Notes 5.2: Work and Kinetic Energy An Adventure created by Billy J. Jenkins

Objective: Understand the Work-Kinetic Energy Theorem and how it is a useful tool for problem solving Analyze the work done by gravitational forces. Analyze the work done by a spring force. Learn how power is the rate of transfer of energy.

Work – Kinetic Energy Theorem:   Idea: Force is a vector, work and energy are scalars. Thus, it is often easier to solve problems using energy considerations instead of using Newton's laws (i.e. it is easier to work with scalars than vectors).

The energy associated with the work done by the net force does not disappear after the net force is removed (or becomes zero), it is transformed into the Kinetic Energy of the body. We call this the Work-Energy Theorem. NOTE: You can get a negative work. If the net work done is negative, then the kinetic energy of the object decreases by that amount of work.

Sample Problem I: A person with a mass of 60.0 kg is traveling at 18 m/s. How much kinetic energy does this person have? How much work is required to stop the person? Calculate the force required to stop the person if the stopping distance is 50.0 m.

CHECKPOINT 1: What is the work-kinetic energy theorem? 2. What is the equation for the work-kinetic energy theorem? What is the importance of the work-kinetic energy theorem? What does it mean to have negative work?

Work done by Gravity: Previously we saw that the Earth exerts a gravitational force of F g = m g on all objects. How can we use this information to determine the work that the Earth’s gravitational force does (recall that W=Fd)? 𝑊 𝑔 = 𝐹 𝑔 𝑑 𝑊 𝑔 =𝑚𝑔𝑑 m = mass g = 9.8 𝑚 𝑠 2 d = displacement

Sample Problem 2: The bowler lifts a 4.5 kg bowling ball from the rack to his chest, a vertical distance of 0.5 m. What is the work done on the bowling ball by the bowler?

Power: Power is how fast work is done by a force. P = power W = work ∆t = time

Instantaneous Power: We can also find the power of an object at an instant as long as we know the force and the velocity of the object through the equation: 𝑃=𝐹∙𝑣 P = power F = force v = velocity

Sample Problem 3: An electric motor lifts a roller-coaster car that weights 10,000 N to the top of the first hill that is 20 m above the ground. To add suspense, the ride up takes 150 s. Calculate the work by the motor. Calculate the power of the motor.

CHECK POINT 2: What is the equation for the work done by a gravitational force? What is power? What is the equation for average power? What is the equation for instantaneous power? What is the SI Unit for power?