Two people push on a box that has a mass of 10kg, the person on the right has a mass of 86kg and applies a horizontal force of 50N. The person on the left has a mass of 45kg. The coefficient of kinetic friction between the box and the floor is .2, the coefficient of static friction is .4. If the box moves to the left with a constant velocity of 10 m/s, what is the force applied by the person on the left?
To find the force applied by the person on the left, we need to consider the forces acting on the box. Let's break it down step by step:
1. The box is moving with a constant velocity, which means that the net force acting on it is zero. In other words, the force applied by the person on the right and the force applied by the person on the left must balance each other out.
2. The force applied by the person on the right is given as 50N.
3. The box experiences a resistive force due to friction, which opposes its motion. There are two types of friction we need to consider in this scenario.
4. First, when the box is at rest, there is static friction. The coefficient of static friction is given as 0.4. The maximum static frictional force can be calculated by multiplying the coefficient of static friction by the normal force, which is the weight of the box (mass * gravitational acceleration).
5. The weight of the box can be calculated by multiplying its mass (10kg) by the acceleration due to gravity (9.8 m/s^2).
Weight = mass * acceleration due to gravity
Weight = 10 kg * 9.8 m/s^2
6. After calculating the weight, we can find the maximum static frictional force by multiplying it by the coefficient of static friction.
Maximum static friction force = coefficient of static friction * weight
7. If the applied force by the person on the right is greater than the maximum static frictional force, the box will start moving. However, we know that the box is moving at a constant velocity, so the static friction cannot be the force opposing the motion.
8. Therefore, the force opposing the motion must be the kinetic friction. The coefficient of kinetic friction is given as 0.2. The kinetic frictional force can be calculated by multiplying the coefficient of kinetic friction by the normal force (which is the weight).
Kinetic friction force = coefficient of kinetic friction * weight
9. Rearranging the equation for the kinetic frictional force, we can find the normal force.
Normal force = kinetic friction force / coefficient of kinetic friction
10. Now that we have the normal force, we can calculate the force applied by the person on the left. Since the box is moving at a constant velocity, the force applied by the person on the left must be equal in magnitude but opposite in direction to the kinetic frictional force.
Force applied by the person on the left = kinetic friction force
11. Finally, substitute the values we calculated into the equations above to find the force applied by the person on the left.