A sled is dragged along a horizontal path at a constant speed of 1.5 m/s by a rope that is inclined at an angle of 30.0° with respect to the horizontal (the figure below). The total weight of the sled is 470 N. The tension in the rope is 240 N. How much work is done by the rope on the sled in a time interval of 15.0 s
To find the work done by the rope on the sled, we need to calculate the force exerted by the rope in the direction of motion and multiply it by the displacement.
First, let's determine the force exerted by the rope in the direction of motion. We can use trigonometry to find the horizontal component of the tension force. The horizontal component is given by:
Force_horizontal = Tension * cos(angle)
where Tension is the tension in the rope and angle is the angle the rope makes with the horizontal.
Substituting the given values, we have:
Force_horizontal = 240 N * cos(30°)
Next, we move onto calculating the displacement. The sled is dragged along a horizontal path at a constant speed, which means the displacement is equal to the distance traveled. We can calculate the distance traveled using the formula:
Distance = Speed * Time
Substituting the given values, we have:
Distance = 1.5 m/s * 15.0 s
Now, we can calculate the work done by multiplying the force and displacement:
Work = Force_horizontal * Distance
Substituting the values we calculated earlier, we have:
Work = (240 N * cos(30°)) * (1.5 m/s * 15.0 s)
Calculating the expression in parentheses first:
Work = (240 N * 0.866) * (22.5 m)
Finally, multiplying the values:
Work = 5634 Joules
Therefore, the work done by the rope on the sled in a time interval of 15.0 s is 5634 Joules.