1. 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?

2. Potential energy of a spring x0x0 x F x F Reference: U=0 where x=0

3. 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. A)Find the maximum speed of the mass. B)Find the work of gravity on the mass during a whole cycle. C)Find the work of the spring on the mass during a whole cycle.

4. Reading Assignment 7.3: Which of the following is NOT a characteristic of a conservative force? A.The work can be expressed as the difference in initial and final value of a potential energy function. B.The work is reversible. C.The force is not path-dependent. D.The total work is zero if the initial and the final point are the same.

5. Conservative force as gradient of potential energy

6. A certain rubber band stores potential energy as a function of its length x as a)Find U at 0, 2.0, 4.0,and 6.0 cm and sketch the function. b)Conservative force? Direction? c)Find the force for those positions. d)How long can it be stretched if its breakdown force is 120 N?

7. Work of non-conservative forces Will the the two energies E1 and E2 be equal? By how much are they different? Nonconservative forces change the mechanical energy of a system by an amount equal to their work

8. Discuss the influence of the non-conservative forces on mechanical energy for the following examples: a)A pendulum is slowing down due to air drag. b)A book is lifted from the table to the upper bookshelf. c)A car engine accelerates a car from zero to 60 km/h. d)The spring of a spring gun is cocked into a compressed position. e)The spring is being released.

9. The first block has a mass m 1 = 2.0 kg and the second block has m 2 = 4.0 kg. The pulley and string are massless. There is no friction in the pulley, but the coefficient of kinetic friction between the first block and the incline is µ k = 0.55. The blocks are released from rest. Use energy considerations to find the speed of the two blocks when the second block has moved down 2.5 m. m1m1 m2m2 37  4.0 m 3.0 m 5.0 m