A 50kg box is sitting on your front porch. The coefficient of sliding friction between the box and floor is .4. You are trying to push the box from the porch into the house. What is the force required to push the box at a constant speed?
F=F(fr)=μN=μmg
To determine the force required to push the box at a constant speed, we need to consider the concept of friction. Friction is the force that acts opposite to the direction of motion when two surfaces are in contact. In this case, we are dealing with sliding friction.
The formula to calculate the force of sliding friction is:
Fs = μs × N
where Fs is the force of sliding friction, μs is the coefficient of sliding friction, and N is the normal force.
First, let's find the normal force acting on the box. The normal force is the force exerted by a surface to support the weight of the object resting on it. In this case, the weight of the box is acting downwards, and the normal force acts in the opposite direction, perpendicular to the floor.
The normal force is equal to the weight of the box (mg), where m is the mass of the box and g is the acceleration due to gravity (9.8 m/s^2).
Given that the mass of the box is 50 kg, the weight would be:
Weight = m × g
Weight = 50 kg × 9.8 m/s^2
Weight = 490 N
Therefore, the normal force acting on the box is 490 N.
Now, let's calculate the force of sliding friction using the given coefficient of sliding friction (μs = 0.4) and the normal force (N = 490 N):
Fs = μs × N
Fs = 0.4 × 490 N
Fs = 196 N
The force required to push the box at a constant speed is equal to the force of sliding friction, which in this case is 196 N.