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# Normal Force and Tension for AP Physics B & C

based on 2 ratings
By McGraw-Hill Professional
Updated on Feb 10, 2011

Practice problems for these concepts can be found at:

Free-Body Diagrams and Equilibrium Practice Problems for AP Physics B & C

### Normal Force

In Figure 10.2, a box is sitting on a table. The force of gravity pulls downward (as with the hippo, we've labeled this force "weight"). We know from experience that boxes sitting on tables do not accelerate downward; they remain where they are. Some force must oppose the downward pull of gravity.

This force is called the normal force,1 and it is abbreviated FN. In fact, whenever you push on a hard surface, that surface pushes back on you—it exerts a normal force. So, when you stand on the floor, the floor pushes up on you with the same amount of force with which gravity pulls you down, and, as a result, you don't fall through the floor.

The normal force is not always equal to the weight of an object! Think about this before we get to the practice problems.

### Tension

Tension is a force applied by a rope or string. Here are two of our favorite tension problems. The first is super easy, but a good introduction to tension; the second is more involved.

A box has a mass of 5 kg and is hung from t he ceiling by a rope. What is the tension in the rope?

Step 1: Free-body diagram.

Step 2: Vector components.

Hey! These vectors already line up. On to Step 3.

Step 3: Equations.

Remember, weight is equal to mass times the gravitational field, or mg.

Fnet,y = Tmg = 0
T – (5 kg) (10 N/kg) = 0

Step 4: Solve.

T = 50 N

The same box is now hung by two ropes. One makes a 45-degree angle with the ceiling; the other makes a 30-degree angle with the ceiling. What is the tension in each rope?

Step 1: Free-body diagram.

Step 2: Vector components.

Step 3: Equations.

Fnet,x = T1xT2x = 0.

And from vector analysis we know that

T1x = T1(cos 30°) and T2x = T2(cos 45°).

so,

T1(cos 30°) – T2(cos
45°) = 0.

Similarly, if we look at the y-direction,

Fnet,y = (T1y + T2y) – mg = 0.

and

T1y = T1(sin 30°) and T2y = T2(sin 45°)

Step 4: Solve.

We can solve Equation 1 and Equation 2 simultaneously and find T1 and T2. We'll let you do this on your own,2 but in case you want to check your answers, T1 = 37 N and T2 = 45 N. (These are reasonable answers, as the tension in each rope is the same power of 10 as the 50 N weight of the box.)

Steps 1, 2, and 3 are the important steps. Step 4 only involves math. "ONLY math?!?" you ask, incredulous. That's the toughest part!

Well, maybe for some people. Getting the actual correct answer does depend on your algebra skills. But, and this is important, this is AP Physics, NOT AP Algebra. The graders of the AP exam will assign most of the credit just for setting up the problem correctly! If you're stuck on the algebra, skip it! Come up with a reasonable answer for the tensions, and move on!

Practice problems for these concepts can be found at:

Free-Body Diagrams and Equilibrium Practice Problems for AP Physics

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