A spring with force constant 311 N/m is in a compressed state, 0.417 m shorter than its relaxed length. In this condition, the spring serves a vital purpose in a device for detecting impending earthquakes. A curious physicist releases the spring and, moreover, stretches it until it is 0.109 m longer than its relaxed length. That renders the earthquake detector useless, and it fails to warn of a very strong earthquake that subsequently shatters all the lawn sculptures in the area, fortunately with no other damage or injury. Although some might consider this to be beneficial, the physicist's boss does not. She had some extremely unattractive plaster gnomes around her yard and loved them dearly. She imposes a punishment on the physicist and requires him to calculate the change of elastic potential energy caused by his meddling. What does he find? change of elastic potential energy:

In your job in a police lab, you must design an apparatus to measure the muzzle velocities of bullets fired from handguns. Your solution is to attach a 2.00 kg wood block that rests on a horizontal surface to a light horizontal spring. The other end of the spring is attached to a wall. Initially the spring is at its equilibrium length. A bullet is fired horizontally into the block and remains embedded in it. After the bullet strikes the block, the block compresses the spring a maximum distance d. You have measured that the coefficient of kinetic friction between the block and the horizontal surface is 0.38. The table below lists some firearms that you will test. A grain is a unit of mass equal to 64.80 mg. Bullet Mass Bullet ID Type Muzzle Velocity (ft/s) (grains) A .38Spec Glaser Blue 80 1667 B .38 Spec Federal 125 945 C .44Spec Remington 240 851 D .44Spec Winchester 200 819 E .45ACP Glaser Blue 140 1355

A hanging scale works because the length a spring stretches is directly proportional to the weight pulling down on the spring. These scales are commonly used in grocery stores. You are shopping for bananas and see that they are on sale for $0.29 a pound. When you weigh the bananas, the scale reads 2.40 pounds (1.09 kg). If the bananas cause the spring to stretch 2.30 cm, what is the spring constant of the spring found in the scale?

, x' A A- 1 Normal 1 No Spac... Heading 1 Heading 2 Title ont Paragraph Styles 4. A steel spring is suspended vertically from its upper end and a monkey is hanging from it. If the spring has a spring constant of 500 N/m and the spring extends 25 cm beyond its normal length, what is the mass of the monkey?

On your first trip to Planet X you happen to take along a 248 g mass, a 40.0-cm-long spring, a meter stick, and a stopwatch. You’re curious about the free-fall acceleration on Planet X, where ordinary tasks seem easier than on earth, but you can’t find this information in your Visitor’s Guide. One night you suspend the spring from the ceiling in your room and hang the mass from it. You find that the mass stretches the spring by 31.2 cm. You then pull the mass down 10.0 cm and release it. With the stopwatch you find that 10 oscillations take 14.5 s. Can you now satisfy your curiosity What is the spring constant of your spring?

An ideal spring is attached to the ceiling. While the spring is held at its relaxed length, a wooden block (M = 850 g) is attached to the bottom of the spring, and a ball of clay (m = 210 g) is pressed onto the bottom of the block so that they stick together. The block+clay are gently lowered through a distance of d = 2.7 cm and are then released, at which point they hang motionlessly from the bottom of the spring. After a few minutes have passed, the clay unsticks itself from the block and falls from rest to the ground. 1. What is the resulting period T of the block’s oscillation after the separation occurs? 2. As d approaches 0, what limit does T approach?

Mickey, a daredevil mouse of mass 0.0201 kg,0.0201 kg, is attempting to become the world's first "mouse cannonball." He is loaded into a spring‑powered gun pointing up at some angle and is shot into the air. The gun's spring has a force constant of 87.5 N/m87.5 N/m and is initially compressed a distance of 0.145 m0.145 m from its relaxed position. If Mickey has a constant horizontal speed of 2.15 m/s2.15 m/s while he is flying through the air, how high ℎh above his initial location in the gun does Mickey soar? Assume ?=9.81 m/s2.

A spring with a spring constant of 383 N/m is initially compressed by a distance of 0.076 m from its equilibrium position. A mass of 0.038 kg is then held against the compressed spring and released from rest while upon a horizontal, frictionless surface. Assuming that the spring then pushes the mass across the surface, with speed does the mass leave the spring? Assume proper SI Units.

As shown in the figure below, a box of mass  m = 7.40 kg is sliding across a horizontal frictionless surface with an initial speed  vi = 3.50 m/s when it encounters a spring of constant k = 2750 N/m. The box comes momentarily to rest after compressing the spring some amount xc. Determine the final compression xc (in m) of the spring.

A spring with a spring constant of 369 N/m is initially compressed by a distance of 0.064 m from its equilibrium position. A mass of 0.031 kg is then held against the compressed spring and released from rest while upon a horizontal, frictionless surface. Assuming that the spring then pushes the mass across the surface, with speed does the mass leave the spring? Assume proper SI Units.