A projectile of mass 0.25 kg moving at 24.0 m/s collides with and sticks to a 1.75-kg block

that is connected to a spring for which k = 40.0 N/m, as in the figure below. The block is

initially on a frictionless part of a horizontal surface but starts to slide on a rough section immediately after the collision. If the maximum compression of the spring is 0.5 m, what is the force of friction on the block?

I need to show all work

A 10.0 g bullet is fired into a 1.0 kg block initially at reston a rough surface and connected to a spring with k = 200N/m.Immediately following the collision the block has a speed of 2.0m/s. The coefficient of friction between the ground and the blockis 0.10.

a) If the ground were frictionless, how far would the blocktravel before reaching its maximum compression point?

b) The friction between the ground and block cause the block toreach its maximum compression 0.04m before it would on africtionless surface. What is the mechanical energy of theblock-spring system when it has reached this maximum compressionpoint?

c) What is the maximum velocity reached by the block as it returnsto its equilibrium point following compress?

A 130 g block on a frictionless table is firmly attached to one endof a spring with k = 26 N/m. The other end of the spring isanchored to the wall. A 26 g ball is thrown horizontally toward theblock with a speed of 5.6 m/s.

1.)If the collision is perfectly elastic, what is the ball's speedimmediately after the collision?
2.)What is the maximum compression of the spring?

A 5.00-g bullet moving with an initial speed of 400. m/s is fired into and passes through a 1.00-kg block, as in Figure P13.68. The block, initially at rest on a frictionless horizontal surface, is connected to a spring with a spring constant of 900. N/m. If the block moves 5.00 cm to the right after impact, find (a) the speed at which the bullet emerges from the block and (b) the mechanical energy lost in the collision.