A 1.5 kg block initially at rest, is launched by a horizontal spring with a spring constant of k-175 N/m. The spring is initially compressed a distance of 25 em from equilibrium. After being launched, the block travels toward the top of a frictionless incline and comes to rest after reaching a maximum height of has shown below. Apply the Conservation of Energy Theorem to determine, a. The object's launch velocity at the spring's point of equilibrium in m/s. b. The maximum height reached by the block (h) in meters. e. Determine the impulse delivered by the spring in kg-m/s. d. (Hint: consider the initial and final locations as x=-25 cm and x=0 cm). Determine the average force exerted by the spring on the block (in Newtons) if the time of contact equals 0.185 seconds. c. Determine the average power delivered by the spring in watts. hud 1.5-kg x= - 25 cm 0 1. 2 3.

A particle of mass m = 1.18 kg is attached between two identical springs on a frictionless, horizontal tabletop. Both springs have spring constant k and are initially unstressed, and the particle is at x = 0. (a) The particle is pulled a distance x along a direction perpendicular to the initial configuration of the springs as shown in Figure P7.50. Show that the force exerted by the springs on the particle is F=2kx(1Lx2+L2)i (b) Show that the potential energy of the system is U(x)=kx2+2kL(Lx2+L2) (c) Make a plot of U(x) versus x and identify all equilibrium points. Assume L = 1.20 m and k = 40.0 N/m. (d) If the panicle is pulled 0.500 m to the right and then released, what is its speed when it reaches x = 0? Figure P7.50

As a simple pendulum swings back and forth, the forces acting on the suspended object are the force of gravity, the tension in the supporting cord, and air resistance, (a) Which of these forces, if any, does no work on the pendulum? (b) Which of these forces does negative work at all times during the pendulums motion? (c) Describe the work done by the force of gravity while the pendulum is swinging.

A block of mass m = 5.00 kg is released from point and slides on the frictionless track shown in Figure P8.3. Determine (a) the blocks speed at points and and (b) the net work done by the gravitational force on the block as it moves from point to point . Figure P8.3

A particle moves in one dimension under the action of a conservative force. The potential energy of the system is given by the graph in Figure P8.55. Suppose the particle is given a total energy E, which is shown as a horizontal line on the graph. a. Sketch bar charts of the kinetic and potential energies at points x = 0, x = x1, and x = x2. b. At which location is the particle moving the fastest? c. What can be said about the speed of the particle at x = x3? FIGURE P8.55

A small 0.65-kg box is launched from rest by a horizontal spring as shown in Figure P9.50. The block slides on a track down a hill and comes to rest at a distance d from the base of the hill. The coefficient of kinetic friction between the box and the track is 0.35 along the entire track. The spring has a spring constant of 34.5 N/m, and is compressed 30.0 cm with the box attached. The block remains on the track at all times. a. What would you include in the system? Explain your choice. b. Calculate d. c. Compare your answer with your answer to Problem 50 if you did that problem.

Rubber tends to be nonlinear as an elastic material. Suppose a particular rubber band exerts a restoring force given by Fx(x) = Ax Bx2, where the empirical constants are A = 14 N/m and B = 3.3 N/m2 so that Fx is in newtons when x is in meters. Calculate the change in elastic potential energy of the rubber band when an external force stretches it from x = 0 to x = 0.20 m.

A certain uniform spring has spring constant k. Now the spring is cut in half. What is the relationship between k and the spring constant k of each resulting smaller spring? Explain your reasoning.

A light spring with spring constant 1 200 N/m is hung from an elevated support. From its lower end hangs a second light spring, which has spring constant 1 800 N/m. An object of mass 1.50 kg is hung at rest from the lower end of the second spring. (a) Find the total extension distance of the pair of springs. (b) Find the effective spring constant of the pair of springs as a system. We describe these springs as in series.

The Flybar high-tech pogo stick is advertised as being capable of launching jumpers up to 6 ft. The ad says that the minimum weight of a jumper is 120 lb and the maximum weight is 250 lb. It also says that the pogo stick uses a patented system of elastometric rubber springs that provides up to 1200 lbs of thrust, something common helical spring sticks simply cannot achieve (rubber has 10 times the energy storing capability of steel). a. Use Figure P8.32 to estimate the maximum compression of the pogo sticks spring. Include the uncertainty in your estimate. b. What is the effective spring constant of the elastometric rubber springs? Comment on the claim that rubber has 10 times the energy-storing capability of steel. c. Check the ads claim that the maximum height a jumper can achieve is 6 ft.