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**Conservative forces and conservation of energy**

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**Work of gravity Final position Final position Final position**

Initial position Final position Initial position Final position Initial position Final position

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**Work of gravity Work is not dependent on path**

Initial position Final position Initial position Final position Initial position Final position Work is not dependent on path Work is only dependent on initial and final position

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**Conservative Force The force of gravity is a conservative force.**

The work of a conservative force is not dependent on path only dependent on initial and final position The force of gravity is a conservative force.

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**Examples for non-conservative forces**

Initial position Final position Initial position Final position Friction force Applied force of pushing or pulling Initial position Final position Initial position Final position

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**Which of the following are conservative forces? Justify answer.**

Gravity close to the surface of the earth Force of the engine of a snow mobile Force exerted by a horizontal spring on a mass The force exerted while pushing a child on a swing Drag force on a parachute at terminal velocity Gravity of Earth in moon’s orbit Normal force

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**If only conservative forces do work:**

Therefore:

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**Use the work-kinetic energy theorem Use conservation of energy **

A shingle is sliding off a 30 inclined roof. The mass of the shingle is 3.0 kg, while its initial speed is 3.0 m/s. It impacts on the ground after falling 8.00 m downwards. Use kinematics Use the work-kinetic energy theorem Use conservation of energy to determine the final speed at impact. L19sp09 8

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From which height must the rollercoaster be released in order for the carts to stay safely in the tracks at the top of the loop-the-loop? What is the speed of the cart when entering the straight part at the bottom? R= 20 m

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**Determine its maximum speed. **

A pendulum with a length of 1.00 m reaches a maximum height above the equilibrium position of 0.20 m. Determine its maximum speed. Determine the height at which the kinetic energy is equal to half of the potential energy difference between lowest and highest point. Determine the height at which the speed is equal to half of the maximum speed. 0.20 m 1.00 m

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**Potential energy of a spring**

x0 x F Reference: U=0 where x=0

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A vertical mass-spring system is released when the mass has been pulled 3.50 cm below its equilibrium point. It took a force of 130 N to pull the 200-g mass to the release point at first. Find the maximum speed of the mass. Find the work of gravity on the mass during a whole cycle. Find the work of the spring on the mass during a whole cycle.

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**What would you suggest he can do to make it anyway?**

A hiker wants to continue on his trail, and finds the situation shown above. He has a long rope which is fixed to a branch above the middle of the river. Behind him is a high climbable rock, but also a lot of space. The opposite bank is higher than the bank the hiker is located on. Why can he not reach the top of the other bank if he just drops off the cliff while holding the rope? What would you suggest he can do to make it anyway?

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-x x The cart is pushed a small distance to the right and then released. Which of the following energy versus distance relations describe the system of trolley and springs? E U A C K U x x D B x x

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