A box have a mass of 50 Kilograms is dragged across a horizontal floor by means of a rope tied on the front of it. The
coefficient of friction between the box and the floor is .3. If the angle between the rope and the floor is 30 degrees, what
force must be exerted on the rope to move the box at a constant speed? (
Please help to answer this question
To find the force required to move the box at a constant speed, we can break down the forces acting on the box along the horizontal plane.
1. Determine the weight of the box:
The weight of the box can be calculated using the formula:
Weight = mass × gravity
Given that the mass is 50 kilograms and the acceleration due to gravity is approximately 9.8 meters per second squared, we can calculate the weight.
Weight = 50 kg × 9.8 m/s^2 = 490 N
2. Identify the force of friction:
The force of friction can be calculated using the formula:
Force of friction = coefficient of friction × normal force
The normal force is equal in magnitude and opposite in direction to the weight of the box, so:
Normal force = Weight = 490 N
Force of friction = 0.3 × 490 N = 147 N
3. Analyze the forces acting along the rope:
To find the force required to move the box, we need to analyze the forces acting along the rope. When the box is being dragged across the horizontal floor, the force exerted on the rope can be decomposed into two components: the vertical component and the horizontal component.
- The vertical component of the force balances the weight of the box and cancels it out.
- The horizontal component of the force is responsible for overcoming the force of friction.
4. Calculate the horizontal component of the force:
The horizontal component of the force can be calculated using the formula:
Horizontal force = Force of friction
Horizontal force = 147 N
Therefore, the force that must be exerted on the rope to move the box at a constant speed is 147 Newtons.
upward force on box: P*sin30=P/1
horizontal force: P cos30
at constant speed,
pulling force=friction force
Pcos30=mu(mg-P/2)
solve for P