Chapter 7
Forces In Two Dimensions
Equilibrant:
Motion along an inclined plane
y
Θ
Θ
x
PSS for Inclined Planes
1. Sketch the problem
2. Choose a coordinate system with the x3.
4.
5.
6.
axis along the incline
Identify and draw the right triangle.
Use trig to resolve the vectors into
components.
Draw your force diagram with the
components.
Solve as previously.
7.2 Projectile Motion
A. Independence of motion in two dimensions.
- A projectile launched horizontally has the same
motion as an object that is dropped.
1. Motion in two dimensions can be solved be
breaking the problem into two one-dimensional
problems: A horizontal problem and a vertical
problem.
2. The vertical motion of a projectile is exactly the
same as an object thrown or dropped straight up or
down.
3. The horizontal motion of a projectile
is the same as solving a constant
velocity problem.
4. Both motions are connected through
time. Solving for time in one dimension
automatically gives you the time in the
other.
B. Projectile Launched horizontally.
- Has no initial vertical velocity
- Downward velocity increases due to
gravity (it is accelerated at a rate of 9.80
m/s2).
Example:
A stone is thrown horizontally at 15.0 m/s from
the top of a cliff 44 m high.
a. How far from the base of the cliff does it hit?
b. How fast is it moving just before it hits?
PSS - Projectile Motion
1.
2.
3.
4.
5.
Sketch the problem
List the knowns and unknowns.
Use the equation for the y – position to get and
solve an equation for time.
Use kinematic equations in the x – direction to
solve for range.
For final velocity, put the components of v
together using Pythagorean relationship.
v = √(vx2 + vy2)