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Chapter 7: Problem 60

A wagon is rolling forward on level ground. Friction is negligible. The person sitting in the wagon throws a rock. Does the momentum of the wagon increase, decrease, or remain the same (a) when the rock is thrown directly forward and (b) when the rock is thrown directly backward? (c) In which case does the wagon have the greater speed after the rock is thrown?

Short Answer

Expert verified
The wagon's momentum decreases when the rock is thrown forward and increases when thrown backward. The wagon has greater speed when the rock is thrown backward.

Step by step solution

01

Understanding Momentum Conservation

Momentum is a conserved quantity in an isolated system where no external forces are acting. Since friction is negligible, we can consider the wagon and rock as an isolated system.
02

Momentum Result of Throwing Forward

(a) When the rock is thrown directly forward, its momentum gained in the forward direction must be balanced by an equal momentum in the backward direction of the wagon to conserve total system momentum.
03

Momentum Result of Throwing Backward

(b) When the rock is thrown directly backward, the momentum of the rock gained in the backward direction is countered by the wagon gaining the equivalent momentum in the forward direction to conserve the system's momentum.
04

Speed and Momentum Conservation

In both scenarios, when the rock is thrown, the system's momentum must be conserved. Therefore, the gain or loss of momentum of the rock must be equal and opposite to that gained or lost by the wagon.
05

Determining the Wagon's Speed Change

(c) The wagon will have a greater speed when the rock is thrown backward. In this case, the rock's backward motion adds to the forward speed of the wagon due to the conservation of momentum.

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Key Concepts

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

Isolated Systems
In physics, an isolated system refers to a group of objects that does not exchange matter or energy with its surroundings. This means no external forces are acting upon the system.
For the wagon and rock scenario, we consider them as an isolated system because friction is negligible.
  • Frictional forces are assumed to be non-significant, meaning they won't interfere with the momentum of the system.
  • Because no external forces, like friction or air resistance, affect the system, the total momentum should remain constant.
By ignoring external factors, we can correctly apply the principle of conservation of momentum.
Friction
Friction is a force that opposes motion between two surfaces that are in contact. Usually, it acts against the direction of motion, reducing speed and altering momentum. However, in this exercise, friction is described as negligible. This means it does not play a role in the wagon and rock's motion analysis.
  • Without friction, we can more easily observe the law of conservation of momentum.
  • The lack of friction ensures that, once the rock is thrown, the momentum calculations are unaffected by this otherwise significant external force.
Thus, the process simplifies to observing the motion resulting from the forces within the system itself.
Momentum
Momentum is one of the fundamental concepts in physics, defined as the product of an object's mass and its velocity. It is given by the equation: \( p = mv \) where \( p \) is momentum, \( m \) is mass, and \( v \) is velocity.The principle of momentum conservation states that, within an isolated system, the total momentum remains constant, provided no external forces act on it.
  • For the wagon scenario, the initial momentum includes both the wagon and the rock moving together.
  • When the rock is thrown, momentum is divided between the rock and the wagon, each acquiring a new velocity that still sums to the original total momentum.
In simple terms, any momentum gained by an object within the system is lost by another object, keeping the overall system momentum constant.
Speed
Speed refers to how fast an object moves, and it is a scalar quantity that only has magnitude, not direction. After the rock is thrown, the speed of the wagon depends on the direction in which the rock is thrown.

In physics problems, changes in speed arise from changes in momentum:
  • Throwing the rock forward results in the wagon moving backward slightly, thereby reducing its speed when considering its forward motion context.
  • Conversely, throwing the rock backward increases the wagon's forward speed significantly, as the backward momentum of the rock imparts an opposite, enhancing effect on the wagon's forward motion.
Therefore, in this scenario, the wagon achieves a greater forward speed when the rock is thrown backward due to momentum conservation, demonstrating how speed and momentum are intricately linked.

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Most popular questions from this chapter

The lead female character in the movie Diamonds Are Forever is standing at the edge of an offshore oil rig. As she fires a gun, she is driven back over the edge and into the sea. Suppose the mass of a bullet is \(0.010 \mathrm{~kg}\) and its velocity is \(+720 \mathrm{~m} / \mathrm{s}\). Her mass (including the gun) is \(51 \mathrm{~kg}\). (a) What recoil velocity does she acquire in response to a single shot from a stationary position, assuming that no external force keeps her in place? (b) Under the same assumption, what would be her recoil velocity if, instead, she shoots a blank cartridge that ejects a mass of \(5.0 \times 10^{-4} \mathrm{~kg}\) at a velocity of \(+720 \mathrm{~m} / \mathrm{s} ?\)

A space probe is traveling in outer space with a momentum that has a magnitude of \(7.5 \times 10^{7} \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}\). A retrorocket is fired to slow down the probe. It applies a force to the probe that has a magnitude of \(2.0 \times 10^{6} \mathrm{~N}\) and a direction opposite to the probe's motion. It fires for a period of 12 s. Determine the momentum of the probe after the retrorocket ceases to fire.

A mine car (mass \(=440 \mathrm{~kg}\) ) rolls at a speed of \(0.50 \mathrm{~m} / \mathrm{s}\) on a horizontal track, as the drawing shows. A \(150-\mathrm{kg}\) chunk of coal has a speed of \(0.80 \mathrm{~m} / \mathrm{s}\) when it leaves the chute. Determine the velocity of the car/coal system after the coal has come to rest in the car.

ssm Starting with an initial speed of \(5.00 \mathrm{~m} / \mathrm{s}\) at a height of \(0.300 \mathrm{~m}\), a \(1.50-\mathrm{kg}\) ball swings downward and strikes a \(4.60\) -kg ball that is at rest, as the drawing shows. (a) Using the principle of conservation of mechanical energy, find the speed of the \(1.50-\mathrm{kg}\) ball just before impact. (b) Assuming that the collision is elastic, find the velocities (magnitude and direction) of both balls just after the collision. (c) How high does each ball swing after the collision, ignoring air resistance?

ssm A golf ball bounces down a flight of steel stairs, striking several steps on the way down, but never hitting the edge of a step. The ball starts at the top step with a vertical velocity component of zero. If all the collisions with the stairs are elastic, and if the vertical height of the staircase is \(3.00 \mathrm{~m}\), determine the bounce height when the ball reaches the bottom of the stairs. Neglect air resistance.
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