1. Ch. 7 Forces and Motion in Two Dimensions
Milbank High School

2. Sec. 7.1 Forces in Two Dimensions
Objectives
Determine the force that produces equilibrium when three forces act on an object
Analyze the motion of an object on an inclined plane with and without friction

3. What is meant by two dimensions?
Consider a golf ball being hit out of a sand trap
It has a horizontal force AND a vertical force
We can solve for many different things using a combination of forces and vectors
Height of the ball
Time in the air
Velocity when it hits the ground

4. Equilibrant A force exerted on an object to produce equilibrium
Same magnitude as the resultant force but opposite in direction

5. Solving problems in two dimensions
Draw it out!
Rearrange vectors to form a triangle if possible
Solve for the resultant vector
Opposite in direction
Example Problem Pg. 151

6. Sec. 7.2 Projectile Motion Objectives
Recognize that the vertical and horizontal motions of a projectile are independent
Relate the height, time in the air, and the initial velocity of a projectile using its vertical motion, then determine the range.
Explain how the shape of the trajectory of a moving object depends upon the frame of reference from which it is observed.

7. Projectiles have independent motions!
Projectiles have two velocities, one in the “x” direction, and one in the “y” direction
x is always constant
y will be changing due to the acceleration due to gravity

8. Displacement y displacement x displacement x = vxot v = 25m/s 
y = yo - 1/2gt2
x displacement
x = vxot
v = 25m/s 

9. Velocity of projectiles launched horizontally
vx = initial velocity
vy = (-g)t
v = resultant velocity vector
Example Pg. 157

10. Effects of air resistance
We ignore the effects of air resistance for these problems
Sometimes it would make a large difference, other times it wouldn’t
Many projectiles modified so that they reduce air resistance

11. Projectiles launched at an Angle
Usually given angle of launch and velocity
What do we have to find?
Maximum height
Range
Horizontal distance
Flight time
hang time

12. Projectiles Launched at an Angle
Two initial velocity components
vxo
vyo
How do we find these?
vx = vo(cosθ)
vy = vo(sinθ)

13. Projectiles Launched at an Angle
tup = vyo/g
ttotal = 2(tup)
Peak Height
y = vyot - ½gt2
Range
R = vxot

14. Projectiles launched at an Angle
The Flight of a Ball
Example Problem Pg. 159

15. Sec. 7.3 Circular Motion Objectives
Explain the acceleration of an object moving in a circle at constant speed
Describe how centripetal acceleration depends upon the object’s speed and the radius of the circle
Recognize the direction of the force that causes centripetal acceleration
Explain how the rate of circular motion is changed by exerting torque on it.

16. Uniform Circular Motion
Movement of an object at constant speed around a circle with a fixed radius
Merry-go-round
Circumference = 2*pi*Radius

17. Vectors

18. Acceleration
Which direction?
Always towards
the center

19. Centripetal Force “Center seeking”
Net force towards the center that causes the object to try to seek the center
What force is pulling it in?
As a bucket of water is
tied to a string and spun
in a circle, the force of tension
acting upon the bucket provides
the centripetal force required for
circular motion.

20. Net Force

21. Example Problem Pg. 165