Question

17. A 25 kg block is initially at rest on a rough, horizontal surface. A horizontal force of 75 N is required to set

the block in motion, and a 60 N force is required to keep it in motion at a constant speed once it is moving.

What are the coefficients of static and kinetic friction?

Answer 1

The coefficient of static friction is 0.3 and the coefficient of kinetic friction is 0.24.

Step-by-step explanation:

To find the coefficients of static and kinetic friction, we can use the given information. The horizontal force required to set the block in motion is the maximum static friction force, while the force required to keep it moving at a constant speed is the kinetic friction force.

So, the coefficient of static friction can be calculated by dividing the maximum static friction force by the normal force, which is the weight of the block. In this case, the maximum static friction force is 75 N and the weight of the block is 25 kg times the acceleration due to gravity (9.8 m/s²). Therefore, the coefficient of static friction is 0.3.

The coefficient of kinetic friction can be calculated by dividing the kinetic friction force by the normal force. In this case, the kinetic friction force is 60 N and the weight of the block is the same as before. Therefore, the coefficient of kinetic friction is 0.24.

Answer 2

0.30581

0.24464

Step-by-step explanation:

`\mu_s` = Coefficient of static friction

`\mu_k` = Coefficient of kinetic friction

`F_f` = 75 N

`F_k` = 60 N

Normal force

`F_n=mg\\\Rightarrow F_n=25* 9.81\\\Rightarrow F_n=245.25\ N`

Frictional force

`F_f=\mu_sF_n\\\Rightarrow \mu_s=(F_f)/(F_n)\\\Rightarrow \mu_s=(75)/(245.25)\\\Rightarrow \mu_s=0.30581`

The coefficient of static friction is 0.30581

Kinetic force

`F_k=\mu_kF_n\\\Rightarrow \mu_k=(F_k)/(F_n)\\\Rightarrow \mu_s=(60)/(245.25)\\\Rightarrow \mu_s=0.24464`

The coefficient of kinetic friction is 0.24464