Conservation of Energy

​- Energy can take many different forms: review forms of energy learned

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​- Energy is conserved as it changes from one form to another

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​- No matter the process of conversion, the amount of energy in the universe remains the same. Conservation of energy.

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​- Consider a set of keys of mass (m) that is dropped to the floor from a height (h). How fast are the keys moving when they hit the ground?

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​- Ignoring friction (air resistance) we know that the total amount of energy in this equation is equal to the summation of potential energy and kinetic energy.

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​E = PE + KE

​- Potential energy is determined by the release height, h.

​PE = mgh

​- The initial kinetic energy is zero because the keys are dropped from rest.

​KE(i) = 0

​-The final potential energy is zero because the final point is at ground level

​PE(f) = 0

​- The final kinetic energy is one-half the mass times the final velocity squared

​KE(f) = (1/2)mv^2

​We can now apply conservation of energy and solve for the final speed

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PE(gravity, i) + KE(i) = PE(gravity, f) + KE(f)

​mgh + 0 = 0 + (1/2)mv^2

​v(f) = √(2gh)

​A set of keys falls to the floor. Ignoring frictional forces, we know that the mechanical energy at the initial (i) and final (f) points must be the same: E(i) = E(f). Using this condition, we can find the speed of the keys just before they land.

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​Keys mass: 1.5 kg

​Height dropped from: 10 m

At position A and G, the ball is motionless on the ground (0 meters).

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think about the transition of energy at the stages the ball is in the air. ​

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Motion of a ball thrown in the air​

A ball is thrown straight up in the air. The figure shows a plot of the ball's position as it is released (A) and as it lands (G). When does the ball have the most kinetic energy?

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Motion of a ball thrown in the air​

For the diagram, at which position is the gravitational potential energy the greatest?

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Motion of a ball thrown in the air​

For the diagram, from the moment it leaves your hand to the moment it hits the ground, describe the motion of the ball during its flight?

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Motion of a ball thrown in the air​

Assume position 1 is the position from which the pendulum begins swinging.

​Simple Pendulum Swinging

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Where is the kinetic energy the greatest in the diagram?

​Simple Pendulum Swinging

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As the pendulum swings back and forth, describe the energy transformation.

​Simple Pendulum Swinging

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As the pendulum swings back and forth, describe the energy transformation.

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*​Kinetic energy --> potential energy

*potential --> kinetic​

*energy conservation?​

​Simple Pendulum Swinging

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type of energy at points 1 and 3?

​Simple Pendulum Swinging

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Given the energy at position 1 is 80J and the mass of the ball is 5kg, what is the height of the pendulum as it begins swinging?

​Simple Pendulum Swinging

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A 3 kg object is placed at the top of the track and released from rest. (Assume the gravitation potential energy is 0 at point C)

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​Conservation of motion

What is the gravitational potential energy of the object at Point A?

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​Conservation of motion

What is the kinetic energy of the object at Point C?

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​Conservation of motion

Compare the total mechanical energy of the objects at Points A, B, and C

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​Conservation of motion

What is the farthest point on the track that the object will reach?

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​Conservation of motion