A bullet with mass m = 0.003 kg moving with an initial speed of v = 600 m/s is fired into a block with mass M = 3 kg. The bullet comes out with a speed of v while the block compresses the spring it is attached to a distance of 5.19 cm. The spring constant is 400 N/m, and the horizontal surface is frictionless. Find the speed of the bullet, v, after it emerges from the block. m/s V = Find the energy lost in the collision. Elost = J E

1. A particle moves in one dimension and is subject to a conservative force, whose potential energy function is given by U(x), where a and b are positive constants. U(r) = ax' – bx ax³ a) Find the two equilibrium positions of the particle. b) For each of the two equilibrium positions, determine whether the equilibrium is stable or unstable.

A spring-loaded toy gun is aimed vertically and fired after a spherical projectile of mass m = 28.0 g is loaded by compressing the spring with force constant k = 830 N/m a distance of 9.20 cm. As the projectile travels a total distance of 56.0 cm along the barrel of the gun, it experiences a friction force of 2.00 N. What is the height reached by the projectile above its initial location with the spring compressed?

A 1.65 kg block slides with a speed of 0.885 m/s on a frictionless horizontal surface until it encounters a spring with a force constant of 751 N/m. The block comes to rest after compressing the spring 4.15 cm. Find the spring potential energy, U, the kinetic energy of the block, K, and the total mechanical energy of the system, E, for compressions of 0 cm.

A block of mass, m 3.30 kg, slides along a frictionless surface. It starts with a velocity, vo = 8.50 m/s. It then encounters a rough surface for a distance, d 2.65 m, where there is a coefficient of kinetic friction, µk = 0.620. At the end, it hits a spring, which it compresses by a displacement, Ax = 10.5 cm, until it comes to a stop. Assume the spring itself is massless. Ax -> a) How much kinetic energy (in joules) does the block have initially? b) How much work (in joules) does the friction from the rough surface do on the block? c) After leaving the rough patch, the block slides without friction again. With what speed (in m/s) does the block hit the spring? d) What is the spring constant (in N/m)? e) When the spring pushes the block back in the opposite direction, will it be able to slide all the way to the opposite end of the rough patch? Justify your answer numerically. Upload Choose a File

A small spring is laying horizontal on a table and is compressed by 0.50 m. A small mass of 0.25 kg is placed in front of the compressed spring. a) When the spring is released it accelerates the box at a = 8.0m/s . What is the value of the spring constant, k for the spring? Ignore friction for part (a). b) When the small mass loses contact with the spring it moves over a part of the table where there exists a friction force between the small mass and the table. If the box comes to a stop after sliding 5.0 m, using your knowledge of work, find the coefficient of friction between the sliding mass and the table.

1. A particle moves in one dimension and is subject to a conservative force, whose potential energy function is given by U(x), where a and b are positive constants. U ( x ) = a x 3 − b x                  a)  Find the two equilibrium positions of the particle.                  b)  For each of the two equilibrium positions, determine whether the equilibrium is stable or unstable.

A 6.00 ✕ 105 kg subway train is brought to a stop from a speed of 0.500 m/s in 0.400 m by a large spring bumper at the end of its track. What is the force constant k of the spring (in N/m)? (Enter a number.)

A toy gun uses a spring to project a 6.2-g soft rubber sphere horizontally. The spring constant is 8.0 N/m, the barrel of the gun is 12 cm long, and a constant frictional force of 0.039 N exists between barrel and projectile. With what speed does the projectile leave the barrel if the spring was compressed 5.7 cm for this launch? (Assume the projectile is in contact with the barrel for the full 12 cm.)

A 2.00-kg block is pushed against a spring with negligible mass and spring constant k = 400 N/m, compressing it 0.220 m. When the block is released, it moves along a frictionless, horizontal surface and then up a frictionless incline with slope 37.0 degrees. (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? k = 400 N/m }}}= wwwwwwww 0.220 m 2.00 kg 37.0°