Question

A force of 300 N is applied to a 50 kg box. The coefficient of friction between the box and floor is 0.4. What is the acceleration of the box?

Answer 1

To find the acceleration of the box, we need to consider the forces acting on it. In this case, we have:

1. Applied force (F_applied) = 300 N
2. Coefficient of friction (μ) = 0.4
3. Mass of the box (m) = 50 kg
4. Acceleration of the box (a) = ?

The net force acting on the box can be calculated as the difference between the applied force and the force of friction:

Net force (F_net) = F_applied - F_friction

The force of friction (F_friction) can be determined using the equation:

F_friction = μ * N

where N is the normal force exerted by the floor on the box. In this case, the normal force is equal to the weight of the box:

N = m * g

where g is the acceleration due to gravity, approximately 9.8 m/s^2.

Substituting these values into the equations, we have:

F_friction = μ * N = μ * (m * g)

F_net = F_applied - F_friction = F_applied - μ * (m * g)

Finally, we can calculate the acceleration (a) using Newton's second law:

F_net = m * a

Now, let's calculate the acceleration:

F_friction = 0.4 * (50 kg * 9.8 m/s^2) = 196 N

F_net = 300 N - 196 N = 104 N

a = F_net / m = 104 N / 50 kg ≈ 2.08 m/s^2

Therefore, the acceleration of the box is approximately 2.08 m/s^2.