A horizontal spring attached to a wall has a force constant of k = 850 N/m. A block of mass m = 1.00 kg is attached to the spring and rests on a frictionless, horizontal sur- face as in Figure P8.35. (a) The block is pulled to a posi- tion x = 6.00 cm from equilibrium and released. Find the elastic potential energy stored in the spring when the block is 6.00 cm from equilibrium and when the block passes through equilibrium. (b) Find the speed of the block as it passes through the equilibrium point. (c) What is the speed of the block when it is at a position x,/2 isn't the answer to part (c) half the answer to part (b)? = 3.00 cm? (d) Why

The Slingshot is a ride for two people. It consists of a single passenger cage, two towers, and two elastic bands. Potential energy is stored in the elastic bands and the passenger cage is released. On the way up, this potential energy in the elastic bands is converted into the kinetic energy of the cage. At the maximum height of the ride, the energy has been converted into gravitational potential energy of the cage. The slingshot has two towers of height h = 71 m. The towers are a distance d = 31 m apart. Each elastic band has an unstretched length of L0 = 42 m and a spring constant of k = 295 N/m. The total mass of the passengers and cage is m = 395 kg. The car is pulled down to the ground in the middle of the two towers.

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 block with mass m = 2.20 kg is placed against a spring on a frictionless incline with angle e = 30.0°. (The block is not attached to the spring.) The spring, with spring constant k = 21.0 N/cm, is compressed 17.0 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 250 g block on a 30° ramp with μk = 0.17 is pushed against a spring. The constant of the spring is 1400 N/m and the spring is compressed 13.0 cm. After being released, the block will travel 3.4 m up the ramp (that includes the 12 cm) before shooting off the end. How fast will the block be going when it shoots off the edge of the ramp?

7.42 · A 2.00-kg block is pushed against a spring with negligible mass and force constant k = 400 N/m, compressing it 0.220 m. When the block is released, it moves along a frictionless, hori- zontal surface and then up a frictionless incline with slope 37.0° (Fig. P7.42). (a) What is the speed of the block as it slides along the horizontal surface after having left the spring? (b) How far does the block travel up the incline before starting to slide back down? Figure P7.42 k = 400 N/m m = 2.00 kg WWWWAAAA wwww 37.0° K-0.220 m-

A small 0.40-kg box is launched from rest by a horizontal spring as shown in the figure below. 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 0.30 along the entire track. The spring has a spring constant of 34.0 N/m and is compressed 30.0 cm with the box attached. The block remains on the track at all times. 30.0 cm This answer has not been graded yet. (b) Calculate d. m 50.0 cm (a) What would you include in the system? Explain your choice. 40° -d = ?

If R = 5.75 cm, M = 786 g, and m = 980 g in the figure, find the speed of the block after it has descended 52.9 cm starting from rest. Solve the problem using energy conservation principles. Number i (a) Units M M M 3 C R m 7₂ (b)