= 1 2 kx2 dw =! F! d! r = Fdr cosθ. T.E. initial. = T.E. Final. = P.E. final. + K.E. initial. + P.E. initial. K.E. initial =

Transcription

1 Practice Template K.E. = 1 2 mv2 P.E. height = mgh P.E. spring = 1 2 kx2 dw =! F! d! r = Fdr cosθ Energy Conservation T.E. initial = T.E. Final (1) Isolated system P.E. initial (2) Energy added E added + P.E. initial (3) Energy leaked P.E. initial + E lost Sketch and indicate the initial and final position. Decide if it is (1) an isolated system, (2) a system with energy added (ex. Someone is keep working on the system), or (3) a system with energy leaking (ex. Friction) Find the potential energy (P.E. gravity, P.E. spring) and the kinetic energy (K.E.) at each point. Set the Total Energy Conservation Equation depending on the system (1, 2, or 3) Problem) A diver of mass, m drops from a board 10.0 m above the water surface. Neglect air resistance and find the speed of the diver at the water level. Initial K.E. initial = P.E. initial = T.E. initial = Final K.E. final= P.E. final= T.E. final= 1

2 Practice Template K.E. = 1 2 mv2 P.E. height = mgh P.E. spring = 1 2 kx2 dw =! F! d! r = Fdr cosθ Energy Conservation T.E. initial = T.E. Final (1) Isolated system P.E. initial (2) Energy added E added + P.E. initial (3) Energy leaked P.E. initial + E lost Sketch and indicate the initial and final position. Decide if it is (1) an isolated system, (2) a system with energy added (ex. Someone is keep working on the system), or (3) a system with energy leaking (ex. Friction) Find the potential energy (P.E. gravity, P.E. spring) and the kinetic energy (K.E.) at each point. Set the Total Energy Conservation Equation depending on the system (1, 2, or 3) Problem) The spring is compressed to a position A in a popgun and the trigger is fired. The bullet of mass (m=0.10kg) rises to a position C. (y A = m, y B=0, y C=5.0 m.) a) Neglecting all resistive forces, find the spring constant. b) Find the speed of the bullet at B. Initial K.E. initial = P.E. initial = T.E. initial = Final K.E. final= P.E. final= T.E. final= 2

3 PartB.[Show Your Works] 1. A worker pushes a sled with a force of 40 N over a level distance of 6.0 m. If a frictional force of 24 N acts on the wheelbarrow in a direction opposite to that of the worker, what net work is done on the wheelbarrow? 2. A horizontal force of 200 N is applied to a 55-kg cart across a 10-m level surface. If the cart accelerates at 2.0 m/s 2, then what is the work done by the force of friction as it acts to retard the motion of the cart? 3. A 7.00-kg bowling ball falls from a 2.00-m shelf. Just before hitting the floor, what will be its kinetic energy? (g = 9.80 m/s 2 and assume air resistance is negligible) 4. A professional skier reaches a speed of 56 m/s on a 30 ski slope. Ignoring friction, what was the minimum distance along the slope the skier would have had to travel, starting from rest? 5. A baseball outfielder throws a baseball of mass 0.15 kg at a speed of 40 m/s and initial angle of 30. What is the kinetic energy of the baseball at the highest point of the trajectory? Ignore air friction. 6. A kg ore car rolls 50.0 m down a frictionless 10.0 incline. If there is a horizontal spring at the end of the incline, what spring constant is required to stop the ore car in a distance of 1.00 m? 7. A 20-N crate starting at rest slides down a rough 5.0-m long ramp, inclined at 25 with the horizontal. 20 J of energy is lost to friction. What will be the speed of the crate at the bottom of the incline? 3

4 8. A constant force of 12 N in the positive x direction acts on a 4.0-kg object as it moves from the origin to the point this displacement? m. How much work is done by the given force during 9. An object moving along the x axis is acted upon by a force F x that varies with position as shown. How much work is done by this force as the object moves from x = 2 m to x = 8 m? 10. A 4.0-kg block is lowered down a 37 incline a distance of 5.0 m from point A to point B. A horizontal force (F = 10 N) is applied to the block between A and B as shown in the figure. The kinetic energy of the block at A is 10 J and at B it is 20 J. How much work is done on the block by the force of friction between A and B? 11. The horizontal surface on which the block slides is frictionless. The speed of the block before it touches the spring is 6.0 m/s. How fast is the block moving at the instant the spring has been compressed 15 cm? k = 2.0 kn/m 12. If,, and, what is the angle between the two vectors when they are drawn starting from the same point? 4

5 13. A pendulum is made by letting a 2.0-kg object swing at the end of a string that has a length of 1.5 m. The maximum angle the string makes with the vertical as the pendulum swings is 30. What is the speed of the object at the lowest point in its trajectory? 14. A 2.0-kg block sliding on a horizontal frictionless surface is attached to one end of a horizontal spring (k = 200 N/m) which has its other end fixed. If the block has a speed of 4.0 m/s as it passes through the equilibrium position, what is its speed when it is 20 cm from the equilibrium position? 15. A 2.0-kg block sliding on a rough horizontal surface is attached to one end of a horizontal spring (k = 250 N/m) which has its other end fixed. The block passes through the equilibrium position with a speed of 2.6 m/s and first comes to rest at a displacement of 0.20 m from equilibrium. What is the coefficient of kinetic friction between the block and the horizontal surface? 16. A skier weighing 0.80 kn comes down a frictionless ski run that is circular (R = 30 m) at the bottom, as shown. If her speed is 12 m/s at point A, what is her speed at the bottom of the hill (point B)? 17. A 2.0-kg block is projected down a plane that makes an angle of 20 with the horizontal with an initial kinetic energy of 2.0 J. If the coefficient of kinetic friction between the block and plane is 0.40, how far will the block slide down the plane before coming to rest? Topic 5. Part B. Solutions 1) 96J 2) 900J 3) 137J 4) 320m 5) 90J 6) 340 kn/m 7) 4.7 m/s 8) 72 J 9) 30J 10) -68J 11) 3.7 m/s 12)103 13) 2.0 m/s 14) 3.5 m/s 15) ) 17 m/s 17) 3.0 m 5