Use the work-kinetic energy theorem to write an equation that relates the work done by gravity on the cart to the change in kinetic energy between its initial release and when it reaches the base of the hill. Assume energy dissipation is small enough to be neglected. Solve your equation for the final velocity of the cart in terms of the vertical release height. (If your equation is in terms of the distance traveled along the incline, use trigonometry to relate this distance to the vertical height of the hill.)

A child of mass m = 16 kg slides down a slide of height h = 2.7 m without friction. Let gravitational potential energy be zero at ground level. a)Write an expression for the child's total mechanical energy, E, at the top of the slide, in terms of the variables in the problem and the acceleration due to gravity g.  b)Calculate the change in the child's potential energy, ΔU in joules, from the top to the bottom of the slide at ground level (i.e. ΔU = Uground - Utop).  c)What is the child's final speed, vf in m/s?

Mehul

Block A, with mass m4, is initially at rest on a horizontal floor. Block B, with mass mB, is initially at rest on the horizontal top surface of A. The coefficient of static friction between the two blocks is u . Block A is pulled with a horizontal force. It begins to slide out from under B if the force is greater than: Discuss Potential Energy Diagrams Given Below: I will draw a Total Energy line and you will be required to discuss turning points, equilibrium points and discuss this diagram in terms of all concepts in Ch 7 and 8. Up Uc SUB UA 1 3 4 5 6. 7 8. 9. x (m)