Question

Calculate the work done in the following situations. A sled is pulled \(10 \mathrm{m}\) along horizontal ground with a constant force of \(5 \mathrm{N}\) at an angle of \(45^{\circ}\) above the horizontal.

Short answer

Answer: The work done in pulling the sled is 25√2 J.

Step-by-step solution

List the given information

We are provided with the following information: - Distance: \(d = 10 \mathrm{m}\) - Force: \(F = 5 \mathrm{N}\) - Angle: \(\theta = 45^{\circ}\)

Convert the angle from degrees to radians

For further calculations, we need to convert the given angle from degrees to radians using the formula: Radians = Degrees * \(\frac{\pi}{180}\) Radians = \(45^{\circ} * \frac{\pi}{180}\) = \(\frac{\pi}{4}\) radians

Calculate the work done

Now we can calculate the work done using the formula: \(W = F\cdot d\cdot \cos\theta\) W = \((5\,\mathrm{N})\cdot(10\,\mathrm{m})\cdot\cos\left(\frac{\pi}{4}\right)\) The value for \(\cos\left(\frac{\pi}{4}\right)\) is \(\frac{\sqrt{2}}{2}\), so we have: W = \((5\,\mathrm{N})\cdot(10\,\mathrm{m})\cdot\left(\frac{\sqrt{2}}{2}\right)\) W = 25\(\sqrt{2}\,\mathrm{J}\) Hence, the work done in pulling the sled is 25\(\sqrt{2}\,\mathrm{J}\).