In a needle biopsy, a narrow strip of tissue is extracted from a patient with a hollow needle. Rather than being pushed by hand, to ensure a clean cut the needle can be fired into the patient's body by a spring. Assume the needle has mass 5.60 g, the light spring has force constant 395 N/m, and the spring is originally compressed 8.10 cm to project the needle horizontally without friction. (The spring is fully uncompressed before the needle contacts the skin.) The tip of the needle then moves through 2.40 cm of skin and soft tissue, which exerts a resistive force of 7.10 N on it. Next, the needle cuts 3.50 cm into an organ, which exerts a backward force of 9.40 N on it. (a) Find the maximum speed of the needle. m/s (b) Find the speed at which a flange on the back end of the needle runs into a stop, set to limit the penetration to 5.90 cm. m/s

An inclined plane of angle = 20.0° has a spring of force constant k = 495 N/m fastened securely at the bottom so that the spring is parallel to the surface as shown in the figure below. A block of mass m = 2.39 kg is placed on the plane at a distance d = 0.282 m from the spring. From this position, the block is projected downward toward the spring with speed v = 0.750 m/s. By what distance is the spring compressed when the block momentarily comes to rest? m www

m = 0.350 kg. (c) Is the original energy in the spring or in the cord? (d) Explain your answer to part (c). (e) Is the momentum of the system conserved in the bursting-apart process? Explain how that is possible considering (f) there are large forces acting and (g) there is no motion before- hand and plenty of motion afterward? 5. Two blocks of masses m allu e QIC are placed on a frictionless, hor- V izontal surface. A light spring is attached to the more mas- sive block, and the blocks are 3m m Before pushed together with the spring between them (Fig. P9.5). A cord initially holding the blocks together is burned; after that happens, the block of mass 3m moves to the right with a 2.00 m/s 3m m speed of 2.00 m/s. (a) What is the velocity of the block of mass m? (b) Find the system's original elastic potential energy, taking After b Figure P9.5

A block of mass 2.9 kg is sitting on a frictionless ramp with a spring at the bottom that has a spring constant of 470 N/m (refer to the figure). The angle of the ramp with respect to the horizontal is 13°.  a) The block, starting from rest, slides down the ramp a distance 54 cm before hitting the spring. How far, in centimeters, is the spring compressed as the block comes to momentary rest?  b)  After the block comes to rest, the spring pushes the block back up the ramp. How fast, in meters per second, is the block moving right after it comes off the spring?  c) What is the change of the gravitational potential energy, in joules, between the original position of the block at the top of the ramp and the position of the block when the spring is fully compressed?

Let's say we have a spring with a constant of K= 300 N/m and this spring is attached to the incline at the top making an angle of θ=44.0° with the horizontal. Now, after we have this problem, there is a projectile that has a mass of 1 kg that is pointing up the plane. The initial position of this projectile is d = 1.3 m and it is from the end 0f a uncompressed spring. Answer the following questions: Let’s say the incline has no friction at all and given the kinetic energy for the projectile is 15 J. How much c0mpression will the spring receive? Let's say we have a coefficient of friction = 0.300 and the spring will have to c0mpress 1.10 the instant the projectile stops..in order for this to happen, what should be the initial speed of the projectile?

The left end of a 1.200 m-long board is raised 0.300 m above the level table and a 0.800 kg cart (frictionless wheels) is placed on the ramp near the top (left) end. The cart is held in place by a compression spring that pushes into the cart horizontally. [ a) compute the ramp's distance along the horizontal. ] b) compute the spring Force magnitude. [c) compute the ramp Force magnitude. ] [ d) calculate the cart's acceleration if released from the spring. ] 2.450 N 7.840 N 2.024 N my answer is very different than any of these others 30.364 N 8.097 N 1.960 N

A mass of 0.4 kg is held against compressed spring and released from rest while upon a horizontal, frictionless surface. The spring constant of the spring is 890 N/m and the mass leaves the spring with a speed of 7.51 m/s. Assume that the spring pushes the mass across the surface. By what amount was the spring initially compressed relative to its equilibrium position?

A spring with spring constant 20 N/m is compressed a distance of 5.5 cm by a ball with a mass of 208.5 g (see figure below). The ball is then released and rolls without slipping along a horizontal surface, leaving the spring at point A. The process is repeated, using a block instead, with a mass identical to that of the ball. The block compresses the spring by 5.5 cm and is also released, leaving the spring at point A. Each object travels up the incline shown in the figure before coming to rest momentarily. Assume the ball rolls, but ignore other effects of friction. (Assume the ball rolls without slipping up the incline until it comes to rest.)   (a) How high above the starting position is the ball when it comes to rest momentarily? m (b) How high above the starting position is the block when it comes to rest momentarily? m

A high jumper, falling at 4.0 m/s, lands on a foam pit and comes to rest, compressing the pit 0.40 m. If thepit is able to exert an average force of 1200 N on the high jumper in breaking the fall, what is the jumper'smass? (60 kg)

A cube, whose mass is 0.700 kg, is attached to a spring with a force constant of 110 N/m. The cube rests upon a frictionless, horizontal surface (shown in the figure below). A cube labeled m is attached to the right end of a horizontal spring, and the left end of the spring is attached to a wall. The spring is stretched horizontally such that the cube is displaced by a distance A to the right of its equilibrium position. The cube is pulled to the right a distance A = 0.110 m from its equilibrium position (the vertical dashed line) and held motionless. The cube is then released from rest. (a) At the instant of release, what is the magnitude of the spring force (in N) acting upon the cube?  N (b) At that very instant, what is the magnitude of the cube's acceleration (in m/s2)?  m/s2 (c) In what direction does the acceleration vector point at the instant of release?