A sled loaded with bricks has a total mass of 18.0 kg and is pulled at constant speed by a rope inclined at 40.0o above the horizontal. The sledge moves a distance of 16.0 m on a horizontal surface. The coefficient of kinetic friction between the sledge and surface is 0.510 .
(a) What is the tension in the rope?
b) How much work is done by the rope on the sled?
c)What is the magnitude of the force of friction?
d) What is the mechanical energy lost due to friction?
To find the answers to these questions, we can use various equations related to forces, work, and energy. Let's go through each question step by step.
(a) Tension in the rope:
The tension in the rope can be determined by analyzing the forces acting on the sled. We know that the sled is being pulled at a constant speed, which means the net force on the sled is zero.
To find the tension, we need to consider the forces acting on the sled:
1. The gravitational force acting vertically downwards, which can be calculated by multiplying the mass (m) with the acceleration due to gravity (9.8 m/s^2).
2. The force of friction opposing the motion, which can be calculated using the coefficient of kinetic friction (μk) and the normal force (Fn) acting perpendicular to the surface.
Since the sled is on a horizontal surface, the vertical component of the tension cancels out with the gravitational force, and the horizontal component of the tension balances the force of friction. Therefore, the tension in the rope is equal to the force of friction.
(b) Work done by the rope:
We can calculate the work done by the rope on the sled using the equation:
Work = Force × Distance × cos(theta)
In this case, the force is the tension in the rope (from part a), the distance is the distance the sled moves (16.0 m), and theta is the angle between the direction of the force and the direction of motion (which is 0 degrees since the force and motion are in the same direction).
(c) Magnitude of the force of friction:
The magnitude of the force of friction can be calculated using the equation:
Force of friction = coefficient of kinetic friction × normal force
To find the normal force, we need to consider the vertical forces acting on the sled. In this case, the normal force is equal to the gravitational force.
(d) Mechanical energy lost due to friction:
The mechanical energy lost due to friction can be calculated as the work done by friction. Since the sled is moving at a constant speed, the work done by friction is equal to the negative of the work done by the rope (from part b).
By applying these equations and calculations, we can find the answers to the given questions.