A ball moves on a frictionless *6 p track as shown below. The horizontal plane passing through the initial point O is taken as a reference for the gravitational potential energy (At O, PEg =0). Assume that the speed of the ball at point O is v_O = 2 m/s and the ball stops at point B. The height of point B is equal to: B PEg=0 0 hs 11

A particle of mass 18.8 kg moves along the x-axis with a potential energy U whose dependence on position x is shown in the figure. If the total mechanical energy E of the particle is 110 J, what is the speed in m/s of the particle at 7 m? 15 U (J) 10 V. 5 4 8 10 X (m) 00 6. 20

A roller coaster starts with a speed of 4.1 m/s at a point 51 m above the bottom of a dip. Neglecting friction, what wil be the speed of the roller coaster at the top of the next slope, which is 30 m above the bottom of the dip? Answer: m/s

Examples 3: Consider a block that is free to slide down a smooth, frictionless plane that is inclined at an angle 0 to the horizontal, as shown in Figure. If the height of the plane is h and the block is released from rest at the top, what will be its speed when it reaches the bottom?

A 1680 kg car skids on a level road with coefficient of kinetic friction 0.64 between the tires of the car and the road.  The car skids a distance of 102 m and comes to a complete stop.  The work done on the car by the force of kinetic friction is (enter your answer with two significant figures) possibly useful: W = (Fcosθ)d w = mg g = 9.81 m/s2

An object of mass m starts at x = A with a speed vi in the +x direction. , where a is a positive 2. For x > A the surface has a coefficient of friction µ(x) constant. Calculate the work done by friction from x = A to an arbitrary point x = B along the box's path of motion. What is the object's kinetic energy at x = B? m Law V1 x = A µ(x) Application

The figure below shows a plot of potential energy U versus position x of a 0.76 kg particle that can travel only along an x axis. (Nonconservative forces are not involved.) In the graphs, the potential energies are UA = 20.0 J, UB = 35.0 J, and Uc = 45.0 J. Uc UB UA 4 х (m) The particle is released at x = 4.5 m with an initial speed of 6.0 m/s, headed in the negative x direction. (a) If the particle can reach x = 1.0 m, what is its speed there, and if it cannot, what is its turning point? m (b) What are the magnitude and direction of the force on the particle as it begins to move to the left of x = 4.0 m? magnitude direction +X Suppose, instead, the particle is headed in the positive x direction when it is released at x = 4.5 m at speed 6.0 m/s. (c) If the particle can reach x = 7.0 m, what is its speed there, and if it cannot, what is its turning point? m (d) What are the magnitude and direction of the force on the particle as it begins to move to the right of x = 5.0 m? magnitude…

A child of mass m = 27 kg slides down a slide of height h = 2.1 m without friction. Let gravitational potential energy be zero at ground level. 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.  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).  What is the child's final speed, vf in m/s?

A center throws a basketball m = 1 kg straight up with an initial speed of vo = 9.5 m's. He releases the ball at shoulder | height ho = 1.9 m. Let gravitational potential energy be zero at ground level. Give the total mechanical energy of the ball E in terms of maximum height h it reaches, the mass m, and the gravitational acceleration g. E= What is the height, hm in meters? 9 HOME

A crate of mass M starts from rest at the top of a frictionless ramp inclined at an angle α above the horizontal. Find its speed at the bottom of the ramp, a distance d from where it started. Do this in two ways.Take the level at which the potential energy is zero to be at the bottom of the ramp with  y  positive upward.Express your answer in terms of the variables M, d, α, and appropriate constants.