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Chapter 5: Problem 22

Pick up a heavy object such as a backpack or a chair, and stand on a bathroom scale. Shake the object up and down. What do you observe? Interpret your observations in terms of Newton's third law.

Short Answer

Expert verified
The scale reading fluctuates due to the equal and opposite forces in action, consistent with Newton's third law.

Step by step solution

01

Initial Observation

Place a heavy object, like a backpack or chair, on a bathroom scale and observe the initial reading. Take note of the weight displayed.
02

Shake the Object Up and Down

While standing on the scale, begin shaking the object up and down. Observe the changes in the scale's reading as you do so.
03

Observe the Scale Reading

Notice that the reading on the scale fluctuates as you move the object. Pay attention to how the reading increases and decreases with your movements.
04

Interpret Observations

According to Newton's third law, for every action, there is an equal and opposite reaction. When you shake the object upwards, you exert a force on it, and it exerts an equal force downwards on you, causing the scale reading to temporarily increase. Similarly, when bringing the object down, the force exerted on you decreases, lowering the scale reading.

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Key Concepts

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

Force
Force is a fundamental concept in physics that describes a push or pull on an object. This can happen due to an interaction with another object or through the influence of a field, like gravity. In the scenario from the exercise, when you lift the backpack or chair, you are applying a force upwards. This force is the effort needed to overcome the gravitational pull on the object and lift it. You may notice that:
  • The force you apply depends on the object's weight and how quickly you want to move it.
  • Applying more force will accelerate the object faster, as per Newton鈥檚 Second Law: \( F = ma \; (\text{force} = \text{mass} \times \text{acceleration}) \).
When you shake the object up and down, you vary the force applied, which causes changes in the scale reading. Understanding force helps clarify why these readings fluctuate as you interact with the object.
Action and Reaction
Newton's Third Law of Motion is often summarized as "For every action, there is an equal and opposite reaction." This means that whenever you apply a force to an object, the object applies an equal force back on you. In our exercise, when you push the object upward, you are exerting an upward force on the object. Simultaneously, the object pushes down on you with equal force in the opposite direction. This interaction is what causes the readings on the scale to change.
  • When the object is pushed up, your body pushes down on the scale more, leading to a higher reading.
  • Conversely, when you bring the object down, the reaction force decreases, causing a lower reading on the scale.
By understanding action and reaction forces, you can better interpret the relationship and balance between forces involved in everyday activities.
Weight Fluctuation
Weight fluctuation in this context does not refer to permanent changes in weight but rather momentary changes in how forces are balanced and measured. The exercise demonstrates how the reading on a scale can change based on your interaction with an object. These fluctuations occur because the forces exerted during shaking alter the dynamic balance temporarily. For instance:
  • As you shake the object upwards, the additional force increases the effective weight on the scale for a brief moment.
  • Conversely, when moving it down, the reduced force causes a temporary decrease in the reading.
Understanding weight fluctuation through dynamic interactions allows you to appreciate how forces in equilibrium shift and affect perceived weight, which is essential for understanding mechanics and dynamics in physics.

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Most popular questions from this chapter

Ginny has a plan. She is going to ride her sled while her dog Foo pulls her, and she holds on to his leash. However, Ginny hasn't taken physics, so there may be a problem: she may slide right off the sled when Foo starts pulling. (a) Analyze all the forces in which Ginny participates, making a table as in section \(5.3\). (b) Analyze all the forces in which the sled participates. (c) The sled has mass \(m\), and Ginny has mass \(M\). The coefficient of static friction between the sled and the snow is \(\mu_{1}\), and \(\mu_{2}\) is the corresponding quantity for static friction between the sled and her snow pants. Ginny must have a certain minimum mass so that she will not slip off the sled. Find this in terms of the other three variables. (d) Interpreting your equation from part c, under what conditions will there be no physically realistic solution for \(M ?\) Discuss what this means physically.

A little old lady and a pro football player collide head-on. Compare their forces on each other, and compare their accelerations. Explain.

Mountain climbers with masses \(m\) and \(M\) are roped together while crossing a horizontal glacier when a vertical crevasse opens up under the climber with mass \(M\). The climber with mass \(m\) drops down on the snow and tries to stop by digging into the snow with the pick of an ice ax. Alas, this story does not have a happy ending, because this doesn't provide enough friction to stop. Both \(m\) and \(M\) continue accelerating, with \(M\) dropping down into the crevasse and \(m\) being dragged across the snow, slowed only by the kinetic friction with coefficient \(\mu_{k}\) acting between the ax and the snow. There is no significant friction between the rope and the lip of the crevasse. (a) Find the acceleration \(a\). (b) Check the units of your result. (c) Check the dependence of your equation on the variables. That means that for each variable, you should determine what its effect on \(a\) should be physically, and then what your answer from part a says its effect would be mathematically.

The following reasoning leads to an apparent paradox; explain what's wrong with the logic. A baseball player hits a ball. The ball and the bat spend a fraction of a second in contact. During that time they're moving together, so their accelerations must be equal. Newton's third law says that their forces on each other are also equal. But \(a=F / m\), so how can this be, since their masses are unequal? (Note that the paradox isn't resolved by considering the force of the batter's hands on the bat. Not only is this force very small compared to the ball-bat force, but the batter could have just thrown the bat at the ball.)

(a) Compare the mass of a one-liter water bottle on earth, on the moon, and in interstellar space. \(\quad \triangleright\) Solution, p. 553 (b) Do the same for its weight.
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