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Chapter 13: Problem 12

You know from experience that if a car you are riding in suddenly stops, heavy objects in the rear of the car move toward the front. Why does a helium-filled balloon in such a situation move, instead, toward the rear of the car?

Short Answer

Expert verified
Answer: When a car suddenly stops, a helium-filled balloon moves toward the rear of the car due to the combined effects of buoyancy and the difference in air pressure inside the car. The air pressure in the front of the car momentarily increases, while the pressure at the back decreases. Since the helium-filled balloon is buoyant and seeks the least dense area (lowest pressure), it moves towards the back of the car.

Step by step solution

01

Understand the situation

When a car suddenly stops, objects inside the car tend to move forward due to inertia - an object in motion tends to stay in motion unless acted upon by an external force (Newton's First law). Here, the car and the objects inside it were initially in motion, and the braking force stops the car, but the objects inside the car still possess inertia and tend to move forward.
02

Introduce the helium-filled balloon

Now, let's consider a helium-filled balloon inside the car when the car stops suddenly. Helium is less dense than air, which is why a helium-filled balloon floats. This is due to buoyancy - the balloon experiences an upward force because it displaces a volume of air that weighs more than the helium inside the balloon.
03

Understand air pressure inside the car

When the car stops suddenly, the air inside the car moves forward due to inertia. This causes the air pressure at the front of the car to momentarily increase and the pressure at the back of the car to decrease.
04

Relate air pressure to the motion of the balloon

As the air pressure in the front of the car increases and the air pressure at the back decreases, the helium-filled balloon experiences a difference in pressure between the front and the rear. Since the balloon is buoyant and wants to be in the least dense area (lowest pressure), it moves to the back of the car.
05

Conclusion

The helium-filled balloon moves toward the rear of the car when the car suddenly stops because of the combined effects of buoyancy and the difference in air pressure inside the car. While most objects move forward due to inertia, the helium-filled balloon behaves differently because of these additional forces acting on it.

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Most popular questions from this chapter

You have two identical silver spheres and two unknown fluids, \(A\) and \(B\). You place one sphere in fluid \(A\), and it sinks; you place the other sphere in fluid \(\mathrm{B}\), and it floats. What can you conclude about the buoyant force of fluid \(\mathrm{A}\) versus that of fluid \(\mathrm{B} ?\)

Brass weights are used to weigh an aluminum object on an analytical balance. The weighing is done one time in dry air and another time in humid air, with a water vapor pressure of \(P_{\mathrm{h}}=2.00 \cdot 10^{3} \mathrm{~Pa}\). The total atmospheric pressure \(\left(P=1.00 \cdot 10^{5} \mathrm{~Pa}\right)\) and the temperature \(\left(T=20.0^{\circ} \mathrm{C}\right)\) are the same in both cases. What should the mass of the object be to be able to notice a difference in the balance readings, provided the balance's sensitivity is \(m_{0}=0.100 \mathrm{mg}\) ? (The density of aluminum is \(\rho_{\mathrm{A}}=2.70 \cdot 10^{3} \mathrm{~kg} / \mathrm{m}^{3} ;\) the density of brass is \(\left.\rho_{\mathrm{B}}=8.50 \cdot 10^{3} \mathrm{~kg} / \mathrm{m}^{3}\right)\)

A basketball of circumference \(75.5 \mathrm{~cm}\) and mass \(598 \mathrm{~g}\) is forced to the bottom of a swimming pool and then released. After initially accelerating upward, it rises at a constant velocity, a) Calculate the buoyant force on the basketball. b) Calculate the drag force the basketball experiences while it is moving upward at constant velocity.

Calculate the ratio of the lifting powers of helium (He) gas and hydrogen (H \(_{2}\) ) gas under identical circumstances. Assume that the molar mass of air is \(29.5 \mathrm{~g} / \mathrm{mol}\).

A very large balloon with mass \(M=10.0 \mathrm{~kg}\) is inflated to a volume of \(20.0 \mathrm{~m}^{3}\) using a gas of density \(\rho_{\text {eas }}=\) \(0.20 \mathrm{~kg} / \mathrm{m}^{3}\). What is the maximum mass \(m\) that can be tied to the balloon using a \(2.00 \mathrm{~kg}\) piece of rope without the balloon falling to the ground? (Assume that the density of air is \(1.30 \mathrm{~kg} / \mathrm{m}^{3}\) and that the volume of the gas is equal to the volume of the inflated balloon).
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