A force of 20 N is applied to push a block across a horizontal floor for a distance of 5 m. If the force is applied at an angle of 30 degrees to the horizontal, calculate the work done.
Question
A force of 20 N is applied to push a block across a horizontal floor for a distance of 5 m. If the force is applied at an angle of 30 degrees to the horizontal, calculate the work done.
Solution
The work done by a force is given by the equation:
Work = Force x Distance x cos(θ)
where:
- Force is the magnitude of the force applied,
- Distance is the distance over which the force is applied, and
- θ is the angle between the direction of the force and the direction of motion.
In this case, the force (F) is 20 N, the distance (d) is 5 m, and the angle (θ) is 30 degrees.
First, we need to convert the angle from degrees to radians because the cosine function in most calculators uses radians, not degrees.
1 degree = π/180 radians
So, 30 degrees = 30*(π/180) = π/6 radians
Now we can substitute the values into the equation:
Work = 20 N x 5 m x cos(π/6) = 100 N.m x 0.866 = 86.6 Joules
So, the work done is 86.6 Joules.
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