1. Forces, Gravity, and Trigonometry

2. Gravity What is Gravity?
It is the Attracting force exerted by EVERY object on every other object.

3. Gravity
The Law of Universal gravitation states that the amount of gravitation force between two objects depends on:
1) The mass of both objects
2) The distance apart

4. Example Answer 1.57 x 1017 N G = 6.67 x 10-11 Nm2 Kg2 Distance =
MASS =
5.972 × 1024 kg
MASS =
5.683 × 1026 kg

5. MASS =
37 kg
Distance = m
Distance =
60 Feet
MASS =
0.17 kg
Answer
1.25 x N

6. G-Forces
G-Forces are used to describe any force by associating it with the gravity of the Earth.
1 G is equal to the force of gravity at the Earth's surface.
2 G’s would be as if there were TWO Earths pulling on you.

7. Types of G’s at Kennywood
Horizontal G’s – Forces that you experience from side to side.
Vertical G’s – Forces that you experience Up and down.

8. Centrifugal Force:
It is the Apparent Force that pushes an object AWAY from the center of a curve.

9. Centrifugal Force:

10. Centripetal Force:
It is the force that Pulls an object to move TOWARDS the center of a curve.

11. Centripetal Force:

12. To Travel in a Circular Path:
Centripetal Force must EQUAL the Centrifugal Force.

13. Using the Gravity Constant
Acceleration of Gravity (g)
9.8 m s2
This number was calculated and found by using a Pendulum.
A Pendulum is constantly FALLING to the Earth because of Gravity.

14. Using the Gravity Constant
Length of Pendulum (L) = T2 x g
4 x ( π)2
Acceleration of Gravity (g) = 4L ( π)2 T2
Acceleration due to Gravity (g) = 9.8 m/s2
A Period (T) = the time required to complete one swing
Length of the Pendulum (L) = the length of the total pendulum (string and Bob)

15. Example:
A child’s swing has a Period of 2.28 seconds. Determine the Length of the chain?
Length of Pendulum (L) = T2 x g
4 x ( π)2
(L) = (2.28 sec)2 x m x ___1____
S x ( π)2
(L) = m

16. Finding Height using Trigonometry
(ANGLES are represented with the GREEK LETTER θ)
Hypotenuse (H)
Opposite Side (O)
COS θ
SIN θ
TAN θ θ
Adjacent Side (A)

17. Finding Height using Trigonometry
TAN θ = O ÷ A
TAN θ = H ÷ D
Finding Height using Trigonometry
H = TAN θ x D
Hypotenuse (H)
Opposite Side (O)
Height (H) θ
Distant Away (D)
Adjacent Side (A)

18. Finding Height for GPE Calculations
Step 1: Measure away FROM the Object and record the distance
(The taller the object, the farther away you should measure)
Step 2: Get as close to the ground as possible and measure the ANGLE to the TOP of the object

19. Finding Height for GPE Calculations
Step3: Change the ANGLE from Degrees to TAN of the angle. Use your Calculator’s TAN button or the Table of Tans
Step4: Multiply the Tan θ by the Distance away to get the height of the object.