A 300 N crate hangs from a crane cable while a worker steadies it from below, applying an 80 N upward force. The crate hangs still.
The cable's tension is not 300 N, because the worker carries part of the load.
Equilibrium tells you exactly how much the cable carries: the forces on a line must balance.
An object in equilibrium has zero net force, so the forces on any one line balance: up equals down, left equals right.
That balance turns an unknown force into arithmetic. Add up each direction, set the two sums equal, and solve for the missing force.
For the hanging crate, the upward forces are the cable's tension and the worker's 80 N. The downward force is the 300 N weight.
So tension + 80 = 300, which gives a tension of 220 N.
A 300 N crate hangs still from a cable while a worker applies an 80 N upward force to it. Calculate the cable's tension.
Write down the values in the question:
w = 300 N down
worker's force = 80 N up
T = ?
The crate is in equilibrium, so up balances down:
T + 80 = 300
Make T the subject:
T = 300 − 80
Simplify:
T = 220 N
The cable's tension is 220 N.
A 90 N crate rests on a floor while a rope applies a 40 N upward force to it. The crate is in equilibrium. Enter the normal force on the crate in N.
A 60 N sign hangs still from two vertical chains. One chain's tension is 35 N. Calculate the other chain's tension.
Write down the values in the question:
w = 60 N down
first chain's tension = 35 N up
T = ?
The sign is in equilibrium, so up balances down:
T + 35 = 60
Make T the subject:
T = 60 − 35
Simplify:
T = 25 N
The other chain's tension is 25 N.
A 180 N flower basket hangs still, held by a hook and a support pole. The pole applies a 75 N upward force. Enter the hook's tension in N.
The same balance works on a horizontal line, with leftward forces against rightward forces.
And it works while things move. An object moving at constant velocity is in equilibrium too: its net force is zero, so each line's forces balance just the same.
A wagon rolls at constant velocity. A rope applies 75 N forward; friction applies 48 N backward; a headwind applies an unknown backward force. Enter the headwind's force in N.
A 240 N generator rests on a floor while a technician presses down on it with 35 N. It stays in equilibrium. Enter the normal force on the generator in N.
A 420 N crate hangs still from a cable while a worker applies a 95 N upward force to it. Enter the cable's tension in N.
A parade float moves at constant velocity. The tow rope applies 130 N forward, rolling friction applies 45 N backward, and a drag chute applies an unknown backward force. Enter the chute's force in N.