Fig. P13.179 and P13.180 13.180 A 5-kg sphere is dropped from a height of y = 3 m to test a new spring floor used in gymnastics. The mass of floor section B is 12 kg, and the sphere bounces back upward a distance of 44 mm. Knowing that the maximum deflection of the floor section is 33 mm from its equilibrium position, determine (a) the coefficient of restitution between the sphere and the floor, (b) the effective spring constant k of the floor section.
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- 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.You fire a bullet at a ballistic pendulum. The large block of wood has a mass M2 = 3 kg, and the bullet has a mass of m1 = 35 g. The bullet completely penetrates the wood and emerges with a speed of vf = 80 m/s. The wood, as part of a pendulum, swings up to a maximum height of h = 11 cm. (a) Determine the speed of the block of wood after the bullet has passed through it. m/s(b) What is the speed of the bullet just before it hits the block? m/s(c) If the pendulum length is 0.8 m, what angle does the pendulum string make with the vertical when it reaches the top of its swing? degrees1. An inventor patents a "golf machine". It consists of a "golf club" which is really a pendulum of length L = 2 (m), with a massles string and a mass M = 30 (kg) on the end. By pulling back on the pendulum until the string makes an angle 0= 10° from the vertical, and then releasing it from rest, the golf club strikes the "golf ball" exactly horizontally. The golf ball is a mass m = that rests on a platform which is h = 20 (cm) above the horizontal ground. Assume that all collisions are elastic and all masses are point masses. Finally you should ignore air resistance but gravity acts down as usual. M) 0.1 (kg) h А. What is the speed of M just before it strikes m? | After m is struck by M, how long is m in the air before it hits the В. ground?
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- A rocket, which is in deep space and initially at rest relative to an inertial reference frame, has a mass of 78.4 × 105 kg, of which 8.68 × 105 kg is fuel. The rocket engine is then fired for 340 s, during which fuel is consumed at the rate of 340 kg/s. The speed of the exhaust products relative to the rocket is 3.78 km/s. (a) What is the rocket's thrust? After the 340 s firing, what are (b) the mass and (c) the speed of the rocket? (a) Number 1290000 Units N (b) Number 7720000 Units kg (c) Number 3830 Units m/sA block of mass 20 kg moves along a frictionless surface, and is in a collision course with a sphere of mass 10 kg tied to an inextensible rope of length 6.00m. If the block collides with the sphere with a velocity of 5.00 m/s, as shown in the figure, and the coefficient of restitution is e = 0.800, determine the following. Neglect friction and air resistance. VB= 5.00 m/s Ө r: 6.00m 9-7-- ↓ 3. To solve for the maximum height, H, which of the following concepts cannot be used? The kinetic energy of the sphere just after its collision with the block is equal to its potential energy at the maximum height, H. The kinetic energy of the sphere just after its collision with the block is equal to its kinetic energy at the maximum height, H. The velocity of the sphere at the maximum height is zero. The work done by gravity on the sphere will DECREASE the sphere's kinetic energy. 1:035111A bullet of mass 12.3 g is fired into an initially stationary block and comes to rest in the block. The block, of mass 1.09 kg, is subject to no horizontal external forces during the collision with the bullet. After the collision, the block is observed to move at a speed of 5.50 m/s. (a) Find the initial speed of the bullet.(b) How much kinetic energy is lost?