A crate is pulled by a rope making 30 degrees with the horizontal. If the work done to move it in 15 m is 2000 J, find the tension in the rope.
To find the tension in the rope, we can use the formula for work:
Work = Force × Distance × cos(θ)
Where:
- Work is the amount of work done (2000 J in this case)
- Force is the tension in the rope (what we need to find)
- Distance is the distance the crate is moved (15 m in this case)
- θ is the angle between the force and the direction of motion (30 degrees in this case)
We can rearrange the formula to solve for the tension:
Force = Work / (Distance × cos(θ))
Now, let's substitute the values into the formula:
Force = 2000 J / (15 m × cos(30°))
To calculate the value, we need to find the cosine of 30 degrees. The cosine of 30 degrees is √3/2, which is approximately 0.866.
Force = 2000 J / (15 m × 0.866)
Now, we can calculate the value of the tension:
Force = 2000 J / 12.99 m
Therefore, the tension in the rope is approximately 154.73 Newtons (N).