Final answer:
The the coefficient of static friction between the ground and the box is approximately 0.408.
Step-by-step explanation:
The student is asking for the coefficient of static friction between the ground and a box. The coefficient of static friction (μs) is the ratio of the maximum static frictional force that resists the initiation of motion to the normal force, which in this scenario is the weight of the 10 kg box. As the box just begins to move when an applied force reaches 40 N, we know that this force is overcoming the maximum static friction.
The weight of the box (W) is calculated by multiplying the mass of the box (10 kg) by the acceleration due to gravity (9.81 m/s²), which gives us the normal force (N):
W = 10 kg × 9.81 m/s² = 98.1 N,
and the coefficient of static friction is calculated using the formula:
μs = F / N,
where F is the applied force that initiates motion and N is the normal force.
By substituting the values, we calculate:
μs = 40 N / 98.1 N = 0.408 (rounded to three decimal places).
Therefore, the coefficient of static friction between the ground and the box is approximately 0.408.