What is the minimum downward force on the box ( m=30 kg)that will keep it from slipping? The coefficients of static and kinetic friction between the box and the floor are 0.40 and 0.30, respectively.One person is pulling the box forward with a force of 125 N.
The weight of the box PLUS the extra downward force F_d determines the maximum static friction force. This must balance or exceed the pulling force F_p if slipping is to be avoided.
0.40*(M g + F_d) = F_p
Solve for F_d
To find the minimum downward force on the box that will keep it from slipping, we need to consider the forces acting on the box.
The force of gravity acting on the box is given by the formula:
F_gravity = m * g
where m is the mass of the box and g is the acceleration due to gravity (approximately 9.8 m/s^2).
F_gravity = 30 kg * 9.8 m/s^2
F_gravity = 294 N
Next, we need to find the maximum static friction force between the box and the floor. The maximum static friction force can be calculated using the formula:
F_static_max = μ_static * F_normal
where μ_static is the coefficient of static friction and F_normal is the normal force acting on the box, which is equal to the force of gravity, since the box is not accelerating vertically.
F_static_max = 0.40 * F_normal
F_static_max = 0.40 * 294 N
F_static_max = 117.6 N
Since there is only one person pulling the box forward with a force of 125 N, we need to check if this force is greater than the maximum static friction force. If it is, the box will start to move (slip).
125 N > 117.6 N
Since the pulling force of 125 N is greater than the maximum static friction force, the box will start to slip.
To calculate the minimum downward force required to prevent slipping, we need to consider the kinetic friction force. The kinetic friction force can be calculated using the formula:
F_kinetic = μ_kinetic * F_normal
where μ_kinetic is the coefficient of kinetic friction and F_normal is the normal force acting on the box.
F_kinetic = 0.30 * F_normal
F_kinetic = 0.30 * 294 N
F_kinetic = 88.2 N
Therefore, to prevent the box from slipping, the minimum downward force on the box should be equal to or greater than 88.2 N.