A cardboard box sits on top of an asphalt driveway. The coefficient of static friction is 0.8 and the coefficient of friction is 0.3 . The mass of the box is 8 Kg and a horizontal force of 8 N is applied. What is the Frictional Force?
To determine the frictional force acting on the cardboard box, we will first calculate the maximum static frictional force. If the applied force exceeds this maximum value, the box will start moving, and then the frictional force will transition from static to kinetic friction.
1. Calculate the maximum static frictional force:
- The coefficient of static friction (μs) is given as 0.8
- The normal force (N) acting on the box is equal to the weight of the box, which is equal to the mass (m) multiplied by the acceleration due to gravity (g ≈ 9.8 m/s^2)
- In this case, N = m * g = 8 kg * 9.8 m/s^2 = 78.4 N
- Maximum static frictional force (fs max) = μs * N = 0.8 * 78.4 N = 62.72 N
2. Determine if the applied force exceeds the maximum static frictional force:
- The applied force (F) is given as 8 N
- Since the applied force (8 N) is less than or equal to the maximum static frictional force (62.72 N), the box remains at rest, and the frictional force equals the applied force.
Therefore, the frictional force acting on the cardboard box is 8 N.