A block of mass M = 5.40 kg, at rest on a horizontal frictionless table, is attached to a rigid support by a spring of constant k = 6230 N/m. A bullet of mass m = 8.00 g and velocity  v→ of magnitude 500 m/s strikes and is embedded in the block (the figure). Assuming the compression of the spring is negligible until the bullet is embedded, determine (a) the speed of the block immediately after the collision and (b) the amplitude of the resulting simple harmonic motion.

A ball is attached to one end of a wire, the other end being fastened to the ceiling. The wire is held horizontal, and the ball is released from rest (see the drawing). It swings downward and strikes a block initially at rest on a horizontal frictionless surface. Air resistance is negligible, and the collision is elastic. The masses of the ball and block are, respectively, 1.7 kg and 2.5 kg, and the length of the wire is 1.36 m. Find the velocity (magnitude and direction) of the ball just after the collision.

The force of that particle 2 exerts on 1 is given by: F→21(t)=Fxe^−(t/T)ı^+Fysin⁡(2πt/T)ȷ^ Where the parameters have the values: Fx=−16.1 N, Fy=101 N, T=67 s.We will consider a time interval that begins at ti=0 s and ends at tf=321 s. the mass of particle 1 is 13.9 kg and its intial velocities are 54 m/s I^ + (-42 m/s)J^. What is the x and y displacement for particle 1?

A car's suspension is modeled by the overdamped oscillator L=(D−1)(D−2)L=(D−1)(D−2).  (a) Find the impulse response of the suspension. (That is, solve Ly=δ(t),y′(0)=y(0)=0Ly=δ(t),y′(0)=y(0)=0.) (b) What happens to the car if the car rolls over three evenly spaced sharp bumps? (That is, solve Ly=δ(t)+δ(t−1)+δ(t−2)Ly=δ(t)+δ(t−1)+δ(t−2).) Hint: convolve with the impulse response.

In the figure, block 2 (mass 1.10 kg) is at rest on a frictionless surface and touching the end of an unstretched spring of spring constant 216 N/m. The other end of the spring is fixed to a wall. Block 1 (mass 1.80 kg), traveling at speed v1 = 5.90 m/s, collides with block 2, and the two blocks stick together. When the blocks momentarily stop, by what distance is the spring compressed?

6) A massless spring, with force constant k=191N/m, connects a wall and a block of wood. The system is initially at rest with the spring neither stretched nor compressed. The block has mass M=54.2g and is free to move without friction on a table. A gun is positioned to fire a bullet of mass m=6.86g into the block along the spring axis. After the gun is fired, the bullet gets embedded in the block, and the spring is compressed a maximum distance d=0.857m. b) What is the speed, in meters per second, of the bullet before it enters the block?  c) What is the frequency, in hertz, of the resulting periodic motion of the block/bullet and spring system?

Two train cars are heading directly at one another on the same track. The first train of mass m1 has initial velocity v1,i and the second train car of mass m2 has initial velocity v2,i. The second train car has a protective bumper mounted on a spring of force constant k to absorb and dissipate impact forces. When the first train car hits the second, the spring bumper is compressed to a maximum compression xmax. At this point in time, the train cars are moving with the same velocity v. In terms of v1,i, v2,i, m1, m2, k, find expressions for: (a) The velocity v at maximum compression; (b) The maximum compression xmax​​​​​​​; and (c) The velocity of each train car after they’ve separated.

I. A lump of clay (m = 3.00 kg) is thrown towards a wall at speed v = 3.00 m/s. The lump sticks to the wall. (a) What kind of collision is it? Is momentum conserved during this collision? Why or why not? (b) Calculate the impulse imparted on the lump by the wall. (c) Calculate percent of initial kinetic energy lost during this collision. II. Same lump is thrown towards the same wall, but this time it bounces off the wall at speed of 3.00 m/s. (a) What kind of collision is it? Is momentum conserved during this collision? Why or why not? (b) Calculate the impulse imparted on the lump by the wall. (c) Calculate percent of initial kinetic energy lost during this collision. III. Same lump is thrown towards the same wall, but this time it bounces off the wall at speed of 2.00 m/s. (a) What kind of collision is it? Is momentum conserved during this collision? Why or why not? (b) Calculate the impulse imparted on the lump by the wall. (c) Calculate percent of initial kinetic energy lost during…

Two blocks of masses m1 = 1.60 kg and m2 = 2.10 kg are placed on a horizontal frictionless surface and a compressed spring of force constant k = 285 N/m is placed between them. Neglect the mass of the spring. The spring is not attached to either block and is compressed a distance of 9.50 cm. If the blocks are released from rest, find the final velocity of each block.