Statics

Let’s say you have an object that is not accelerating. The only time an object doesn't accelerate is if the net force on it is zero. For example, it could be an object that is stationary...

• a book sitting on a table (upwards normal force equals the weight)
• a sign hanging from cables (upwards tension equals the weight)
• a helicopter that is hovering (lift equals weight)

...or it could be an object moving in a straight line with a constant speed...

• a car driving on a highway at a constant speed (the air resistance equals the friction of the tires pushing the car forward and the normal force equals the weight of a car)
• a skydiver who is falling at terminal velocity (air resistance equals the weight)
• an airplane flying straight and level (engine thrust forward equals the drag, and lift equals weight)

In all of these situations, the object in question is said to be in equilibrium.

Activities & Practice
to do as you read

Steps

Draw a free-body diagram, drawing all the forces acting on the object. (Usually there's just one object we care about, but occasionally there are more.) Remember, the tail of each force vector is drawn attached to the object feeling that force.

Break all the forces into components. In many problems these will be horizontal and vertical components, in some they will be North-South and East-West components. In both these cases, we usually call the two axes x and y. In problems involving ramps, we will break the forces into components parallel to and perpendicular to the ramp.

Sum the components. If one of the forces is unknown, but you know the net force, you can solve for the unknown. On the other hand, if you know all the forces, you can determine the net force.

Additional Activities & Practice

1. A spring is hanging vertically, and is 13 cm long. A 6.0-kilogram mass is hung from the spring, stretching the spring so it is now 17 cm long.

(a) How much does the 6.0-kilogram mass weigh?
(b) What is the stiffness (k) of the spring?
(c) If you hang a 18-kilogram mass from the spring, how long will the spring be?

2. A sign of mass 6.0 kilograms is hanging from a single rope. What is the tension in the rope?

3. A sign of mass 6.0 kg is hanging from two ropes, which are both vertical. What is the tension in each rope?

4. A sign of mass 6.0 kg is hanging from two ropes, which are both 25 degrees from vertical. What is the tension in each rope?

5. A 6.0-kg box is sitting on the floor. What is the magnitude of the normal force?

6. A 6.0-kg box is sitting on the floor. The coefficient of static friction between the box and the floor is 0.35, and the coefficient of kinetic friction is 0.25. If you push sideways on the box with a force of 8 Newtons, will the box start sliding or not?

7. A 6.0-kg box is sitting on the floor. The coefficient of static friction between the box and the floor is 0.35, and the coefficient of kinetic friction is 0.25. How hard do you need to push on the box (horizontally) for the box to start moving? How hard do you need to push on the box (horizontally) to slide the box at a constant velocity.

8. A ship has a mass of 500 tonnes, and it's floating on the ocean. (One tonne is 1000 kg.) (a) What is the weight of that ship? (b) What is the magnitude of the buoyant force?

9. Three dogs are fighting over a toy hedgehog. It's a three-way tie --- the hedgehog is staying stationary. Artemis is pulling with 34 N of force, straight to the north. Beelzebub is pulling with 22 N, 35 degrees south of east. How hard, and in what direction, is the third dog (Charlie) pulling?

10. A sign of mass 6.0 kg is hanging from two ropes, which are both 25 degrees from horizontal. What is the tension in each rope?