## Work

7.1 Work

### Learning Objectives

By the end of this section, you will be able to:

- Represent the work done by any force
- Evaluate the work done for various forces

### Work Done by a Force

In physics, **work** is done on an object when energy is transferred to the object. In other words, work is done when a force acts on something that undergoes a displacement from one position to another.

### Work Done by a Constant Force

The simplest work to evaluate is that done by a force that is constant in magnitude and direction.

**Discuss!**

Consider how you would answer these questions. Then bring this to class for a group discussion.

For each pair of vectors and , is the sign of positive, negative, or zero?

For each of the following situations:

- Draw a before-and-after pictorial diagram
- Draw and label the displacement vector ∆r on your diagram
- Draw a FBD showing all the forces acting on the object
- For each force acting on the object, is the work done by that force +, -, or zero?
- Is the net work done by all the forces +, -, or zero?

(a) An elevator moves upward at a constant speed.

(b) A descending elevator brakes to a halt.

(c) A box slides down a frictionless slope.

(d) A box slides up a frictionless slope.

(e) A ball is thrown straight up. Consider the ball from one microsecond after it leaves your hand until the highest point of its trajectory.

(f) You toss a ball straight up. Consider the ball from the instant you begin moving your hand until you release the ball.

**Practice!**

Practice 7.1.1 |
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A 2.5-kg object falls vertically downward in a viscous medium at a constant speed of 2.5 m/s. How much work is done by the force the viscous medium exerts on the object as it falls 80 cm? |

(a) +2.0 J |

(b) +20 J |

(c) -2.0 J |

(d) -20 J |

(e) +40 J |

Practice 7.1.2 |
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A rock of mass m is twirled on a string in a horizontal plane. The work done by the tension in the string on the rock is… |

(a) + (positive) |

(b) – (negative) |

(c) 0 (zero) |

Practice 7.1.3 |
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A constant force of 12 N in the positive x-direction acts on a 4.0-kg object as it moves from the origin to the point m. How much work is done by the given force during this displacement? |

(a) +60 J |

(b) +84 J |

(c) +72 J |

(d) +48 J |

(e) +57 J |

### Work Done by a Variable Force

**Practice!**

Practice 7.1.4 |
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An object is pushed by a variable force, plotted below as a function of position, x. How much work has the force done on the object when it has moved from x = 0 to x = +6 m? |

(a) 12 J |

(b) 10 J |

(c) 8 J |

(d) 2 J |

(e) 0 J |

Practice 7.1.5 |
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A tiny rocket engine accelerates a toy car over a distance of twelve meters. The thrust of the engine vs. the distance is shown on the graph. Which of these is the best estimate of the work performed by the little engine? (Note: The axes are each calibrated from 0 – 12.) |

(a) 114 J |

(b) 60 J |

(c) 46 J |

(d) 0 J |

### Work Done by the Force of a Spring

**Discuss!**

Consider how you would answer these questions. Then bring this to class for a group discussion.

A spring with spring constant *k* = 350 N/m is initially compressed *x* = 1.90 cm. It is now allowed to relax back to its equilibrium length and then it is stretched an additional 2.10 cm. How much work is done by the spring during this process?