June drags a sled by a rope that applies a 65 N force at 37° above the horizontal. Take sin 37° = 0.60 and cos 37° = 0.80. Enter the component that moves the sled forward, in N.
A canoe is towed from a lakeside path. The rope's force on the canoe is 100 N, at 60° to the canoe's motion, and the canoe moves 5 m.
Only the parallel component does work. Exactly how many joules is that here?
Resolve the rope's force. The component parallel to the motion is the full force times the cosine of the angle: 100 × cos 60°.
Your calculator gives cos 60° as 0.5.
So the parallel component is 100 × 0.5 = 50, which is 50 N.
That component acts through the 5 m: the work is 50 × 5 = 250, so 250 J.
θ is the angle between the force and the direction of motion.
The equation contains the old cases. At θ = 0° the cosine is 1, and W = Fd returns. At θ = 90° the cosine is 0, and the work is zero: the perpendicular case.
A rope at 60° to a loaded sledge's motion applies 40 N while the sledge moves 7 m. Calculate the work done by the rope's force on the sledge.
Write down the values:
F = 40 N, d = 7 m, θ = 60°, W = ?
Write down the equation:
W = Fd cos θ
The parallel component first: 40 × 0.5 = 20.
Substitute in the values, and calculate:
W = 20 × 7 = 140
The work done is 140 J.
A harness strap at 30° to a cart's motion applies 90 N while the cart moves 4 m. Calculate the work done by the strap's force on the cart, to the nearest joule.
Write down the values:
F = 90 N, d = 4 m, θ = 30°, W = ?
Write down the equation:
W = Fd cos θ
The parallel component first, with cos 30° = 0.866 from the calculator: 90 × 0.866 = 77.94.
Substitute in the values, and calculate:
W = 77.94 × 4 = 311.76
The work done is about 312 J.
Talia tows a toboggan with a rope at 60° to its motion, applying 30 N while the toboggan moves 8 m. Enter the work done by the rope's force on the toboggan in J.
Ugo says: 'A rope's force of 20 N at 60° to a wagon's motion does 10 J of work over each 1 m the wagon moves.' Is Ugo correct?
A mover's slanted strap force on a dresser keeps the same size, but she lowers the strap so the angle θ to the motion shrinks toward 0°. What happens to the work done over the same distance?
A park crew tows a fallen log with a cable at 60° to the log's motion, applying 90 N while the log slides 11 m. Enter the work done by the cable's force on the log in J.
A rescue sledge is towed with a strap at 30° to its motion: the force is 70 N and the sledge moves 10 m. Enter the work done by the strap's force on the sledge in J, to the nearest joule. Answers within 1 J are accepted.
Soren computes the work done by a 40 N rope at 50° to a cart's motion while the cart moves 3 m. Which calculation is correct?