The Falling Balloon
A student drops a water balloon from a second-floor window, 5.0 m above the ground. The balloon has a mass of 0.50 kg and a volume of 0.50 L. The student observes that the balloon hits the ground with a splash and does not bounce. A friend suggests that if the balloon were filled with air instead of water, it would bounce higher. The student has a stopwatch, a meter stick, and a balance. They also have a slow-motion camera that can record the fall. The student wants to understand the motion of the balloon and the forces involved.
1. Describe the forces acting on the water balloon as it falls, and explain whether the balloon is in free fall. Use the given data to estimate the time it takes to hit the ground, ignoring air resistance.
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The forces acting on the water balloon are gravity (weight) downward and air resistance upward. The weight is W = mg = 0.50 kg × 9.8 m/s² = 4.9 N. The buoyant force from the air is also present but very small: the volume is 0.50 L = 0.00050 m³, so buoyant force = density of air × volume × g ≈ 1.2 kg/m³ × 0.00050 m³ × 9.8 ≈ 0.0059 N, negligible. Air resistance depends on speed and shape; initially it is zero, so the balloon starts in free fall (only gravity). As speed increases, air resistance increases, so acceleration decreases slightly. However, for a 5 m drop, the speed remains low enough that air resistance is small compared to weight. Thus the balloon is approximately in free fall. Ignoring air resistance, time t = sqrt(2h/g) = sqrt(2×5.0/9.8) ≈ 1.0 s. The impact speed would be v = gt ≈ 9.8 m/s.
2. The friend says an air-filled balloon would bounce higher. Evaluate this prediction using ideas about energy and collisions. What would the student need to measure to compare the two balloons fairly?
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The prediction is likely incorrect. When the water balloon hits the ground, its kinetic energy is dissipated in splashing and deforming the water; water is not very elastic, so little energy is stored and returned as bounce. An air-filled balloon would compress on impact, storing elastic energy in the stretched rubber and compressed air, and then rebound, converting some stored energy back to kinetic energy. So an air-filled balloon could bounce, but whether it bounces higher depends on the drop height and the balloon's properties. However, the friend's claim that it would bounce higher than the water balloon is plausible because the water balloon does not bounce at all. To compare fairly, the student should drop both balloons from the same height, with the same mass (or account for mass difference), same volume, and measure the rebound height using the meter stick and slow-motion camera. They should also ensure the ground surface is the same. They could measure the coefficient of restitution for each.