To find the friction force acting on a box at rest, we can use the formula for static friction:
\[ f_{\text{friction}} = \mu_s \cdot F_n \]
where:
- \( f_{\text{friction}} \) is the force of static friction,
- \( \mu_s \) is the coefficient of static friction,
- \( F_n \) is the normal force.
The normal force \( F_n \) on a flat surface is equal to the weight of the object, which can be calculated using:
\[ F_n = m \cdot g \]
where:
- \( m \) is the mass of the object,
- \( g \) is the acceleration due to gravity.
On the Moon, the acceleration due to gravity is approximately \( g \approx 1.625 , \text{m/s}^2 \).
Given:
- Mass of the box \( m = 60 , \text{kg} \)
- Coefficient of static friction \( \mu_s = 0.6 \)
First, we calculate the weight of the box (and hence the normal force):
\[ F_n = 60 , \text{kg} \cdot 1.625 , \text{m/s}^2 = 97.5 , \text{N} \]
Now, we can calculate the friction force using the static friction coefficient:
\[ f_{\text{friction}} = 0.6 \cdot 97.5 , \text{N} = 58.5 , \text{N} \]
Therefore, the maximum friction force before the box starts to move is 58.5 N. However, since the box is at rest, the actual friction force acting on it will be equal to the applied force up to this maximum value. If no external force is applied, the friction force will be 0 N.