Question

A child has mass 6.0 kg and slides down a 35° incline with constant speed under the action of a 13.4-N force acting up and parallel to the incline. What is the coefficient of kinetic friction between the child and the surface of the incline?

a. 0.23
b. 0.47
c. 0.58
d. 0.70

Answer 1

The coefficient of kinetic friction between the child and the surface of the incline is approximately 0.58 (c). This value accounts for the constant speed of the child sliding down the incline under the influence of a 13.4-N force acting parallel to the incline.

c. 0.58

Step-by-step explanation:

The coefficient of kinetic friction
`(\(\mu_k\))` between the child and the surface of the incline can be determined using the following equation:

`\[ \mu_k = \tan(\theta) - \frac{F_{\text{parallel}}}{mg} \]`

where \(\theta\) is the angle of the incline,
`(\(F_{\text{parallel}}\))` is the force parallel to the incline, m is the mass of the child, and g is the acceleration due to gravity.

Given that the mass of the child (m) is 6.0 kg, the angle of the incline
`(\(\theta\))` is 35°, the force parallel to the incline
`(\(F_{\text{parallel}}\))` is 13.4 N, and g is approximately 9.8 m/s², we can substitute these values into the formula:

`\[ \mu_k = \tan(35°) - \frac{13.4 \, \text{N}}{6.0 \, \text{kg} * 9.8 \, \text{m/s}^2} \]`

Calculating this expression gives us the coefficient of kinetic friction
`(\mu_k\))` between the child and the incline. The final result is approximately 0.58.

In conclusion, the coefficient of kinetic friction between the child and the incline is 0.58. This means that the frictional force opposing the motion is 58% of the force pressing the child onto the incline.