Download ∑ = F ma F ma ∑ = μ

Forces
Force
Newton’s 1st Law
Newton’s 2nd Law
Newton’s 3rd Law
F
Any push or pull
Law of inertia (Restatement of Galileo’s principle of inertia)
 F  ma
Equal and opposite forces. For every action force there is an equal & opposite reaction force.
Forces come in action - reaction pairs.
Key to all problems.  Fx
 F
 F in x direction on traditional coordinate axis.  Fy  F in y direction.
 F parallel to a slope (direction of motion).  F  F perpendicular to slope.
 F  ma
Sum of force is Net Force. You may need to solve for a using the kinematic equations, then solve
for force, or given force you solve for a and then use it in the kinematic equations to find v, x, or t.
1
v = 0 (object is static)
a=0
F = 0
2
Velocity is constant
a=0
F = 0
3
v increasing or decreasing
a = +/- a constant value
F = m a
FP
Push or Pull.
Fg
Force of gravity.
FT
Tension is a rope, string, etc. This force has no equation. You either solve for it, or it cancels, or it’s given.
FN
Force Normal. A contact force, always perpendicular to the surface. (On a tilted surface use  F  &  F)
Ffr
Fg  mg
F   FN
Friction force. fr
Always opposes motion. Static friction: not moving. Kinetic friction: object moving.
. Kinetic friction is not as strong as static friction, but it still opposes motion.
Far
Force of air resistance. This force has no equation. You either solve for it, or it cancels, or it’s given.
Fc
Force Centripetal. It is the F in circular motion problems. So Fc can be any force that keeps an object in
circular motion. Always pointed towards the center (centripetal) and is constant. Velocity is also constant and
pointed tangent to the curve.
Object on a Horizontal Surface:
Scenarios:
1. Friction and the forward force are equal. Object could be standing still or moving at constant velocity.
∑
∑
2. Object being pushed has been let go and the only force acting on it is friction to slow it down.
∑
∑
3. Object is accelerating in the forward direction while overcoming friction. If there is no friction involved, just
eliminate it from the free body diagram and equations.
∑
∑
Lawn Mower Problem:
Exactly same problem as the object on a horizontal surface however the force pushing (or pulling) is at some angle and
must be split into forces in the x-direction and y-direction. In these cases, we will call the retarding force, friction; assume
the object is moving at a constant velocity; and consider the angle is between the Fp vector and the horizontal ground.
∑
∑
If the object is being pulled along the ground with some force pulling, the x-direction equation will not differ, however the
y-direction equation will be different due to the normal force being lessened due to the pulling vector being pointed
upward.
∑
∑
Object on a hill problem:
F parallel = Fg sin Θ (x-direction)
F perpendicular = Fg cos Θ (y-direction)
3 Scenarios:
1. No friction.
∑
∑
∑
2. Velocity = 0 or velocity is constant.
∑
∑
From the y-direction: ∑
∑
3. Accelerating with friction present.
∑
∑
From the y-direction: ∑
∑
)
Horizontal Pulley Problem:
Tension is the same for both blocks. Rearrange to get equations in terms of tension, then set them equal so tension
cancels. Then substitute and solve.
Box A:
∑
∑
Box B:
∑
Combine and solve:
=
+
=
Pulley Problem:
If it doesn’t say which is more massive, pick one. In this case I picked B as the heavier object and used this to set the
direction of motion. Find what does not change, T, and rearrange in terms of this. Set the equations as equal, substitute
and solve.
Box A:
∑
Box B:
∑
Combine and solve:
+
=