Chapter 7 Motion and Forces in Two Dimensions

1. Chapter 7 Motion and Forces in Two Dimensions Quiz 7

2. Chapter 7 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 • Recognize that the vertical and horizontal motions of a projectile are independent

3. Chapter 7 Objectives • Relate the height, time in the air, and initial vertical velocity 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 • Explain the acceleration of an object moving in a circle at constant speed

4. Chapter 7 Objectives • 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

5. Normal Force

6. Take note of the Vectors • The Normal force is directed at 90 degrees, some of the weight of the object is not supported by the plane

7. Take note of the Vectors • This means that if the friction force is not large enough, the block will slide

8. Normal Force Question • If the angle of incline is 30 degrees, what % of the weight is supported by the normal force? What % is “falling/sliding” down the ramp?

9. Answer Normal Force Cos 30 Supported 30 Sin 30 Falling

10. Question • An penguin of mass 3.5 kg is resting on an icy inclined plane. The Us value between the penguin’s feet and the ice is 0.25. If the angle of incline is 20 degrees, analyze the normal force to determine how much of the penguin’s weight is falling and determine whether the friction value is large enough.

11. Projectile Motion • Refers to objects in free fall with a horizontal velocity as well • Actual velocity of object depends on • Magnitude of X (Constant throughout) • Magnitude of Y (Constantly changing)

12. Projectile Motion • Acceleration of object only affects the Y axis • -9.8 m/s2 • At peak of throw, Y axis velocity is 0 m/s, but acceleration is still 9.8 m/s2. • Only force that acts on projectile is gravity. • If air resistance is ignored • Angle of projectile varies time of flight and range

13. Projectile Motion Simulator

14. What does each represent? Which are equivalent to one another? (On quiz)

15. Centripetal Acceleration • Acceleration towards the center of a circular path (directed at 90 degrees to path of motion) • Ac = V2/ R • We will tackle more with this idea when it comes to universal gravitation • Inertia + Centripetal acceleration results in orbits

16. Centripetal Acceleration • How does changing the velocity of the object affect the Ac? • How does changing the radius of the rotating object affect the Ac? • If you double the radius of the rotating object, what happens to the Ac? • For a roller coaster which travels at 30 m/s, what is the maximum radius for 1 G?

17. Centripetal Acceleration • The force that causes the Ac is in the same direction as the acceleration. • When a merry-go-round is spinning, your inertia carries you off and without a force to maintain you, you slide off. • Future space colonies will rotate to create artificial gravity through Centripetal Acceleration • Centrifugal force? What force! (inertia!)

18. Torque • Torque is a force directed at 90 degrees to the path of motion (causes circular motion) • Torque is equal to the Force times the Distance away it is applied • Torque = F (perpendicular) x Distance (From Axis) • Larger torques are produced by increasing the distance away