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Chapter 6: Problem 64

You are working out on a rowing machine. Each time youpull the rowing bar (which simulates the oars) toward you, it moves a distance of \(1.2 \mathrm{m}\) in a time of \(1.5 \mathrm{s}\). The readout on the display indicates that the average power you are producing is 82 W. What is the magnitude of the force that you exert on the handle?

Short Answer

Expert verified
The magnitude of the force exerted is 102.5 N.

Step by step solution

01

Understand Power Formula

Power is the rate at which work is done. The formula for power is \( P = \frac{W}{t} \), where \( P \) is power, \( W \) is work, and \( t \) is time. Here, we know \( P = 82 \) watts and \( t = 1.5 \) seconds.
02

Use Work Formula

Work \( W \) is defined as the product of the force \( F \) and the distance \( d \) over which the force is applied, given by \( W = F \cdot d \). We know the distance \( d = 1.2 \) meters.
03

Relate Power to Force

By combining the formulas for power and work, we can express power as \( P = \frac{F \cdot d}{t} \). This allows us to express the force as \( F = \frac{P \cdot t}{d} \).
04

Substitute Values and Solve for Force

Substitute the known values into the formula: \( F = \frac{82 \text{ W} \times 1.5 \text{ s}}{1.2 \text{ m}} \). Carry out the division: \( F = \frac{123}{1.2} = 102.5 \text{ N} \).

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Key Concepts

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

Work-Energy Principle
The Work-Energy Principle is a fundamental concept in physics that helps us understand how forces doing work can transfer energy. In the context of our rowing exercise, every time you pull the bar, you are doing work on the machine. This work is what the machine measures as your power output.
This principle states that the work done on an object is equal to the change in its kinetic energy. For situations where mass and velocity are constant, like with the rowing machine, we focus more on the work done through force and distance. As you pull on the rowing machine's handle, your force over a certain distance becomes the work done, directly linking it to the power displayed on the machine.
Force Calculation
Calculating force involves understanding its relationship with work and power. From the Work-Energy Principle, we know that work is the force applied over a certain distance. But how do we find the force specifically?
  • Since power is given as energy per unit time and relates to work, we start with the power formula: \( P = \frac{W}{t} \).
  • Rewriting work as force times distance gives us: \( W = F \cdot d \).
  • Substituting for work into the power formula, we link power and force: \( P = \frac{F \cdot d}{t} \).
Finally, solving for force, we get: \( F = \frac{P \cdot t}{d} \). By applying known values, we can determine how much force you exert with every pull.
Physics Formulas
Physics is all about finding relationships between different quantities. In this exercise, several key formulas are used:
  • Power Formula: Power is calculated by the amount of work done over time, expressed as \( P = \frac{W}{t} \).
  • Work Formula: Work is the product of force and distance, given by \( W = F \cdot d \). This shows how much effort is needed to move something over a distance.
  • Force Formula: Derived from combining the above, to calculate force we rearrange the power equation to \( F = \frac{P \cdot t}{d} \).
By mastering these equations, students can solve many physics problems, including those involving power, work, and force like in our rowing machine scenario.

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Most popular questions from this chapter

A slingshot fires a pebble from the top of a building at a speed of \(14.0 \mathrm{m} / \mathrm{s} .\) The building is \(31.0 \mathrm{m}\) tall. Ignoring air resistance, find the speed with which the pebble strikes the ground when the pebble is fired (a) horizontally, (b) vertically straight up, and (c) vertically straight down.

The motor of a ski boat generates an average power of \(7.50 \times 10^{4} \mathrm{W}\) when the boat is moving at a constant speed of \(12 \mathrm{m} / \mathrm{s}\) When the boat is pulling a skier at the same speed, the engine must generate an average power of \(8.30 \times 10^{4}\) W. What is the tension in the tow rope that is pulling the skier?

A water-skier is being pulled by a tow rope attached to a boat. As the driver pushes the throttle forward, the skier accelerates. A \(70.3-\mathrm{kg}\) water-skier has an initial speed of \(6.10 \mathrm{m} / \mathrm{s}\). Later, the speed increases to \(11.3 \mathrm{m} / \mathrm{s} .\) Determine the work done by the net external force acting on the skier.

A husband and wife take turns pulling their child in a wagon along a horizontal sidewalk. Each exerts a constant force and pulls the wagon through the same displacement. They do the same amount of work, but the husband's pulling force is directed \(58^{\circ}\) above the horizontal, and the wife's pulling force is directed \(38^{\circ}\) above the horizontal. The husband pulls with a force whose magnitude is \(67 \mathrm{N}\). What is the magnitude of the pulling force exerted by his wife?

A car, starting from rest, accelerates in the \(+x\) direction as in the figure. It has a mass of \(1.10 \times 10^{3} \mathrm{kg}\) and maintains an acceleration of \(+4.60 \mathrm{m} / \mathrm{s}^{2}\) for \(5.00 \mathrm{s}\). Assume that a single horizontal force (not shown) accelerates the vehicle. Determine the average power generated by this force.
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