The diagram shows an astronaut using a tool kit outside a space station. The astronaut and suit have mass 90 kg. Initially, the astronaut and a 5.0 kg tool ...
Question 1 Report
The diagram shows an astronaut using a tool kit outside a space station. The astronaut and suit have mass 90 kg. Initially, the astronaut and a 5.0 kg tool kit are stationary relative to the station. The astronaut throws the kit at 6.0 m/s to the right. There is no significant external horizontal force on the astronaut-tool-kit system. Engineers use this example to show why an astronaut must hold a handrail before throwing an object. The diagram shows the direction of the tool kit after release.
(a) What is the momentum of the tool kit after it is thrown? [2]
(b) What is the total momentum of the astronaut-tool-kit system before the throw? [1]
(c) Which direction does the astronaut move after the throw? [1]
(d) What is the astronaut's speed after the throw? [1]
Table 1 contains results from a fairground bumper-car trial. Car P and car Q approach each other on a smooth floor. Their rubber buffers make them stick together after impact. The mass of car P with its driver is 180 kg and the mass of car Q with its driver is 220 kg. Directions are included because velocity, unlike speed, has direction. Take movement to the right as positive. The operator uses the results to check that the cars will move slowly enough after a collision near the loading area.
| car | mass / kg | velocity before collision / m/s |
|---|---|---|
| P | 180 | +2.0 |
| Q | 220 | -1.0 |
(a) What is the momentum of car P before the collision? [2]
(b) What is the total momentum of both cars before collision? [1]
(c) Which direction do the joined cars move after collision? [1]
(d) What is their velocity after collision? [1]
Answer Details
Astronaut and tool kit
- (a) \[p=mv=5.0\times6.0=30\text{ kg m/s}\]30 kg m/s to the right. [2]
- (b) Before the throw both objects are stationary, so total momentum is 0 kg m/s. [1]
- (c) To keep total momentum zero, the astronaut moves to the left, opposite to the tool kit. [1]
- (d) The astronaut has momentum \(30\text{ kg m/s}\) to the left, so:
\[v=\frac{30}{90}=0.33\text{ m/s}\]0.33 m/s to the left. [1]
Bumper cars
- (a) \[p_P=180\times2.0=+360\text{ kg m/s}\]\(+360\text{ kg m/s}\). [2]
- (b) \[p_{total}=+360+(220\times-1.0)=+140\text{ kg m/s}\]\(+140\text{ kg m/s}\). [1]
- (c) The positive total momentum means the joined cars move to the right. [1]
- (d) \[v=\frac{140}{180+220}=0.35\text{ m/s}\]0.35 m/s to the right. [1]
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