A box is held against a wall (not resting on the ground). What minimum horizontal force will JUST prevent the 5.0kg box from sliding if the coefficient of friction betweent he wall and the box is 0.65?
force down = m g
normal force = F
up force = .65 F
so
.65 F = 5 * 9.81
F = 75.5 Newtons
To find the minimum horizontal force needed to prevent the box from sliding, we can analyze the forces acting on the box. In this case, the only force that opposes the motion of the box is the friction force.
The friction force between two surfaces can be calculated using the equation:
friction force = coefficient of friction * normal force
where the normal force is the force exerted by the wall on the box perpendicular to the surface of contact.
In this scenario, the normal force is equal to the weight of the box since it is not resting on the ground. The weight of an object can be calculated using the equation:
weight = mass * acceleration due to gravity
Given that the mass of the box is 5.0 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight of the box:
weight = 5.0 kg * 9.8 m/s^2 = 49 N
Now, we can calculate the friction force:
friction force = 0.65 * 49 N = 31.85 N
Therefore, the minimum horizontal force needed to prevent the box from sliding against the wall is approximately 31.85 Newtons.