A constant force of 40.7 N, directed at 29.9° from horizontal, pulls a mass of 13.7 kg horizontally a distance of 2.93 m. Calculate the work done by the force.
Force in direction of motion * distance
40.7 cos(29.9) * 2.93 Joules
To calculate the work done by a force, you can use the formula:
Work = Force * Distance * cos(θ)
where:
- Force is the magnitude of the force in Newtons (N),
- Distance is the distance over which the force is applied in meters (m),
- θ is the angle between the force and the direction of motion in degrees.
In this case, the force is 40.7 N, the distance is 2.93 m, and the angle is 29.9°.
First, convert the angle from degrees to radians:
θ_radians = θ * π/180
Substitute the given values into the formula:
Work = 40.7 N * 2.93 m * cos(29.9°)
Now, calculate the cosine of the angle (29.9°) using a calculator:
cos(29.9°) ≈ 0.8746
Substitute the value of cosine back into the formula:
Work = 40.7 N * 2.93 m * 0.8746
Calculate the final result:
Work = 111.2962 Joules
Therefore, the work done by the force is approximately 111.3 J.