A 35 kg block is pulled at a constant speed along a horizontal surface by a rope with tension FT . The rope is inclined at an angle from the horizontal as shown. The block moves a
distance 15 m along the horizontal surface.
What is the net work done by all the forces acting on the block? The acceleration of gravity is 9.8 m/s
1. Wnet = 5145 J
2. Wnet = −2726.85 J
3. Wnet = −5145 J
4. Wnet = 2726.85 J
5. Wnet = 1968.75 J
6. Wnet = −1430.38 J
7. Wnet = 0
The kinetic energy does not change. What does that tell you?
To find the net work done by all the forces acting on the block, we need to consider the work done by each force separately and then sum them up. The forces acting on the block are the tension force and the force due to gravity.
The work done by the tension force can be calculated using the formula:
Work = Tension * Displacement * cos(theta)
where Tension is the magnitude of the tension force, Displacement is the distance along the horizontal surface (15 m), and theta is the angle between the tension force and the horizontal surface.
The work done by the force due to gravity can be calculated using the formula:
Work = Force * Displacement * cos(theta)
where Force is the magnitude of the force due to gravity, which is the weight of the block. The weight of the block can be calculated as:
Weight = mass * gravity
where mass is the mass of the block (35 kg) and gravity is the acceleration due to gravity (9.8 m/s^2).
Since the block is moving at a constant speed, the net work done by all the forces must be zero. This means that the work done by the tension force must be equal in magnitude and opposite in sign to the work done by the force due to gravity.
Let's calculate the net work done by all the forces:
1. Calculate the Weight: Weight = mass * gravity = 35 kg * 9.8 m/s^2 = 343 N
2. Calculate the work done by the tension force: Work_tension = Tension * Displacement * cos(theta)
3. Calculate the work done by the force due to gravity: Work_gravity = Weight * Displacement * cos(theta)
4. Calculate the net work done: Net work = Work_tension + Work_gravity
Since we don't have the value of tension or the angle theta, we cannot directly calculate the net work. Therefore, we cannot choose any of the given options for the net work done by all the forces acting on the block.
To find the net work done by all the forces acting on the block, you need to consider the work done by each force individually and then add them up.
First, let's consider the work done by the tension force. The work done by a force is given by the equation: work = force * distance * cosine(theta), where theta is the angle between the force and the direction of displacement.
In this case, the distance along the horizontal surface is 15 m, so the work done by the tension force is: workT = FT * 15 * cos(theta).
Next, let's consider the work done by the force of gravity. Since the block is moving horizontally, the force of gravity does not contribute any work along the horizontal surface. Therefore, the work done by gravity is zero.
Now, we can calculate the net work done by adding up the work done by each force:
Wnet = workT + workgravity
Since the work done by gravity is zero, we have:
Wnet = workT
Now we need to determine the sign of the work done by the tension force. If the angle theta is between 0 and 90 degrees, the cosine of theta is positive, which means the work done by the tension force is positive. If the angle theta is between 90 and 180 degrees, the cosine of theta is negative, which means the work done by the tension force is negative.
Since the block is being pulled horizontally, the angle theta is 0 degrees, and the work done by the tension force is positive.
Therefore, the net work done by all the forces acting on the block is positive.
Based on the given answer choices, the correct option would be:
1. Wnet = 5145 J