Mike pulls a 4.5 kg sled across level snow with a force of 250 N along a rope that is 35.0° above the horizontal. If the sled moves a distance of 63.8 m, how much work does Mike do?
please show steps/equation!
To find the work done by Mike, we can use the equation:
Work = Force * Distance * cos(theta)
Where:
- Work is the work done by Mike in joules (J)
- Force is the applied force by Mike in newtons (N)
- Distance is the distance covered by the sled in meters (m)
- theta is the angle between the applied force and the direction of motion of the sled in degrees
In this problem:
- Force = 250 N (given)
- Distance = 63.8 m (given)
- theta = 35.0° (given)
Step 1: Convert theta from degrees to radians
theta_radians = theta * (π / 180)
theta_radians = 35.0° * (π / 180)
theta_radians ≈ 0.6109 radians
Step 2: Calculate the work done
Work = 250 N * 63.8 m * cos(theta_radians)
Calculating the value of cos(theta_radians):
cos(0.6109) ≈ 0.8053
Work ≈ 250 N * 63.8 m * 0.8053
Work ≈ 12825 J
Therefore, Mike does approximately 12825 joules of work to pull the sled across the snow.