Hi! please help
A sledge loaded with bricks has a total mass of 17.8 kg and is pulled at constant speed by a rope inclined at 20.8° above the horizontal. The sledge moves a distance of 20.6 m on a horizontal surface. The coefficient of kinetic friction between the sledge and surface is 0.500.
(a) What is the tension in the rope?
_____ N
(b) How much work is done by the rope on the sledge?
_____ kJ
(c) What is the mechanical energy lost due to friction?
_____ kJ
Thank you so much
remember the rope lifts (reduces force normal) and pulls the sled. So break up the pulling force into vertical and horizontal components.
I will be happy to critique your thinking.
To solve this problem, we'll need to break it down into several steps.
(a) Finding the tension in the rope:
The tension in the rope can be found by analyzing the forces acting on the sledge. The only horizontal force acting on the sledge is the force of kinetic friction. The force of kinetic friction (Fk) can be calculated using the formula:
Fk = μ * N
Where μ is the coefficient of kinetic friction and N is the normal force. The normal force (N) can be calculated by multiplying the mass of the sledge (m) by the acceleration due to gravity (g):
N = m * g
Once we have the force of kinetic friction, we can find the tension in the rope by analyzing the vertical forces. Since the sledge is moving at a constant speed, the vertical forces must be balanced. The vertical force balance equation is:
T - N * cos(θ) = 0
Where T is the tension in the rope and θ is the angle of inclination.
Solving these equations simultaneously will give us the tension in the rope.
(b) Finding the work done by the rope:
The work done by the rope can be calculated using the formula:
Work = Force * Distance * cos(θ)
Where Force is the tension in the rope, Distance is the horizontal distance the sledge moves, and θ is the angle of inclination.
(c) Finding the mechanical energy lost due to friction:
The mechanical energy lost due to friction can be calculated using the formula:
Energy lost = Force * Distance * sin(θ)
Where Force is the force of kinetic friction, Distance is the horizontal distance the sledge moves, and θ is the angle of inclination.
By plugging in the given values, we can find the answers to all the questions.