You attach one end of a spring with a force constant k = 913 N/m to a wall and the other end to a mass m = 2.62 kg and set the mass-spring system into oscillation on a horizontal frictionless surface as shown in the figure. To put the system into oscillation, you pull the block to a position x, 4.76 cm from equilibrium and release it. (a) Determine the potential energy stored in the spring before the block is released. (b) Determine the speed of the block as it passes through the equilibrium position. m/s (c) Determine the speed of the block when it is at a position x/4.

The pendulum below consists of a bob of mass m in motion.  During the motion, the supporting wire of length l maintains a constant angle θ with the vertical. Once it reaches the lowest point of the arc, use the conservation of energy, to determine the following:   a) Velocity of the bob in terms of g, L and θ b) Tension in the supporting wire in terms of m, g, and θ

A block of mass m is attached to a spring of spring constant k = 100 N/m. The block-spring system oscillates on a frictionless horizontal surface with a total mechanical energy of 4 J. At what positions, x, is the kinetic energy 68% of the total energy? (K = 0.68E → x = ?) x = +0.24 m O x = ±0.08 m x = ±0.16 m O x = ±0.32 m simple pendulum is oscillating with a maximum angular displacement @max. At t in moving to the left

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?

A 25.0-kg block is released from rest at point A. The track is frictionless except for the portion between points B and C, which has a length of 10.00 m. The block travels down the track, hits a spring of force constant 2000 N/m, and compresses the spring 0.50 m from its equilibrium position before coming to rest momentarily. Determine the coefficient of kinetic friction between the block and the rough surface between points B and C.

A particle that can move along the x-axis is part of a system with potential energy U(x) = A x 2 − B x , where A and B are positive constants. (a) Make a sketch of U(x) vs x. (b) Where are the particle’s equilibrium positions? (You may neglect the “point” where x is very large) (c) Describe how a particle would move if given small displacements from the equilibrium positions. For each of the points you identified in Part A, identify if it is a point of stable or unstable equilibrium.

A mass of 4.0 kg traveling at 5.0 m/s along a smooth, horizontal plane hits a relaxed spring. The mass is slowed to zero velocity when the spring has been compressed by 0.18 m. What is the final spring force when the mass is stopped?

A horizontal spring has a 2.00 kg mass attached at the end is stretched 10 cm. The mass has a maximum acceleration of 1.75 m/s2. (a) How long will it take to reach the maximum compression point? (b) What is the total mechanical energy of the spring?

A mass resting on a horizontal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. It takes 3.1 J of work to compress the spring by 0.15 m . If the spring is compressed, and the mass is released from rest, it experiences a maximum acceleration of 12 m/s2. Find the value of the spring constant. Find the value of the mass.

A block of mass, 1.5 kg is attached and secured to an end of a spring with a spring constant of 10,000 N/cm. The other end of the spring is secured to the wall. The block is pushed against the spring, which compresses the spring to a position of x = -0.04 cm. When uncompressed, the end of the spring that is attached to the block is at a position of x = 0.00 cm. The block/spring system is then released from rest, and the block travels along a rough horizontal track for the length of the spring. At 0.00 cm the surface changes. Can you help me calculate the block's velocity once it leaves the spring? Thank you.