A rightward force of 302 N is applied to a 28.6-kg crate to accelerate it across the floor. The coefficient of friction between the crate and the floor is 0.750.
Determine the acceleration of the crate.
To determine the acceleration of the crate, we need to find the net force acting on it.
The force of friction can be calculated using the formula:
Force of friction = coefficient of friction * normal force
The normal force is the force perpendicular to the surface and is equal to the weight of the crate, which is given by:
Normal force = mass * gravitational acceleration
Using the known values:
Normal force = 28.6 kg * 9.8 m/s² = 280.28 N
Now, we can calculate the force of friction:
Force of friction = 0.750 * 280.28 N = 210.21 N
The net force acting on the crate is equal to the applied force minus the force of friction:
Net force = 302 N - 210.21 N = 91.79 N
Finally, we can substitute this net force and the mass of the crate into Newton's second law of motion:
Net force = mass * acceleration
Plugging in the known values:
91.79 N = 28.6 kg * acceleration
Solving for acceleration:
acceleration = 91.79 N / 28.6 kg ≈ 3.21 m/s²
Therefore, the acceleration of the crate is approximately 3.21 m/s².