a 254-kg crate is pushed horizontally with a force of 740 N. if the coefficient of friction is .20, calculate the acceleration of the crate
To calculate the acceleration of the crate, we need to consider the net force acting on it. The net force is the difference between the applied force and the force of friction.
The force of friction can be calculated using the formula:
Force of friction = coefficient of friction × normal force
First, we need to find the normal force acting on the crate. In this case, since the crate is on a horizontal surface, the normal force is equal to the weight of the crate.
Weight = mass × acceleration due to gravity
Weight = 254 kg × 9.8 m/s²
Now, we can calculate the force of friction:
Force of friction = 0.20 × (254 kg × 9.8 m/s²)
Next, we can determine the net force:
Net force = applied force - force of friction
Net force = 740 N - force of friction
Finally, we can use Newton's second law of motion to calculate the acceleration:
Net force = mass × acceleration
Rearranging the equation:
Acceleration = net force / mass
Substituting the values we have:
Acceleration = (740 N - force of friction) / 254 kg
Now, we can calculate the force of friction and substitute it into the acceleration equation to find the final answer.