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 Gravitational Force?
What is the Frictional Force?
What is the Acceleration?
To answer these questions, we need to understand the concepts of gravitational force, frictional force, and acceleration.
1. Gravitational Force: The gravitational force is the force with which Earth attracts any object with mass toward its center. It is usually calculated using the equation F = m * g, where F is the gravitational force, m is the mass of the object, and g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth).
To calculate the gravitational force, multiply the mass of the box (8 kg) by the acceleration due to gravity (9.8 m/s^2):
Gravitational force = 8 kg * 9.8 m/s^2 = 78.4 N
2. Frictional Force: The frictional force is the force that opposes the motion of two surfaces in contact. In our case, we have two coefficients of friction: the coefficient of static friction (0.8) and the coefficient of friction (0.3).
The frictional force depends on whether the object is at rest or in motion. If the object is at rest, we should use the coefficient of static friction. If the object is in motion, we should use the coefficient of friction.
In this case, a force of 8 N is being applied horizontally to the box. Since the applied force is less than or equal to the force of static friction, the box remains at rest. Therefore, we will use the coefficient of static friction (0.8) to calculate the frictional force.
To calculate the frictional force, multiply the coefficient of static friction (0.8) by the gravitational force:
Frictional force = 0.8 * 78.4 N = 62.72 N
3. Acceleration: To calculate the acceleration, we need to consider the net force acting on the box. In this case, the applied force (8 N) is less than the force of static friction (62.72 N), so the net force is the difference between the two.
To calculate the net force, subtract the force of static friction from the applied force:
Net force = Applied force - Frictional force = 8 N - 62.72 N = -54.72 N
Since the net force is negative, it indicates that the box experiences a force in the opposite direction of the applied force. Therefore, the box does not accelerate.
In summary:
- Gravitational force = 78.4 N
- Frictional force = 62.72 N
- Acceleration = 0 m/s^2