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A: spring constant (k) = 25 N/m M = 3 kg mb = 0.3 kg vo = 200 m/s
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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 upwards 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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- Two masses hang next to each other from a support. Each mass has a pendulum length R = 30 cm. Object A is raised to a 66 degree angle with respect to vertical and allowed to fall as a pendulum, eventually colliding elastically with object B. Let object A have a mass ma=45g and object B have mass mb=65g. For all answers, work symbolically and then plug in numbers at the end. (a) What is the velocity of the object A before the collision? (Ignore the physical size of A and B, that is, assume y = 0 for both during the collision) (b) What quantities are conserved during the collision? (c) What are the maximum heights of each object after the collision?Two rigid bodies, A and B, both 1 kg in mass, are connected by a linear spring with a spring constant of 0.2 N/m. Initially, the spring is unstretched and the bodies are at rest. If multiple forces and moments are applied to the two bodies that result in the speed of body A increasing to 10 m/s, the speed of body B increasing to 4 m/s, and the stretch of the spring increasing by 10 m, then -20 Nm of work was done by the spring on the body A, B system. Two rigid bodies, A and B, both 1 kg in mass, are connected by a linear spring with a spring constant of 0.2 N/m. Initially, the spring is unstretched and the bodies are at rest. If multiple forces and moments are applied to the two bodies that result in the speed of body A increasing to 10 m/s, the speed of body B increasing to 4 m/s, and the stretch of the spring increasing by 10 m, then -20 Nm of work was done by the spring on the body A, B system. True FalseConsider two cars that can roll on a frictionless track. Initially, both cars are at rest. One car is launched from rest with a spring, and the cars undergo a completely inelastic collision. The spring constant is 850 N/m, and the spring is initially compressed by 0.075 m. The first car has a mass of 0.50 kg and the second has a mass of 1.0 kg. An identical spring is located to the right of the cars. a. The velocity of the first car just before collision. b. The velocities of the cars after collision. c. The distance the spring on the right will be compressed when the cars are completely stopped by the spring.
- A block of mass M = 8 kg rests on a horizontal frictionless floor, and is connected to a vertical wall by a spring of force constant k = 200 N/m. When the spring is in its equilibrium position (neither stretched nor compressed), the block just touches a second lighter block of mass m = 4 kg at rest on the frictionless floor. The spring with mass M attached is now compressed by 0.1 m and released. The two blocks undergo a completely inelastic collision, i.e., they stick together after collision. Draw a diagram and define all relevant variables. Just before the collision, what is the velocity of mass MT Just after the collision, what is the common velocity of the two blocks? (What is the maximum stretching of the spring after the collision?: How long after the collision do the masses reach their first maximum stretch?Consider the following system: A spring has stiffness 598 N/m and is initially uncompressed. It is oriented vertically and placed on hard surface. A mass of size 2.3 kg is released from rest 9 m above the spring. Calculate the speed of the mass at the moment when the spring is compressed 0.5 m. Use g = 10 m/s2. (Please answer to the fourth decimal place - i.e 14.3225)A 0.2-kg pendulum bob A hangs from a 0.75 m cord attached to a fixed pivot. It is released from rest at point 1 when the cord is horizontal and without slack, and swings down to strike 0.2-kg bob B at point 2. The coefficient of restitution between the two bobs is e = 0.7. Neglect the size of the bobs and the mass of the cords. 0.75 m 1 For parts b-f below, consider bob A at the instant the cord is vertical, when it has reached point 2, and immediately before the collision: a) ) What is the tension in the cord of the stationary bob B? b) ( Draw a clear and complete free body diagram of bob A. с) ( Find the speed of bob A. d) Find the tangential acceleration of bob A. e) Find the normal acceleration of bob A. f) Find the tension in the cord of bob A. g) Find the speed of bob A immediately after the collision.
- A block of mass M = 5.10 kg, at rest on a horizontal frictionless table, is attached to a rigid support by a spring of constant k = 6040 N/m. A bullet of mass m = 9.30 g and velocity v of magnitude 690 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. %3D M m (a) Number i Units (b) Number Units(a) A spring of negligible mass and with spring constant k = 400 N/m is hung vertically; a pan of mass mp = 0.2 kg is suspended from its lower end. A piece of meat of mass mm = 2.2 kg is dropped onto the pan from a height of 0.4 m above the pan. The meat makes a totally inelastic collision with the pan, and sets the system into vertical simple harnoіс тotion. Find: (i) the speed of the meat and pan immediately after the collision; (ii) the amplitude of the subsequent motion; and (iii) the period of that motion.A block A, of mass m = 10 Kg, compresses a spring of constant K = 1000 N / m in a length x = 3 cm. Starting from rest, the block is released, which moves from that moment on a horizontal surface without friction until it collides with another block B of mass m = 40 Kg, which was at rest. (Perfectly inelastic shock) and together they go up the channel (inclined surface) without friction, to later continue along a second horizontal plane without friction, at a height h with respect to the first (see Figure). Determine the energy variation that occurs in the collision .
- A bullet with a mass m, = 12.7 g is fired into a block of wood at velocity v, 253 m/s. The block is attached to a spring that has a spring constant k of 205 N/m. The block and bullet continue to move, compressing the spring by 35.0 cm before the whole system momentarily comes to a stop. Assuming that the surface on which the block is resting is frictionless, determine the mass mw of the wooden block. mw = kgA rocket motor is undergoing a "bench test." It is attached to a fixed support by four large springs of constant 10^6 N/m. The motor burns fuel at a rate of 50 kg/s. When the motor is running the springs are observed to stretch 1.5 cm. Determine the exhaust speed of the burned fuel.A block of mass M = 5.00 kg, at rest on a horizontal frictionless table, is attached to a rigid support by a spring of constant k = 6390 N/m. A bullet of mass m = 8.30 g and velocity v of magnitude 530 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. M (a) Number Units (b) Number Units