A 3.6 g marble is fired vertically upward using a spring gun. The spring must be compressed 2.9 cm if the marble is to just reach a target 18 m above the marble's position on the compressed spring. (a) What is the change AU in the gravitational potential energy of the marble-Earth system during the 18 m ascent? (b) What is the change AU, in the elastic potential energy of the spring during its launch of the marble? (c) What is the spring constant of the spring? (a) Number i (b) Number i (c) Number i Units Units Units

The force required to compress a non-standard spring as a function of displacement is given by the equationF(x) = -Asin(bx) + kx,where A = 11 N, b = 11 rad/m, and k = 78 N/m. Part (b)  Calculate the work done in joules as the spring is compressed from x = 0 to x1 = 32 cm.  Part (c)  Calculate the work done in joules as the spring is compressed from x1 = 32 cm to x2 = 69 cm

A spring is connected on one end to a wall and the other is free to be compressed.  The spring constant is 25 N/cm for the spring.  A 2.0 kg mass is pressed against the spring and then released and the entire system is placed on horizontal frictionless surface.   (a)  How much is the spring compressed when 15.0 J of energy is stored in the spring? (10.9 cm)  (b)  What is the acceleration when the spring is at 1/2 the maximum compression distance? (68.5 m/s2)  (c)  What is the maximum speed of the mass?

The figure below shows a plot of potential energy U versus position x of a 0.96 kg particle that can travel only along an x axis. (Nonconservative forces are not involved.) In the graphs, the potential energies are UA = 10.0 J, Ug = 25.0 J, and UC = 35.0 J. (r) Ucr UB 2 4 6 x (m) The particle is released at x = 4.5 m with an initial speed of 8.5 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? ---Select-- C ---Select- (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 N direction Suppose, instead, the particle is headed in the positive x direction when it is released at x = 4.5 m at speed 8.5 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? Select C

A block with mass m = 1.14 kg is placed against a spring on a frictionless incline with angle = 22.0° (see the figure). (The block is not attached to the spring.) The spring, with spring constant k = 15 N/cm, is compressed 24.1 cm and then released. (a) What is the elastic potential energy of the compressed spring? (b) What is the change in the gravitational potential energy of the block-Earth system as the block moves from the release point to its highest point on the incline? (c) How far along the incline is the highest point from the release point?

A pendulum consists of a 1.2 kg stone swinging on a 4.2 m string of negligible mass. The stone has a speed of 8.3 m/s when it passes its lowest point. (a) What is the speed when the string is at 56" to the vertical? (b) What is the greatest angle with the vertical that the string will reach during the stone's motion? (c) If the potential energy of the pendulum-Earth system is taken to be zero at the stone's lowest point, what is the total mechanical energy of the system? (a) Number i Unit (b) Number i Unit (c) Number i Unit

.  A pogo stick has a spring with a spring constant of 2.5×104N/m,, which can be compressed 12.0 cm. To what maximum height from the uncompressed spring can a child jump on the stick using only the energy in the spring, if the child and stick have a total mass of 40 kg?