Instructor: Dr. Tatiana Erukhimova Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lecture 18

Problem 4 You and your bicycle have combined mass 80.0 kg. When you reach the base of a bridge, you are traveling along the road at 5.00 m/s. At the top of the bridge, you have climbed a vertical distance of 5.2 m and have slowed to 1.5 m/s. You can ignore work done by friction and any inefficiency in the bike or your legs. a) What is the total work done on you and your bicycle when you go from the base to the top of the bridge? b) How much work have you done with the force you apply to the pedals?

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Quiz A sled slides down a hill H m high with a slope of θ. The total mass of the sled plus contents is M. It starts from rest. There is no friction. Use the Work Energy Theorem to find the velocity of the sled at the bottom, and to show that it doesn’t depend on the angle of the hill.

Quiz A block of mass m is attached to a vertical spring, spring constant k. The spring is unstretched at y=0. A If the spring is compressed an amount A and the block released from rest, how high will it go?

All force are CONSERVATIVE or NON-CONSERVATIVE

or A force is conservative if: The work done by the force in going from to is independent of the path the particle follows or The work done by the force when the particle goes from to around a closed path, back to , is zero.

Non-conservative: doesn’t satisfy the above conditions

If a force can be written as the derivative of some function, that force is conservative. 1D case: U(x) is called the potential energy function for the force If such a function exists, then the force is conservative

does NOT depend on path! 1D case:

does NOT depend on path! If Fx(x) is known, you can find the potential energy function as

2D case:

Have a great day! Reading: Chapter 8 Hw: All Chapter 8 problems and exercises