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Small water drops leave a tap with zero velocity at intervals of 0.20 s - AQA - A-Level Physics - Question 21 - 2020 - Paper 1
Question 21
Small water drops leave a tap with zero velocity at intervals of 0.20 s. They then fall freely 0.80 m to reach a horizontal surface. How far has a drop fallen when ... show full transcript
Worked Solution & Example Answer:Small water drops leave a tap with zero velocity at intervals of 0.20 s - AQA - A-Level Physics - Question 21 - 2020 - Paper 1
Step 1
Calculate the time taken for the drop to hit the surface
Answer
Using the formula for free fall, we can calculate the time taken for the drop to fall 0.80 m:
d = rac{1}{2} g t^2
where:
- is the distance fallen (0.80 m)
- is the acceleration due to gravity (approximately 9.81 m/s²)
- is the time in seconds.
Rearranging for , we get:
t = ext{sqrt} rac{2d}{g} = ext{sqrt} rac{2 imes 0.80}{9.81} \approx 0.40 ext{ s}
Step 2
Determine the distance fallen by subsequent drops
Answer
Since the drops are released every 0.20 s, there will be multiple drops in the time taken for the first drop to hit the surface:
-
First drop: Falls for 0.40 s Using the formula: d_1 = rac{1}{2} g t^2 = rac{1}{2} imes 9.81 imes (0.40)^2 = 0.78 ext{ m}
Correction for time intervals: The previous drop hits the surface after that time, so for 0.20 s time interval: 2. Second drop: Falls for 0.20 s d_2 = rac{1}{2} g (0.20)^2 = rac{1}{2} imes 9.81 imes (0.20)^2 \approx 0.20 ext{ m}
Therefore, the drop has fallen 0.20 m when the previous drop hits the surface.