A sledge loaded with bricks has a total mass of 18.0 kg nd is plled at constant speed of a rope incllined at 20 degres above the horizontal. The sledge moves a distance of 20.0 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? (b) How much work is done by the rope on the sledge? (c) What is the mechanical energy lost due to friction?
The subject s physics.
(a) T cos 20 = friction force uk*M*g
Solve for T, in Newtons
uk is the kinetic friction coefficient
(b) T cos20 * 20 m = ___ Joules
(c) same as (b). The kinetc energy does not change. (constant speed is specified)
(a) What is the tension in the rope?
Well, since the sledge is pulled at a constant speed, we can conclude that the tension in the rope is equal to the force of kinetic friction acting on the sledge. So, first let's find the force of kinetic friction:
Force of kinetic friction = coefficient of kinetic friction * normal force
The normal force is the force exerted by the surface on the sledge, and it is equal to the weight of the sledge.
Weight of the sledge = mass * gravitational acceleration
Using the given mass of 18.0 kg, and the gravitational acceleration of approximately 9.8 m/s², we can find the weight of the sledge.
Weight of the sledge = 18.0 kg * 9.8 m/s² = 176.4 N
Now, let's calculate the force of kinetic friction:
Force of kinetic friction = 0.500 * 176.4 N = 88.2 N
Therefore, the tension in the rope is also 88.2 N.
(b) How much work is done by the rope on the sledge?
Since the sledge moves a distance of 20.0 m on a horizontal surface, we need to calculate the work done against the force of kinetic friction.
Work = Force * Distance * cos(angle)
The angle between the force and the displacement is 180 degrees (since the force and displacement are in opposite directions). Therefore, the cos(180) = -1.
Work = 88.2 N * 20.0 m * cos(180) = -1764 J
Note that the negative sign indicates that work is done against the applied force of kinetic friction.
(c) What is the mechanical energy lost due to friction?
The mechanical energy lost due to friction is equal to the negative work done by the rope on the sledge. So, the mechanical energy lost is 1764 J. However, let's remember to keep our spirits high and not dwell on the loss. After all, there's always something to gain, like a lesson in physics or a good laugh!
To solve this problem, we can break it down into three parts.
(a) What is the tension in the rope?
To find the tension in the rope, we need to analyze the forces acting on the sledge. The only horizontal force is the force of friction opposing the motion. The force of friction can be calculated using the formula:
Frictional force = coefficient of friction * normal force
The normal force is equal to the weight of the sledge, which can be calculated as:
Weight = mass * gravitational acceleration
Gravitational acceleration (g) is approximately 9.8 m/s^2.
So, the normal force is:
Normal force = mass * gravitational acceleration
The frictional force can then be calculated as:
Frictional force = coefficient of friction * normal force
Since the sledge is being pulled at a constant speed, the tension in the rope is equal to the frictional force.
Therefore, the tension in the rope is:
Tension = Frictional force
(b) How much work is done by the rope on the sledge?
Work can be calculated using the formula:
Work = force * distance * cos(theta)
In this case, the force is the tension in the rope, the distance is the distance moved by the sledge, and theta is the angle between the direction of the force and the direction of motion.
Work = Tension * distance * cos(theta)
Since the sledge is being pulled horizontally, the angle between the tension force and the direction of motion is 0 degrees. Therefore, the cos(0) is 1 and can be ignored.
Therefore, the work done by the rope on the sledge is:
Work = Tension * distance
(c) What is the mechanical energy lost due to friction?
The mechanical energy lost due to friction can be calculated as the difference between the work done by the rope and the work done against friction.
Mechanical energy lost = Work done by the rope - Work done against friction
Now, let's calculate the values.
(a) Tension in the rope:
First, calculate the weight of the sledge:
Weight = mass * gravitational acceleration
Weight = 18.0 kg * 9.8 m/s^2
Next, calculate the normal force:
Normal force = Weight
Then, calculate the frictional force:
Frictional force = coefficient of friction * normal force
Finally, the tension in the rope is equal to the frictional force.
(b) Work done by the rope on the sledge:
Work = Tension * distance
(c) Mechanical energy lost due to friction:
Mechanical energy lost = Work done by the rope - Work done against friction
Remember to plug in the given values for mass, distance, coefficient of friction, and gravitational acceleration into the calculations.
To solve this problem, we can break it down into multiple parts.
(a) To find the tension in the rope, we can use the fact that the sledge is being pulled at a constant speed. This means that the force of friction is equal to the force applied by the rope.
The force of friction can be calculated using the equation:
Frictional Force = coefficient of kinetic friction * normal force
The normal force is the force exerted by the surface on the sledge and is equal to the weight of the sledge. The weight can be calculated by multiplying the mass (18.0 kg) by the acceleration due to gravity (9.8 m/s^2).
So, the normal force = (mass of sledge) * (acceleration due to gravity) = 18.0 kg * 9.8 m/s^2
The frictional force = (coefficient of kinetic friction) * (normal force)
Since the sledge is being pulled at a constant speed, the tension in the rope is equal and opposite to the frictional force. Therefore, the tension in the rope = frictional force.
(b) The work done by the rope on the sledge can be calculated using the equation:
Work = Force * Distance
In this case, the force is the tension in the rope, and the distance is the distance the sledge moves on the horizontal surface (20.0 m).
(c) The mechanical energy lost due to friction can be calculated using the formula:
Energy lost = Work done by friction = Frictional Force * Distance
Now that we have the variables and formulas, let's plug in the values to solve the problem.
(a) Tension in the rope:
- Calculate the normal force: Normal force = (mass of sledge) * (acceleration due to gravity)
- Calculate the frictional force: Frictional force = (coefficient of kinetic friction) * (normal force)
- Tension in the rope = Frictional force
(b) Work done by the rope:
- Work = Tension in the rope * Distance
(c) Energy lost due to friction:
- Energy lost = Frictional force * Distance
By plugging in the given values into the formulas, you can find the numerical answers.