Tension: Force That Results From Stretching

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Tension Force

Tension or tensile force in a rope or stand that results from that object being stretched. See how to approach a variety of tension problems here.

Tension (F_T) is the pulling force exerted by a strand (ie. string) in the opposite direction of a force applied. (Unit: N)

When tension up is equal to weight down

There is no net force and therefore no acceleration. The state of motion remains. Inertia would keep a moving object moving and an object at rest would remain at rest.

Static Equilibrium: When tension up is equal to weight down but the object is at rest (no motion)
Dynamic Equilibrium: When tension up is equal to weight down an object moves with constant velocity

When tension up is greater than weight down

Net force (F_net) would be up
An object would accelerate up
The amount of acceleration would depend on mass (m) following Newton's Second Law (F_net = ma)

When tension up is less than weight down

Net force (F_net) would be down
An object would accelerate down
The amount of acceleration would depend on mass (m) following Newton's Second Law (F_net = ma)

When tension up is less than weight down but on a horizontal surface

If the object comes to rest on a horizontal surface, normal force would make up the difference putting the system in equilibrium
F_T + F_N = -F_W
Tension and normal force up would equal the magnitude of weight down. The negative in the equation representing the opposite direction

Example Problems

Q1: What is the tension in the rope necessary to lift a 150 N object at a constant velocity up?

Answer: 150 N

Because constant motion means there is no acceleration so net force equals zero. In order to have no net force the force of tension up must equal the weight down.

Q2: What is the normal force of a 15 kg object when on the ground and a rope with 50N of tension is pulling up?

Because the object is at rest the net force is zero. The weight down is:

F_w = mg

F_w = (15)(10) = 150 N down

The force up must be equal since the object is at rest.

Sum of forces = 0 so force up must equal force down

Normal Force Up + Tension Up = Weight Down

F_N + F_T = F_w

F_N + 50 = 150

F_N = 100 – 50 = 100 N Up

Answer: 100 N Up

Tension with Multiple Vertical Ropes

When there is one rope up all of the weight is supported by that one rope and the tension is equal to weight.

When there are multiple ropes all directed straight up each will support an equal amount of weight. To find this you would divide the weight by number of strands.

Q3: Susie, who weighs 650 N, suspends herself from the monkey bars holding herself up with both hands horizontal. What is the tension in each arm?

650 N total weight and two arms and the force is up opposing the weight down.

650/2 = 325 N up

Answer: 325 N Up

Divide by the number of ropes for tension in each when you have multiple ropes suspending an object vertically.

Tension at Equal Angles From the Vertical

As the angle from the vertical increases tension increases. Tension is the most when the painting is at the highest point in the animation and the angle (Ө) is the most.