The coefficients of static and kinetic friction between the paper used in a cardboard box and a particular wooden floor are 0.5 and 0.3, respectively. Calculate the force that must be applied to slide a box with a weight of 40 N over the floor at a constant speed.(1 point)%0D%0AResponses%0D%0A%0D%0A40 N%0D%0A40 N%0D%0A%0D%0A12 N%0D%0A12 N%0D%0A%0D%0A32 N%0D%0A32 N%0D%0A%0D%0A20 N
The force that must be applied to slide a box with a weight of 40 N over the floor at a constant speed can be calculated using the formula:
Force = weight * coefficient of kinetic friction
Given that the coefficient of kinetic friction is 0.3, and the weight of the box is 40 N, we can substitute these values into the formula to find the force:
Force = 40 N * 0.3
Force = 12 N
Therefore, the force that must be applied to slide the box at a constant speed is 12 N.
To calculate the force required to slide the box at a constant speed, we need to consider the forces acting on the box.
First, let's calculate the maximum force of static friction (Fs) using the coefficient of static friction (μs) and the weight of the box (W).
Fs = μs * W
= 0.5 * 40 N
= 20 N
Since the box is already moving at a constant speed, the force of kinetic friction (Fk) will be equal to the force applied to the box to balance the friction force. In other words, Fk = Fs.
Therefore, the force required to slide the box at a constant speed is 20 N.
To calculate the force required to slide the box at a constant speed, we need to consider the coefficients of static and kinetic friction.
The force required to overcome static friction and initiate the motion is given by:
F_static = coefficient of static friction * weight of the box
F_static = 0.5 * 40 N = 20 N
Once the box is in motion, we need to consider kinetic friction. The force required to maintain constant speed is given by:
F_kinetic = coefficient of kinetic friction * weight of the box
F_kinetic = 0.3 * 40 N = 12 N
Therefore, the force that must be applied to slide the box at a constant speed is 12 N.
The correct answer is 12 N.