Chapter 6: Problem 2
Using a cable with a tension of 1350 N, a tow truck pulls a car 5.00 km along a horizontal roadway. (a) How much work does the cable do on the car if it pulls horizontally? If it pulls at 35.0\(^\circ\) above the horizontal? (b) How much work does the cable do on the tow truck in both cases of part (a)? (c) How much work does gravity do on the car in part (a)?
Short Answer
Step by step solution
Understand the Work Formula
Calculate Work for Horizontal Pull
Calculate Work for Pull at 35 Degrees
Evaluate Work Done on Tow Truck
Assess Work Done by Gravity
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Work Done by a Force
- \( W = F \cdot d \cdot \cos(\theta) \)
To understand how much work is done, think of the force as needing a specific path. If the force doesn't contribute to the distance in its direction, no work is recorded along that axis. Thus, the angle \( \theta \) plays a key role in determining how effectively the force contributes to performing the work.
Angle of Force Application
As the angle increases away from this direct line, the cosine value decreases, indicating that only a component of the force is doing work in the direction of movement.
For example, when the angle is 35 degrees, the cosine function reduces the effective force, making it less impactful than when fully aligned. Therefore, understanding the angle helps predict how much force contributes to moving an object in a particular direction.
Horizontal and Angled Forces
Angled forces, like one at 35 degrees, have to be broken down into components. The calculation involves using trigonometry to find how much of that force moves the object horizontally and how much might contribute to other effects, like lifting the object somewhat.
- Horizontal forces: Full force acts on movement.
- Angled forces: Effectiveness depends on cosine of the angle.
Gravitational Work
In scenarios like a tow truck pulling a car horizontally, gravity's force is perpendicular to the horizontal motion. This alignment means gravity does no work along the car's path because its displacement occurs without any vertical distance.
Without vertical displacement, gravitational work remains zero, even if the object weighs significantly. This concept simplifies calculations where vertical contributions by forces like gravity are not part of the analysis.
Physics Problem Solving
Here's a simple step-by-step approach to tackle such problems:
- Identify the forces in action and their directions.
- Determine the distance over which these forces are playing a role.
- Assess the angle of each force with respect to direction of movement.