The resultant force on the astronaut is constant for 1.2s, but then it decreases to zero instantly as the rope becomes slack. On [Figure 9.2], sketch the speed-time graph for the astronaut for the first 3.0s of his motion.[2]
- (b)(ii)Describe how the distance moved by the astronaut during the first 3.0s may be found using the speed-time graph.[2]
- (c)(i) 1.The space station is travelling at a constant speed in a circular orbit around the Earth as shown in [Figure 9.3]. A force acts on the space station to keep it in this orbit. On [Figure 9.3], draw an arrow to show the direction of this force.[1]
- (c)(i) 2.Explain what causes this force.[2]
- (c)(ii)State what is meant by the velocity of an object.[2]
- (c)(iii) 1.State and explain what happens during the orbit to the velocity of the space station,[1]
- (c)(iii) 2.the kinetic energy of the space station.[1]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.
- [C1] (F =) ma or 160 × 0.35
- [A1] 56 N
- [C1] (v = u +) at or 0.35 × 1.2
- [A1] 0.42 m/s
- [B1] straight line of positive gradient from origin to t = 1.2 s
- [B1] horizontal line after t = 1.2 s
- [B1] area mentioned
- [B1] area under the line or convert cm² (of graph paper) to distance or in terms of the scales
- [B1] arrow from space-station towards centre of Earth
- [B1] gravitational field/attraction
- [B1] of Earth
- [M1] I change of displacement
- [A1] per unit time or divided by time
- or II
- [M1] rate of change of distance or distance moved per unit time
- [A1] in specified direction
- [B1] (it/velocity) changes and (because its) direction changes/force perpendicular to velocity
- [B1] (remains) constant and depends on speed/g.p.e. remains constant/(k.e.) is a scalar quantity/speed is constant
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