The velocity-time graph in Fig. 1 shows a plastic shuttlecock released from an indoor viewing gallery. Downwards is taken as the positive direction. Its mas...
Question 1 Report
The velocity-time graph in Fig. 1 shows a plastic shuttlecock released from an indoor viewing gallery. Downwards is taken as the positive direction. Its mass is 0.050 kg. At first, its speed increases, but the graph becomes horizontal after 4.0 s. Air resistance is the only significant upward force. Use g = 10 N/kg.
(a) Which force acts upwards on the shuttlecock? [1]
(b) Describe the change in the shuttlecock's velocity between 0 s and 4.0 s. [2]
(c) Calculate the weight of the shuttlecock. [2]
(d) Explain why the air resistance changes before the shuttlecock reaches terminal velocity. [3]
(e) Calculate the resultant force on the shuttlecock after 4.0 s. [1]
(f) Sketch two force arrows on the shuttlecock when it is moving at terminal velocity. [2]
(g) Explain the energy transfers as the shuttlecock falls through the air. [3]
Answer Details
The graph shows terminal velocity. At terminal velocity, upward air resistance equals downward weight, so resultant force and acceleration are both zero.
- (a) The upward force is air resistance, also called drag. [1]
- (b) The downward velocity increases between 0 s and 4.0 s, but the increase becomes smaller. It then becomes constant at about 5.0 m/s. [2]
- (c) \[W=mg=0.050\ \text{kg}\times10\ \text{N/kg}=0.50\ \text{N}\]Weight = 0.50 N. [2]
- (d) At release the shuttlecock has little or no speed, so air resistance is small. As its speed increases, it collides with more air each second, so air resistance increases. Eventually air resistance equals weight, so resultant force and acceleration become zero. [3]
- (e) After 4.0 s the resultant force is 0 N. [1]
- (f) At terminal velocity, draw equal-sized opposite arrows: weight down and air resistance up. [2]
- (g) The gravitational potential energy store decreases. While speed is increasing, energy is transferred to the shuttlecock's kinetic energy store. Due to air resistance, energy is also transferred to the thermal energy stores of the air and shuttlecock. [3]
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