Question

#1. A person has a mass of 65 kg. The coefficient of static friction μs, between their shoes and the floor = 0.8. Calculate the force required to slide them across the floor.
#2. The person in problem #1 begins to slide and the coefficient of kinetic friction μk = 0.6. What is the acceleration of the person, given that the force calculated in problem #1 is maintained?

#3. A 13-N force moves through a displacement of 42 m, at an angle of 35o to the displacement. What work is now done by the force? What if the angle is 90o?
#4. A motor pumps 50 kg of water into a tower which is 35 m high. It does this in a time of 5 minutes. What is the power of the motor in this case?

Answer 1

#1. The force must be equal to the force of static friction:

$$F=\mu_sN=\mu_smg=509.6\text{ N}.$$

#2. According to Newton's second law:

$$F_\text{net}=F-f=ma, \\\space\\ a=\frac{F-f}{m}=\frac{\mu_smg-\mu_kmg}{m}=g(\mu_s-\mu_k)=1.96\text{ m/s}^2.$$

In this equation, f is the force of kinetic friction.

#3. The work is

$$W=Fd\text{ cos}35°=447\text{ J}.$$

If the angle is 90°, the work is zero.

#4. The power is how quickly work can be done. The work required to lift this mass of water is

$$W=F_gh=mgh,$$

the power is

$$P=\frac{W}{t}=\frac{mgh}{t}=17\text{ W}.$$