How far has the spring compressed by the time the block first momentarily comes to rest? Assume the positive direction is to the right.

A7. Consider a spring-mass system as shown in the diagram, which consists of 1.0 kg block held by three identical springs with force constant k = 100 Nm', as shown in Fig. A7. Fig. A7 (a) Consider the block being displaced by a distance x m to the left. Determine the net force (both magnitude and direction) acting on the block by the springs. (b) The block is then released from rest. Show that the block performs simple harmonic motion, and determine the frequency of oscillation.

A block with a mass m₁ = 9.20 kg is attached to a lightweight spring with a spring constant k = 100 N/m that is attached to a wall. Initially the block is at rest and the spring is relaxed, as shown in figure (a). A second block with a mass m₂ = 7.00 kg is pushed up against block m₁, compressing the spring a distance A = 0.140 m, as shown in figure (b). The two blocks are released from rest, and both start moving to the right with negligible friction. a b d k m₁ m₂ cm k m1 my m₂ m₁ m₂ (a) When block m₁ reaches the equilibrium point, as shown in figure (c), block m₂ loses contact with block m₁. Block m₂ continues to move right at a speed v. What is the speed v (in m/s)? m/s (b) Block m, continues to move right, reaching the point where the spring is at the maximum stretch (for the first time), as shown in figure (d). At this point, what is the distance D between the two blocks (in cm)? (Assume the widths of the blocks are much smaller than D.)

Problem #1: The massless spring of a spring gun has a force constant =10N/cm. When the gun is aimed vertically, a 12-g projectile is shot to a height of 5.0 m above the end of the expanded spring. (See below.) a. What distance, d, was the spring compressed initially? b. What speed does the ball have when it is a height of 2.0m above the equilibrium position of the spring? 5.0 m d NNNNNNNN CNNNNNNN

A brick of mass m = 0.48 kg is set against a spring with a spring constant of k1 = 619 N/m which has been compressed by a distance of 0.1 m. Some distance in front of it, along a frictionless surface, is another spring with a spring constant of k2 = 244 N/m. The brick is not connected to the first spring and may slide freely. Now assume friction is present on the surface in between the ends of the springs at their equilibrium lengths, and the coefficient of kinetic friction is μk = 0.5. If the distance between the springs is x = 1 m, how far d2, in meters, will the second spring now compress?

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

Choose the correct answer choice. Answer must be in scientific notation with SI units that do not have prefixes except for kg. (m/s NOT cm/s). Answer must be in standard scientific notation

I'm not sure how to work this problem. The solutions give the answer to be V1f=0.20 m/s, v2f=2.75 m/s for part A. For part B the solutions give the answer to be x=0.22 for maximum compression for the spring. I attached a picture of the problem.

m2 m₁ Q8. A small object of mass m₂ = 4 kg is placed on top of another object of mass m1 = 6 kg, and which is connected to a spring with spring constant k = 50 N/m, as shown in the figure. Accessibility: Investigate Styles There is no friction between the larger object and the horizontal surface underneath, and the system is in equilibrium. ////// The system is pushed with an initial speed vo= √10 m/s, and then it continues to move freely. a) Find the amplitude of the oscillations if the two masses are moving together. b) Find the smallest value of the friction coefficient such during the oscillations the smallest object of mass m₂ will not slide on the larger object of mass m₁. c) Find the maximum acceleration and the maximum potential energy of the system containing the two masses. O

Example 13-12 depicts the following secnario. A 0.990kg block slides on a frictionless, horizontal surface with a speed of 1.38 m/s. The block encounters an unstretched spring with a force constant of 218 N/m, as shown in the sketch. Before the block comes to rest, the spring is compressed by 9.30 cm .