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 answer these questions, we need to use the equations of motion and the principles of work and energy. Here's how we can approach each part of the problem:
(a) To find the tension in the rope, we need to consider the forces acting on the sled. The force of tension in the rope is balanced by the component of weight parallel to the incline and the force of friction. The equation we can use is:
Tension = Weight * sin(theta) + Friction
Given:
Mass of sled (m) = 18.0 kg
Angle of incline (theta) = 40.0 degrees
Coefficient of kinetic friction (μ) = 0.510
Weight = mass * gravity, where gravity is approximately 9.8 m/s^2.
Now, substituting the values into the equation, we have:
Tension = (m * g) * sin(theta) + (μ * m * g)
Substituting the known values, we can calculate the tension in the rope.
(b) The work done by the rope on the sled can be found using the formula:
Work = Force * Distance * cos(theta)
Since the sled is moving at a constant speed, the net force and acceleration are both zero. Therefore, the net work done on the sled is zero.
(c) The magnitude of the force of friction can be calculated using the equation:
Force of friction = μ * Normal force
The normal force is equal to the weight of the sled, which is m * g in this case.
(d) The mechanical energy lost due to friction can be calculated using the equation:
Mechanical energy lost = Force of friction * Distance
Substituting the values, we can calculate the mechanical energy lost due to friction.
By following these steps, we can find the answers to all the questions.