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Chapter 6: Problem 15

A girl of mass \(49.0 \mathrm{~kg}\) is on a swing, which has a mass of \(1.0 \mathrm{~kg} .\) Suppose you pull her back until her center of mass is \(2.0 \mathrm{~m}\) above the ground. Then you let her \(\mathrm{go},\) and she swings out and returns to the same point. Are all forces acting on the girl and swing conservative?

Short Answer

Expert verified
Answer: Yes, all the forces acting on the girl and the swing are conservative. The gravitational force is conservative, and the tension force does no work on the girl and the swing.

Step by step solution

01

Consider the gravitational force

The gravitational force is a conservative force. This is because the work done by the gravitational force on an object only depends on the object's initial and final heights, not the path taken. In this problem, the girl and swing move from an initial height of 2.0 meters to a final height of 2.0 meters, so the work done by the gravitational force is the same regardless of their path.
02

Consider the tension force

The tension force is the force exerted by the swing's rope on the girl and the swing as they move. This force always acts perpendicular to the path of the girl and the swing. Since the work done by a force is the product of the force and the distance moved along the path, and the angle between the force and the path, the work done by the tension force is zero (0 J) for any path taken by the girl and the swing since the angle between the tension force and the path is always 90 degrees.
03

Determine if all forces are conservative

Since the gravitational force is conservative and the tension force does no work on the girl and the swing, we can conclude that all forces acting on the girl and the swing are conservative.

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Most popular questions from this chapter

A father exerts a \(2.40 \cdot 10^{2} \mathrm{~N}\) force to pull a sled with his daughter on it (combined mass of \(85.0 \mathrm{~kg}\) ) across a horizontal surface. The rope with which he pulls the sled makes an angle of \(20.0^{\circ}\) with the horizontal. The coefficient of kinetic friction is \(0.200,\) and the sled moves a distance of \(8.00 \mathrm{~m}\). Find a) the work done by the father, b) the work done by the friction force, and c) the total work done by all the forces.

One end of a rubber band is tied down and you pull on the other end to trace a complicated closed trajectory. If you were to measure the elastic force \(F\) at every point and took its scalar product with the local displacements, \(\vec{F} \cdot \Delta \vec{r},\) and then summed all of these, what would you get?

A spring with a spring constant of \(500 . \mathrm{N} / \mathrm{m}\) is used to propel a 0.500 -kg mass up an inclined plane. The spring is compressed \(30.0 \mathrm{~cm}\) from its equilibrium position and launches the mass from rest across a horizontal surface and onto the plane. The plane has a length of \(4.00 \mathrm{~m}\) and is inclined at \(30.0^{\circ} .\) Both the plane and the horizontal surface have a coefficient of kinetic friction with the mass of \(0.350 .\) When the spring is compressed, the mass is \(1.50 \mathrm{~m}\) from the bottom of the plane. a) What is the speed of the mass as it reaches the bottom of the plane? b) What is the speed of the mass as it reaches the top of the plane? c) What is the total work done by friction from the beginning to the end of the mass's motion?

A package is dropped on a horizontal conveyor belt. The mass of the package is \(m,\) the speed of the conveyor belt is \(v\), and the coefficient of kinetic friction between the package and the belt is \(\mu_{\mathrm{k}}\) a) How long does it take for the package to stop sliding on the belt? b) What is the package's displacement during this time? c) What is the energy dissipated by friction? d) What is the total work supplied by the system?

A 70.0 -kg skier moving horizontally at \(4.50 \mathrm{~m} / \mathrm{s}\) encounters a \(20.0^{\circ}\) incline. a) How far up the incline will the skier move before she momentarily stops, ignoring friction? b) How far up the incline will the skier move if the coefficient of kinetic friction between the skies and snow is \(0.100 ?\)
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