Acceleration of a Crate: Friction and Newton's Second Law

To find the acceleration of the crate being dragged across the floor, we need to consider the forces acting on the crate and apply Newton's second law of motion.

1. Determine the force of static friction (fs) acting on the crate. The force required to overcome static friction is given by:

fs = coefficient of static friction * normal force

The normal force is equal to the weight of the crate, which can be calculated as:

normal force = mass * gravitational acceleration

Given that the mass of the crate is 100 kg and the gravitational acceleration is approximately 9.8 m/s^2, we can calculate the normal force:

normal force = 100 kg * 9.8 m/s^2 = 980 N

The coefficient of static friction is 0.75, so the force of static friction is:

fs = 0.75 * 980 N = 735 N

2. Determine the applied force (F) acting on the crate, which is given as 60 N.

3. Compare the applied force with the force of static friction. If the applied force is less than the force of static friction, the crate will not move and the acceleration will be 0. However, if the applied force is greater than the force of static friction, the crate will start moving and we need to consider the force of dynamic friction.

4. The force of dynamic friction (fd) is given by:

fd = coefficient of dynamic friction * normal force

The coefficient of dynamic friction is 0.60, so the force of dynamic friction is:

fd = 0.60 * 980 N = 588 N

5. **Since the applied force (F = 60 N) is less than the force of static friction (fs = 735 N), the crate will not move. **

6. Therefore, the acceleration of the crate is 0 m/s^2.