7.1 Work

Can kinetic friction ever be a constant force for all paths?

Can Earth’s gravity ever be a constant force for all paths?

Find the work done by the same force in the example over a cubic path, $y = \left(0.25 \text{m}^{−\text{2}}\right) x^{3}$, between the same points $A = \left(0 , 0\right)$ and $B = \left(2 \text{m}, 2 \text{m}\right) .$

The spring in the example is compressed 6 cm from its equilibrium length. (a) Does the spring force do positive or negative work and (b) what is the magnitude?

Give an example of something we think of as work in everyday circumstances that is not work in the scientific sense. Is energy transferred or changed in form in your example? If so, explain how this is accomplished without doing work.

Describe a situation in which a force is exerted for a long time but does no work. Explain.

Suppose you throw a ball upward and catch it when it returns at the same height. How much work does the gravitational force do on the ball over its entire trip?

As a young man, Tarzan climbed up a vine to reach his tree house. As he got older, he decided to build and use a staircase instead. Since the work of the gravitational force mg is path independent, what did the King of the Apes gain in using stairs?

How much work does a supermarket checkout attendant do on a can of soup he pushes 0.600 m horizontally with a force of 5.00 N?

(a) Calculate the work done on a 1500-kg elevator car by its cable to lift it 40.0 m at constant speed, assuming friction averages 100 N. (b) What is the work done on the elevator car by the gravitational force in this process? (c) What is the total work done on the elevator car?

A shopper pushes a grocery cart 20.0 m at constant speed on level ground, against a 35.0 N frictional force. He pushes in a direction $25.0 °$ below the horizontal. (a) What is the work done on the cart by friction? (b) What is the work done on the cart by the gravitational force? (c) What is the work done on the cart by the shopper? (d) Find the force the shopper exerts, using energy considerations. (e)…

A constant 20-N force pushes a small ball in the direction of the force over a distance of 5.0 m. What is the work done by the force?

A 5.0-kg box rests on a horizontal surface. The coefficient of kinetic friction between the box and surface is $\mu_{K} = 0.50 .$ A horizontal force pulls the box at constant velocity for 10 cm. Find the work done by (a) the applied horizontal force, (b) the frictional force, and (c) the net force.

Suppose that the sled plus passenger of the preceding problem is pushed 20 m across the snow at constant velocity by a force directed $30 °$ below the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.

How much work is done against the gravitational force on a 5.0-kg briefcase when it is carried from the ground floor to the roof of the Empire State Building, a vertical climb of 380 m?

Engineers desire to model the magnitude of the elastic force of a bungee cord using the equation
$F \left(x\right) = a \left[\frac{x + 9 \text{m}}{9 \text{m}} - \left(\frac{9 \text{m}}{x + 9 \text{m}}\right)^{2}\right]$,
where x is the stretch of the cord along its length and a is a constant. If it takes 22.0 kJ of work to stretch the cord by 16.7 m, determine the value of the constant a.

A particle moves along a curved path $y \left(x\right) = \left(10 \text{m}\right) \left\{1 + \text{cos} \left[\left(0.1 \left( \text{m}\right)^{−1}\right) x\right]\right\} ,$ from $x = 0$ to $x = 10 \pi \text{m},$ subject to a tangential force of variable magnitude $F \left(x\right) = \left(10 \text{N}\right) \text{sin} \left[\left(0.1 \left( \text{m}\right)^{−1}\right) x\right] .$ How much work does the force do? (Hint: Consult a table of integrals or use a numerical integration program.)