Mechanical Energy

Section 2.4

Objectives

• define mechanical energy • solve problems calculating mechanical energy, potential and kinetic energy • describe the law of conservation of energy and relate to energy conversion examples

Mechanical Energy

• Energy due to motion and the position of the object • Includes both kinetic and potential energy Mechanical energy = kinetic energy + potential energy

E m = E k + E p

Practice

• Grandin Ghosts football quarterback throws a 0.500 kg football towards the end zone in a straight line. At the height of 9.5 m above the Earth, it has a speed of 18.0 m/s. What is the total mechanical energy of the football?

Practice

• A Grandin Ghost Marching Band Color Guard member is practicing tossing her flag up in the air. At the top of the throw, the 0.650 kg flag has a total mechanical energy of 40.0 J and is moving at 2.60 m/s. Calculate the gravitational potential of the flag.

Practice

• Nigel, the pelican, is flying horizontally at 8.00 m/s, carrying Nemo from the dentist’s office back to the ocean. If Nemo has a mass of 300 g, and Nigel is 30.0 m above the ground, calculate the mechanical energy.

Practice

• Rapunzel drops her 2800 g worth of hair down to the prince from her tower. When her hair is 50.0 m above the ground, it has a total mechanical energy of 3.65 x 10 3 J. Calculate the kinetic energy of her hair.

Law of Conservation of Energy

• What does this law mean?

• • • Total amount of energy in a given situation remains constant Energy converted from one form to another Total energy

does not

change • Kinetic energy converted to potential and vice versa, but total mechanical E remains constant

E m = E k + E p

Law of Conservation of Energy

• Example: Energy Conservation – Weighed Spring http://www.learnalberta.ca/Search.aspx?lang=en&search=energy+conser vation+weighted+spring&grade=&subject=&audience=&language=&form at=&type=

Law of Conservation of Energy

Rearranging formulas

• When potential energy = kinetic energy, then solve for the following quantities: • Height • velocity

Practice

• Ms Sinclair decides that as an end of the semester joke, she will drop a 10.0 kg water balloon on her students. If the water balloon is dropped from the third floor stairwell all the way to the bottom floor, a distance of 12.0 m, what will be the speed of the balloon just before it hits the floor?

Practice

• The Cullens and wolves are preparing to battle the oncoming newborn vampire army. Jasper jumps vertically in the air to avoid a clash between Jacob and a newborn. If he has a mass of 65.0 kg and jumps with a initial speed of 14.3 m/s, how high will he rise?

Practice

• Merry and Pippin are travelling through Fangorn forest with Treebeard, the Ent. Merry is eating an apple when he suddenly drops it while laughing at a hobbit joke that Pippin made. If Merry is 11.0 m from the ground, what velocity does the apple reach just before it hits the ground?

Pendulum

• How does a pendulum work?

• Draw out the movement of the pendulum: where would it have maximum gravitational potential energy? Maximum kinetic energy? How does it demonstrate law of conservation of energy?

Practice

• A pendulum consists of a 500 g metal ball suspended on a 50.0 cm string. The ball is pulled horizontally and up a total vertical distance of 10.0 cm. It is then released. At the bottom of the arc, the mechanical energy of the ball was determined to be 0.491 J. What was the speed of the ball at the bottom of its arc?

What do we look for in a question?

• What are key words I should look for when solving a problem?

• • • • • How can I tell the difference between: Kinetic energy?

Potential energy?

Mechanical energy?

Conservation of energy?

Practice

• A 60.0 kg athlete jumps vertically upward from the ground to a height of 0.910 m above the ground. What was the athlete’s initial vertical speed?

• A baseball with a mass of 300 g has a kinetic energy of 304 J. Calculate the speed of the baseball.

Practice

• Standing on level ground, a person with a mass of 55.0 kg jumps straight up into the air to a position where the person has gained 800J of gravitational potential energy. How high did the person leap?

• A construction worker drops a 2.00 kg hammer from a roof. When the hammer is 50.0 m above the ground, it has a total mechanical energy of 1.88 x 10 3 J. Calculate the kinetic energy of the hammer.