DAY 39

#Goals: SWBAT...

1. Write & understand the equations for Kinetic and Potential Energy

2. Set an appropriate reference (zero) line.

3. Solve KE and PE problems

***Warm up check for Day 30-38 (9 warm-ups total) will be today, Monday 03/05***

Warm-Up (4min): Review KE and PE from this weekend's learning at home videos

1. Write the equation for Potential Energy (PE_g)

2. If you're measuring the PE_g of a basketball being thrown above the ground, which location of the reference (zero) line makes the most sense?

i. setting the line at the ball's highest possible position?

ii. setting the line at the ball's lowest possible position?

iii. setting the line at the average of the ball's lowest and highest positions?

3. Write the equation for Kinetic Energy (KE).

4. If you double the velocity of an object, the KE value quadruples. If instead, you triple the velocity, what happens to the value of the KE? Hint: think about what the v² part of the equation means....

5. Is PE_g a vector or scalar? What about KE?

CLASSWORK

1. #039A: Potential Energy: Notes

• Definition: Potential energy is the stored energy of position possessed by an object.
• What does that mean? There is a direct relation between gravitational potential energy and the mass of an object. More massive objects have greater gravitational potential energy. There is also a direct relation between gravitational potential energy and the height of an object. The higher that an object is elevated, the greater the gravitational potential energy.
• Equation: PEg = mass • gravity • height
• or... PEg = m • g • h
• In the above equation, m represents the mass of the object, h represents the height of the object and grepresents the gravitational field strength (9.8 N/kg on Earth) - sometimes referred to as the acceleration of gravity
• Check for Understanding: If you double the height of an object, what happens to the PE_g?

2. #039B: Kinetic Energy: Notes

• Definition: Kinetic energy is the energy of motion
  • The kinetic energy of an object is directly proportional to the square of its speed.
  • That means that for a twofold increase in speed, the kinetic energy will increase by a factor of four. For a threefold increase in speed, the kinetic energy will increase by a factor of nine. And for a fourfold increase in speed, the kinetic energy will increase by a factor of __________. The kinetic energy is dependent upon the square of the speed.
• Equation: KE = 1/2 • m • v2
• where m = mass of object
• v = speed of object
  • You can often trade KE for PE, and vise versa. We'll learn more about that kind of Conservation of _________ tomorrow

3. #039C: PE_g and KE Practice Problems

1. A cart is loaded with a brick and pulled at constant speed along an inclined plane to the height of a seat-top. If the mass of the loaded cart is 3.0 kg and the height of the seat top is 0.45 meters, then what is the potential energy of the loaded cart at the height of the seat-top?

2. If a force of 14.7 N is used to drag the loaded cart (from previous question) along the incline for a distance of 0.90 meters, then how much work is done on the loaded cart?

***Note that the work done to lift the loaded cart up the inclined plane at constant speed is equal to the potential energy change of the cart. This is not coincidental! More on Mechanical Energy, and how energies change from one type to another...tomorrow. ***

3. Determine the kinetic energy of a 625-kg roller coaster car that is moving with a speed of 18.3 m/s.

4. If the roller coaster car in the above problem were moving with twice the speed, then what would be its new kinetic energy?

5. Missy Diwater, the former platform diver for the Ringling Brother's Circus, had a kinetic energy of 12,000-J just prior to hitting the bucket of water. If Missy's mass is 40-kg, then what is her speed?

6. A 900-kg compact car moving at 60 mi/hr has approximately 320 000 Joules of kinetic energy. Estimate its new kinetic energy if it is moving at 30 mi/hr. (HINT: use the kinetic energy equation as a "guide to thinking.")

7. THE BIG KAHUNA:

A comet with a mass of 7.85 x 10¹¹ kg strikes Earth at a speed of 25.0 km/s. Find the kinetic energy of the comet in joules, and compare the work that is done by Earth in stopping the comet to the 4.2 x 10¹⁵ J of energy that was released by the largest nuclear weapon ever built. (post-class notes: I prematurely assigned this problem - should have given it to you in a few days. That said, you can still solve it with this one piece of information. In addition to Work being equal to Fdcos(Θ), Work is also equal to the change in Kinetic Energy (KE). This is called the Work-Energy Theorem, and the equation for it is this: W= ΔKE. Consider that Δ means KE_f-KE_i, and that you know the final KE of the comet (it's at rest) and you should have no problem solving).

At Home Learning (HW)

1. Complete all problems from #039C

If you got stuck, answers and more help are here at these links:

- PE LINK

- KE LINK

2. #039D: Tuesday we will cover Mechanical Energy: Watch/take notes/complete edPuzzle on the following:

1. (8:26) Introduction to Conservation of Mechanical Energy with Demonstrations - EDpuzzle