A man carries a 10 kg sack of groceries in his arms with a force of 50 N as he walks forward a distance of 10 m. How much work has he done?
To determine the amount of work the man has done, you can use the formula for work:
Work = Force × Distance × cos(θ)
where:
- Work is the amount of work done (in joules, J)
- Force is the applied force (in newtons, N)
- Distance is the distance moved in the direction of the force (in meters, m)
- θ is the angle between the applied force and the direction of motion (in degrees)
Since the man is walking forward, the force and the direction of motion are aligned, so θ = 0 degrees. Therefore, the cosine of 0 degrees is 1, so cos(0) = 1. In this case, you can ignore the angle term since the cosine of 0 degrees is 1.
Plugging in the given values:
Force = 50 N
Distance = 10 m
θ = 0 degrees (ignored)
Work = 50 N × 10 m × 1
= 500 J
Therefore, the man has done 500 joules of work while carrying the groceries.