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End Of Chapter Exercises

Exercise 5.5

How much work does a person do in pushing a shopping trolley with a force of \(\text{200}\) \(\text{N}\) over a distance of \(\text{80}\) \(\text{m}\) in the direction of the force?

\begin{align*} W&= F \Delta x \cos\theta \\ &= (200) (80) \cos(0) \\ &= 16000 (1) \\ &= \text{16 000}\text{ J} \end{align*} \(\text{16 000}\) \(\text{J}\)

How much work does the force of gravity do in pulling a \(\text{20}\) \(\text{kg}\) box down a \(\text{45}\)\(\text{°}\) frictionless inclined plane of length \(\text{18}\) \(\text{m}\)?

The component of the gravitational force parallel to the slope (i.e. in line with the direction of the displacement) is \(F_{gx} = F_g\sin\alpha_{slope} = mg\sin\alpha_{slope}\). The work done can then be calculated:

\begin{align*} W&= F \Delta x \cos\theta \\ &= mg\sin\alpha_{slope} \Delta x \cos\theta \\ &= (20)(9,8)\sin(45) (18) \cos(0) \\ & = \text{2 494,67}\text{ J} \end{align*} \(\text{2 494,67}\) \(\text{J}\)

[IEB 2001/11 HG1] Of which one of the following quantities is \(\text{kg·m$^{2}$·s$^{-3}$}\) the base S.I. unit?

a

Energy

c

Power

b

Force

d

Momentum

Power

[IEB 2003/11 HG1] A motor is used to raise a mass m through a vertical height h in time t. What is the power of the motor while doing this?

a

\(mght\)

c

\(\frac{mgt}{h}\)

b

\(\frac{mgh}{t}\)

d

\(\frac{ht}{mg}\)

\(\frac{mgh}{t}\)

[IEB 2002/11 HG1] An electric motor lifts a load of mass M vertically through a height h at a constant speed v. Which of the following expressions can be used to calculate the power transferred by the motor to the load while it is lifted at constant speed?

a

\(Mgh\)

c

\(Mgv\)

b

\(Mgh+\frac{1}{2}\) Mv \({}^{2}\)

d

\(Mgv+\frac{1}{2}\)\(\frac{{\text{Mv}}^{3}}{\text{h}}\)

\(Mgv\)

A set 193 kg containers need to be lifted onto higher floors during a building operation. The distance that they need to be raised is 7.5 m, at constant speed. The project manager has determined that in order to keep to budget and time this has to happen in as close to 5,0 s as possible. The power ratings for three motors are listed as 1,0 kW, 3,5 kW, and 5,5 kW. Which motor is best for the job?

The best motor to use is the 3.5 kW motor. The 1.0 kW motor will not be fast enough, and the 5.5 kW motor will be too fast.

[IEB 2003/11 HG1] In which of the following situations is there no work done on the object?

  1. An apple falls to the ground.

  2. A brick is lifted from the ground to the top of a building.

  3. A car slows down to a stop.

  4. A box moves at constant velocity across a frictionless horizontal surface.

A box moves at constant velocity across a frictionless horizontal surface.