You pull your little sister across a flat snowy field on a sled. Your sister plus the sled have a mass of 39 kg. The rope is at an angle of 39 degrees to the ground. As you pull with a force of 31 N, the sled travels a distance of 47 m.
To find the work done in pulling the sled, we need to calculate the force component in the direction of motion and multiply it by the distance traveled. The force component can be determined using trigonometry.
1. Calculate the force component in the direction of motion:
- Firstly, calculate the horizontal component of the force by multiplying the force magnitude (31 N) by the cosine of the angle (39 degrees).
Horizontal force = 31 N * cos(39 degrees)
- Secondly, multiply the result by -1 because the force is in the opposite direction to the motion of the sled.
Horizontal force = -1 * (31 N * cos(39 degrees))
2. Calculate the work done:
- Multiply the horizontal force by the distance traveled.
Work = Horizontal force * distance
- Plug in the values:
Work = (-1 * (31 N * cos(39 degrees))) * 47 m
Now, let's calculate the work done using these steps:
1. Calculate the horizontal force:
Horizontal force = -1 * (31 N * cos(39 degrees)) = -23.63 N (round to two decimal places)
2. Calculate the work done:
Work = -23.63 N * 47 m = -1111.61 J (round to two decimal places)
Therefore, the work done in pulling the sled is approximately -1111.61 Joules. The negative sign indicates that the force is opposite to the direction of motion, which means work is being done against the force.