An airline pilot pulls her 12.0 kg rollaboard suitcase along the ground with a force of 25.0 N for 10.0 meters. The handle she pulls on makes an angle of 42.5 degrees with the horizontal. How much work does she do over the ten-meter distance?
Tried doing: (Cos(42.5) * 25N) * 10 = W
Didn't seem to work though?
W = (25*cos42.5) * 10 = 184.3 Joules.
Your setup for calculating the work done is almost correct, but there is a small mistake in the equation you used. Let me guide you through the correct calculation step by step.
To calculate the work done, we need to multiply the force applied by the displacement produced by that force. In this case, the force exerted by the pilot is 25.0 N and the displacement is 10.0 meters. However, we have to take into account the angle between the force and the displacement.
To find the component of the force in the direction of the displacement, we need to multiply the force magnitude by the cosine of the angle. So the equation should be:
Work (W) = Force (F) * displacement (d) * cos(angle)
Let's plug in the values to calculate the work done:
W = 25.0 N * 10.0 m * cos(42.5°)
To find the cosine of an angle, we need to use a scientific calculator or refer to a trigonometric table. In this case, cos(42.5°) is approximately 0.7314.
W = 25.0 N * 10.0 m * 0.7314
W ≈ 182.85 Joules
So, the pilot does approximately 182.85 Joules of work over the ten-meter distance.