a force of 48.0N is required to start a 5.Okg box moving across a horizonatl concrete floor.what is the coefficient of static friction between the box and the floor?If the 48.0-N force continues, the box accelerates at 0.70 m/s squared . What is the coefficient of kinetic friction?
To find the coefficient of static friction between the box and the floor, we can use the formula:
\( F_{\text{static friction}} = \text{coefficient of static friction} \times F_{\text{normal}} \)
Where:
- \( F_{\text{static friction}} \) is the force of static friction. In this case, it is equal to the applied force required to start the box moving, which is 48.0 N.
- \( \text{coefficient of static friction} \) is the unknown we need to find.
- \( F_{\text{normal}} \) is the normal force exerted on the box by the floor.
To determine \( F_{\text{normal}} \), we need to consider that the normal force is equal to the weight of the box. The weight is given by the formula:
\( F_{\text{weight}} = m \times g \)
Where:
- \( m \) is the mass of the box, which is 5.0 kg.
- \( g \) is the acceleration due to gravity, approximately equal to 9.8 m/s².
Substituting the given values, we find:
\( F_{\text{weight}} = 5.0 \, \text{kg} \times 9.8 \, \text{m/s²} \)
Next, we will use the formula for the coefficient of kinetic friction:
\( F_{\text{kinetic friction}} = \text{coefficient of kinetic friction} \times F_{\text{normal}} \)
Where:
- \( F_{\text{kinetic friction}} \) is the force of kinetic friction. In this case, it is equal to the force that causes acceleration, which is 48.0 N.
- \( \text{coefficient of kinetic friction} \) is the unknown we need to find.
- \( F_{\text{normal}} \) is again the weight of the box.
Using the same value for \( F_{\text{normal}} \) as in the previous calculation, we can solve for the coefficient of kinetic friction.
Therefore, the coefficient of static friction can be found by dividing the force of static friction by the weight of the box, and the coefficient of kinetic friction can be found by dividing the force of kinetic friction by the weight of the box.