A rope is used to pull a metal box 18.0 m across the floor. The rope is held at an angle of 46.0° with the floor and a force of 556 N is used. How much work does the force on the rope do?
Question
A rope is used to pull a metal box 18.0 m across the floor. The rope is held at an angle of 46.0° with the floor and a force of 556 N is used. How much work does the force on the rope do?
Solution
To solve this problem, we need to use the formula for work done, which is:
Work = Force x Distance x cos(θ)
where:
- Force = 556 N
- Distance = 18.0 m
- θ = 46.0°
First, we need to convert the angle from degrees to radians because the trigonometric functions in most calculators use radians.
1 radian = 180/π degrees So, 46.0° = 46.0 * π/180 = 0.802 rad
Now we can substitute the values into the formula:
Work = 556 N x 18.0 m x cos(0.802 rad)
Calculate the cosine:
cos(0.802 rad) = 0.696
Then multiply:
Work = 556 N x 18.0 m x 0.696 = 6967.2 Joules
So, the force on the rope does 6967.2 Joules of work.
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