A rope tows a box 4 m across a floor with a 20 N force, while 5 N of friction acts on the box against its motion.
Two forces, two works, one box. What did the box receive overall?
Each force does its own signed work on the box.
The rope's force acts with the motion: its work is 20 × 4 = 80, so +80 J.
Friction acts against the motion: its size of work is 5 × 4 = 20, so its work is -20 J.
Add the signed works: 80 + (-20) = 60. The box receives +60 J overall.
More forces add the same way, each with its own sign.
Forces that do zero work add nothing: the box's weight and the floor's normal force are perpendicular to the motion, so each contributes 0 J.
Keep each force's sign from its own direction, then let the addition settle the total.
A rope tows a wagon 6 m with a 25 N force while 9 N of friction acts against the motion. Calculate the net work done on the wagon.
Write down the values:
rope: 25 N with the motion; friction: 9 N against; d = 6 m
The rope's work: 25 × 6 = 150, so +150 J.
Friction's work: 9 × 6 = 54, so -54 J.
Write down the equation:
W_net = W_1 + W_2
Substitute in the values, and calculate:
W_net = 150 + (-54) = 96
The net work done on the wagon is +96 J.
A handle's force of 18 N moves a dolly 7 m, with the motion, against 6 N of friction. The floor's normal force is perpendicular to the motion. Calculate the net work done on the dolly.
Write down the values:
handle: 18 N with the motion; friction: 6 N against; normal force: perpendicular; d = 7 m
The handle's work: 18 × 7 = 126, so +126 J.
Friction's work: 6 × 7 = 42, so -42 J.
The normal force is perpendicular to the motion: 0 J.
Write down the equation:
W_net = W_1 + W_2 (zero-work forces add nothing)
Substitute in the values, and calculate:
W_net = 126 + (-42) + 0 = 84
The net work done on the dolly is +84 J.
A winch applies 40 N to a crate, with its motion, over 3 m, while 14 N of friction acts against the motion. Which sum gives the net work on the crate?
The same crate: the 40 N winch force with the motion and the 14 N friction against it, over 3 m. Enter the net work done on the crate in J.
A rowboat is towed 8 m to a dock: the towline applies 22 N with the motion, and water resistance of 13 N acts against it. Enter the net work done on the rowboat in J.
Ugo's wheelbarrow rolls 8 m along a path: his forward force on it is 35 N, and 11 N of friction acts against the motion. Enter the net work done on the wheelbarrow in J.
Four forces act on a van towed 20 m along a level road: the towline (forward), friction (backward), the van's weight (down), and the road's normal force (up). Which pair of forces contributes 0 J to the net work?
A loading cart is towed 12 m along a dock. The towline applies 28 N with the motion, rolling friction of 16 N acts against it, and the dock's normal force of 400 N acts upward. Enter the net work done on the cart in J.