Answer to Question #191421 in Classical Mechanics for Kaitlyn Hosking

Question

1. A car of mass 1000kg, travelling at 20ms^-1 is brought to rest on 40s.  What is the power of the brakes?

1. A pupil of mass 50kg climbs stairs of vertical height 7m in a time of 9s.  What power does the student have in climbing the stairs?

1. A 2kW motor pulls a load of 3000N for 8m.  How long does it take?

1. A man pushes a wheelbarrow for 60 m using a 50 N force. If he takes 10 s, what is his average power?

1. A machine lifts a load of 4000 N to a height of 5 m in 20 s. What is its power?

1. A lift can raise a total mass of 800 kg up 10 m in 40 s. What is its power?

1. What is the efficiency of a machine which has a power input of 800 W and a power output of 600 W?

1. How efficient is a machine that takes in 24000J of energy and produces 8000J of useful energy?

Answer 1

1. The power is

$$P=\frac Wt=\frac{mv^2}{2t}=5000\text{ W}.$$

2. The power is

$$P=\frac Wt=\frac{mgh}{t}=381\text{ W}.$$

3. The time is

$$t=\frac{E}{P}=\frac{Fd}{P}=\frac{3000·8}{2000}=12\text{ s}.$$

4. The power is

$$P=\frac Wt=\frac{Fd}{t}=300\text{ W}.$$

5. The power is

$$P=\frac Wt=\frac{Fd}{t}=1000\text{ W}.$$

6. The power is

$$P=\frac Wt=\frac{mgh}{t}=1960\text{ W}.$$

7. The efficiency is

$$\eta=\frac{P_o}{P_i}=\frac{600}{800}=0.75$$

8. The efficiency is

$$\eta=\frac{P_o}{P_i}=\frac{8000}{24000}=0.33$$