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Chapter 4: Problem 25

When I cook rice, some of the dry grains always stick to the measuring cup. To get them out, I turn the measuring cup upside-down and hit the "roof" with my hand so that the grains come off of the "ceiling." (a) Explain why static friction is irrelevant here. (b) Explain why gravity is negligible. (c) Explain why hitting the cup works, and why its success depends on hitting the cup hard enough.

Short Answer

Expert verified
Static friction doesn't apply since grains detach due to the hit; gravity is too weak to dislodge grains on its own; hitting the cup works by providing a sudden force strong enough to release the grains.

Step by step solution

01

Understanding the Problem

We need to understand why certain forces don't play a role in getting rice grains out of an upside-down measuring cup, and why hitting the cup effectively releases the grains.
02

Role of Static Friction

Static friction is the force that prevents stationary objects from moving. In the case of rice grains stuck to the 'ceiling' of the cup, hitting the cup overcomes the force holding them in place. The dynamic force of hitting creates a downward force on the grains, making static friction irrelevant since the grains have already detached due to the hit.
03

Negligibility of Gravity

Even though gravity is always acting on the rice grains, its force is too weak to overcome the adhesion forces that hold the grains to the cup when the cup is upside-down. Thus, in the initial situation, gravity is negligible until the grains are loose enough to fall.
04

Effectiveness of Hitting the Cup

Hitting the cup creates a sudden force that overcomes the forces holding the rice grains to the surface of the cup, replacing the necessary static friction to keep the grains fixed. The sudden jolt from hitting the cup provides enough force to separate the grains, much stronger than the slow pull of gravity would be alone.
05

Dependence on Force Intensity

For the grains to come off, the hit needs to be hard enough to overcome the adhesion and any residual static friction. A gentle tap might not provide enough force, whereas a stronger hit can exceed the threshold needed to dislodge the grains.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Static Friction
Static friction is what keeps an object at rest when a force tries to move it. However, when it comes to the rice grains sticking to the top of a measuring cup, static friction becomes less important once you introduce higher forces. In this scenario, the grains are not heavily gripped by static friction once you flip the cup and hit it. Instead, the force from the hit effectively disconnects them from the surface. The hit generates enough motion to surpass static friction's holding capability, allowing the grains to detach and fall.
Adhesion Forces
Adhesion forces are like invisible "glue" keeping different materials together. These forces cause the rice grains to stick to the measuring cup's surface. When the cup is flipped upside down, the grip of adhesion forces holds the rice grains longer than gravity can pull them down. It's the primary reason why grains remain stuck until more force is applied. Helping to release the rice involves applying a more significant force鈥攍ike hitting the cup鈥攚hich breaks the adhesion bond. Without such an impact, the grain's adhesion to the cup would continue to defy gravity.
Gravity
Gravity pulls objects towards the Earth, and while it is always at play, it's often subtle when fighting against other forces like adhesion. In this exercise, gravity alone isn't strong enough to free the rice grains from the cup. The grains' weight is minor, and thus, gravity's pull is weak in comparison to the adhesion. For gravity to work effectively here, the adhesion force has to be reduced or counteracted by another force, such as when the cup is hit hard enough to dislodge the grains. Until then, gravity remains a silent but insufficient partner.
Force and Motion
Force and motion are at the heart of why hitting the cup works to free the grains. When you hit the cup, you're applying a dynamic force鈥攁 force in motion鈥攖hat shifts the equilibrium. This is unlike static friction, which holds still objects. The sudden force from hitting the cup offsets the adhesion forces that keep the grains stuck. If the hit is powerful enough, it provides the necessary change in motion to break the rice grains' hold and lets them fall due to gravity. Adequate force intensifies the motion effect, ensuring successful release.

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Most popular questions from this chapter

A rocket ejects exhaust with an exhaust velocity \(u\). The rate at which the exhaust mass is used (mass per unit time) is \(b\). We assume that the rocket accelerates in a straight line starting from rest, and that no external forces act on it. Let the rocket's initial mass (fuel plus the body and payload) be \(m_{i}\), and \(m_{f}\) be its final mass, after all the fuel is used up. (a) Find the rocket's final velocity, \(v\), in terms of \(u, m_{i}\), and \(m_{f} .\) Neglect the effects of special relativity. (b) A typical exhaust velocity for chemical rocket engines is \(4000 \mathrm{~m} / \mathrm{s}\). Estimate the initial mass of a rocket that could accelerate a one-ton payload to \(10 \%\) of the speed of light, and show that this design won't work. (For the sake of the estimate, ignore the mass of the fuel tanks. The speed is fairly small compared to \(c\), so it's not an unreasonable approximation to ignore relativity.) (answer check available at lightandmatter.com)

A bird is initially flying horizontally east at \(21.1 \mathrm{~m} / \mathrm{s}\), but one second later it has changed direction so that it is flying horizontally and \(7^{\circ}\) north of east, at the same speed. What are the magnitude and direction of its acceleration vector during that one second time interval? (Assume its acceleration was roughly constant.) (answer check available at lightandmatter.com)

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A bullet leaves the barrel of a gun with a kinetic energy of \(90 \mathrm{~J}\). The gun barrel is \(50 \mathrm{~cm}\) long. The gun has a mass of \(4 \mathrm{~kg}\), the bullet \(10 \mathrm{~g}\). (a) Find the bullet's final velocity. (answer check available at lightandmatter.com) (b) Find the bullet's final momentum. (answer check available at lightandmatter.com) (c) Find the momentum of the recoiling gun. (d) Find the kinetic energy of the recoiling gun, and explain why the recoiling gun does not kill the shooter. (answer check available at lightandmatter.com)

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