# Force and Acceleration

### Newton's Second Law of Motion

## Learning Targets

- I can interpret and construct a force (free-body) diagram.
- I can diagram and calculate the components of force acting in two dimensions.
- I can describe the relationship between net force, mass, and acceleration.
- I can calculate the net force, mass, or acceleration of an object.
- I can explain the difference between mass and weight given a changing gravitational field.
- I can calculate apparent weight given a situation of vertical acceleration.
- I can evaluate and develop a mathematical model for elastic (spring) forces.
- I can predict the force required to slide an object relating to the coefficient of friction.
- I can predict an object's motion and the associated forces of objects moving in a circle.

## Formulas

- Fnet = m a
- a = Δv / Δt
- Δx= ½ at2 (if v0 = 0)
- v12 = v02 + 2a (Δx)
- Felastic = k Δx
- Fk = μkFN
- ac = v2 / r
- Fc = mv2 / r

## Vocabulary

**circular-**have the form of a circle**centripetal**-a force that acts on a body moving in a circular path and is directed towards the center around which the body is moving.

**centrifugal**-moving or tending to move toward a center**free-body diagram**-diagrams used to show the relative magnitude and direction of all forces acting upon object in a given situation.**friction**-the resistance that one surface or object encounters when moving over another.**kinetic**-of, relating to, or resulting from motion**static**-lacking in movement, action, or change, especially in a way viewed as undesirable or uninteresting**linear**-arranged in or extending along a straight or nearly straight line**normal force**-the component, perpendicular to the surface of contact, of the contact force exerted on an object by, for example, the surface of a floor or wall, preventing the object from falling**net force**-the overall force acting on an object**tangent**-a straight line or plane that touches a curve or curved surface at a point, but if extended does not cross it at that point**torque**-a twisting force that tends to cause rotation**weight**-a relative mass or the quantity of matter contained by it, giving rise to a downward force**apparent**-clearly visible or understood, obvious**weightlessness**-having little weight or lacking apparent gravitational pull

## Practice Problem #1

What is the estimated acceleration due to the gravitational force on the moon if a person on Earth weighs 550 N- but only 75 N on the Moon?

## Practice Problem #2

A rider on a motorcycle with a combined mass of 300 kg are going down the road at 40 m/s. The rider wants to stop and applies the brakes until coming to rest. What force will the brakes need to apply in order for the rider to stop in a distance of 150 m?

## Practice Problem #3

Suppose a net force of 34 N is applied horizontally while pushing a desk weighing 545 N. Assuming there is no friction, what is the displacement of the desk after 10 seconds?

## Main Points

This unit covers:

- problems involving gravitational forces, elastic forces, and frictional forces.
- calculating the weight using force diagrams and Newton's laws of motion.
- the difference between mass and weight.
- kinetic and friction forces
- net forces acting in two dimensions with vector addition trigonometry or diagrams.
- solving for net force, final velocity, time , displacement, and acceleration for objects sliding down different types of inclines.
- calculating centripetal force by using a separate equation.