You are pulling a crate across the floor. The crate has a mass of 75.0 kg. You exert a horizontal force of 120. N to the left. Friction exerts a force of 82.0 N to the right. What is the magnitude (fill in box) and direction of the acceleration of the crate?
120 - 82 = 38 newtons to LEFT
F = m a
38 = 75 a
a = 0.507 m/s^2 to the left
To find the magnitude and direction of the acceleration of the crate, we need to apply Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
First, let's calculate the net force acting on the crate. The net force is the difference between the force applied by you and the force exerted by friction.
Net force = Force applied - Force of friction
= 120 N (to the left) - 82 N (to the right)
= 38 N (to the left)
Since the net force is only in the horizontal direction, we can directly use it to calculate the acceleration of the crate.
Using Newton's second law:
Net force = mass × acceleration
Rearranging the equation to solve for acceleration:
Acceleration = Net force / mass
Plugging in the values:
Acceleration = 38 N / 75.0 kg
≈ 0.507 m/s²
Therefore, the magnitude of the acceleration of the crate is approximately 0.507 m/s² to the left.
Note: The direction of the acceleration is consistent with the net force acting on the crate, which is to the left in this case.