The observation deck of the CN Tower is approximately 345 m above ground level. Neglecting resistance due to the air, if a lead ball with a mass of 10kg is on the observation deck: a. Calculate its gravitational potential energy. [3.4x10* J] b. What's the lead ball's speed half way down? Calculate using two methods. [58m/s] i. Conservation of Energy ii. Kinematics c. Compare the sum of Ek and Eg at the halfway point to E, when it is on the observation deck.

Q1 An object with a mass 100 kg decrease in kinetic energy of 500 ki and an increase in potential energy of 1500 kJ. The initial velocity and elevation of the object, each relative to the surface of the earth, are 40 m/s and 30 m, respectively. Determine (a) the final velocity, in m/s. (b) the final elevation, in m

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2. A 3.2 kg ball that is moving straight upward has 17 J of kinetic energy and its total mechanical energy is 25 1. a. Find the gravitational potential energy of the ball. b. What is its height above the ground? c. What is the speed of the ball? d. What will be its gravitational energy when it is at Its highest point above the ground? e. What is the maximum height above the ground? f. What will be its speed Just before it lands on the ground? and Given: quired: ution:

Conservation of energy Suppose an object with mass m moves in a region R in a conservative force field given by F = -Vọ, where o is a potential function in a region R. The motion of the object is governed by Newton's Second Law of Motion, F = ma, where a is the acceleration. Suppose the object moves from point A to point B in R. dv a. Show that the equation of motion is m - -Vọ. dt 1 d 2 dt c. Take the dot product of both sides of the equation in part (a) with v(t) = r'(t) and integrate along a curve between A and B. Use part (b) and the fact that F is conservative to show that dv b. Show that - dt the total energy (kinetic plus potential) - m|v]² + q is the same at A and B. Conclude that because A and B are arbitrary, energy is conserved in R.

2. Consider the concepts of kinetic energy (KE) and gravitational potential energy (GPE) as you complete these questions. A ball is held 1.4 meters above the floor. Use the terms KE of GPE as your answers. A. When the ball is held motionless above the floor, the ball possesses only B. If the ball is dropped, its energy decreases as it falls. C. If the ball is dropped, its energy increases as it falls. D. In fact, in the absence of air resistance, the amount of impact with the floor. energy. energy when the ball is held motionless above the floor equals the amount of energy at

Superman can throw a ball (mass 145 g) 1000 m/s. Suppose Supermanthrows a ball straight up into the air at 1000 m/s. i. What is the initial kinetic energy of the ball? ii. How high would the ball go if the force ofgravity is constant F = −mg? (use conservation of energy and neglect air resistance). iii. How high would the ball go if you use F = − (GMEm/ r2) ? ME = 5.97 × 1024 kg, and assume the ball is thrown from rE = 6.37 × 106 m

A 1.5 kg ball is thrown upward with a velocity of 6 m/s. a). What is the kinetic energy of the ball as it is thrown upward? b). What is the gravitational potential energy of the ball when it reaches its highest point? c). To what height above the thrower’s hand will the ball rise? (for c only, round answer to nearest hundredth).

1. A roller-coaster car with a mass of 1200 kg starts at rest from a point 20 m above the ground. At point B, it is 9 m above the ground. [Express your answers in kilojoules (kJ).] a. What is the initial potential energy of the car? b. What is the potential energy at point B? c. If the initial kinetic energy was zero and the work done against friction between the starting point and point B is 40 000 J (40 kJ), what is the kinetic energy of the car at point B 2. The time required for one complete cycle of a mass oscillating at the end of a spring is 0.80 s. What is the frequency of oscillation?

QUESTION 9 While moving a package up and down on a storage shelf the mover does +500 J of work and gravity does-500 J of work. Which statement is true about the Potential Energy and the Kinetic Energy of the package: A. The Potential Energy of the package is decreased. B. The Potential Energy of the package is increased. C. The Kinetic Energy of the package is increased. D. The Kinetic Energy of the package is decreased. E, The Potential Energy of the package does not change.