A 250-kg crate is pushed horizontally with a force of 710 N. If the coefficient of friction is 0.20, calculate the acceleration of the crate.
To calculate the acceleration of the crate, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the net force is the force applied minus the force of friction.
Step 1: Calculate the force of friction:
The force of friction can be calculated using the formula: force of friction = coefficient of friction * normal force. The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the weight of the crate (mg) is equal to the normal force (since the crate is on a horizontal surface with no vertical acceleration).
The weight (mg) of the crate is calculated as follows: weight = mass * gravitational acceleration (g). Assuming the acceleration due to gravity is 9.8 m/s^2, we can calculate the weight as follows: weight = 250 kg * 9.8 m/s^2 = 2450 N.
Therefore, the force of friction = coefficient of friction * normal force = 0.20 * 2450 N = 490 N.
Step 2: Calculate the net force:
The net force acting on the crate is equal to the applied force minus the force of friction. In this case, the applied force is 710 N, so the net force is calculated as follows: net force = applied force - force of friction = 710 N - 490 N = 220 N.
Step 3: Calculate the acceleration:
Now that we have the net force and the mass, we can use Newton's second law to calculate the acceleration. Rearranging the equation, we get: acceleration = net force / mass.
Therefore, the acceleration of the crate is: acceleration = 220 N / 250 kg = 0.88 m/s^2.
So, the acceleration of the crate is 0.88 m/s^2.