COLLEGE PHYSICS
2nd Edition
ISBN: 9781464196393
Author: Freedman
Publisher: MAC HIGHER
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Chapter 12, Problem 81QAP
To determine
The position function for the bullet-block system after collision.
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The spring of a spring gun has force constant k = 435 N/m and negligible mass. The spring is compressed 6.8 cm, and a ball with mass 23 g is placed in the horizontal barrel against the compressed spring. The spring is then released, and the ball is propelled out the barrel of the gun. The barrel is 6.8 cm long, so the ball leaves the barrel at the same point that it loses contact with the spring. The gun is held so the barrel is horizontal. What is the greatest speed the ball has along the barrel if a constant resisting force of 6.7 N acts on the ball as it moves along the barrel? (Your result must be in units of m/s and include 2 digits after the decimal point. Maximum of 3% of error is accepted in your answer.)
An 8.0-g bullet is suddenly shot into a 4.0-kg block that is at rest on a frictionless horizontal surface, as shown in the figure. The bullet remains lodged in the block. The block then runs into a spring bumper and compresses it by 3.7 cm. The force constant (spring constant) of the spring is 2500 N/m. What was the initial speed v of the bullet?
7. The Dread Pirate Roberts is trying to fire a 12 kg cannon ball from a 250 kg cannon. In order to prevent the cannon from recoiling across the deck of the ship, he attaches a large spring behind the cannon, with the spring's other end braced firmly against the ship's frame. When the cannon is fired, the ball is launched forward at 90 kilometers per hour. Subsequently, the cannon pushes backwards and compresses the spring by 60 cm. What is the spring constant k of the spring?
Chapter 12 Solutions
COLLEGE PHYSICS
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- A 5.00-g bullet moving with an initial speed of i = 400 m/s is fired into and passes through a 1.00-kg block as shown in Figure P9.89. The block, initially at rest on a frictionless, horizontal surface, is connected to a spring with force constant 900 N/m. The block moves d = 5.00 cm to the right after impact before being brought to rest by the spring. Find (a) the speed at which the bullet emerges from the block and (b) the amount of initial kinetic energy of the bullet that is converted into internal energy in the bullet-block system during the collision.arrow_forwardAn inclined plane of angle = 20.0 has a spring of force constant k = 500 N/m fastened securely at the bottom so that the spring is parallel to the surface as shown in Figure P6.61. A block of mass m = 2.50 kg is placed on the plane at a distance d = 0.300 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?arrow_forwardIn a laboratory experiment, 1 a block of mass M is placed on a frictionless table at the end of a relaxed spring of spring constant k. 2 The spring is compressed a distance x0 and 3 a small ball of mass m is launched into the block as shown in Figure P11.22. The ball and block stick together and are projected off the table of height h. Find an expression for the horizontal displacement of the ballblock system from the end of the table until it hits the floor in terms of the parameters given. FIGURE P11.22arrow_forward
- A 5.00-g bullet moving with an initial speed of v = 400 m/s is fired into and passes through a 1.00-kg block as shown in Figure P8.57. The block, initially at rest on a frictionless, horizontal surface, is connected to a spring with force constant 900 N/m. The block moves d = 5.00 cm to the right after impact before being brought to rest by the spring. Find (a) the speed at which the bullet emerges from the block and (b) the amount of initial kinetic energy of the bullet that is converted into internal energy in the bullet-block system during the collision. Figure P8.57arrow_forwardReview. This problem extends the reasoning of Problem 41 in Chapter 9. Two gliders are set in motion on an air track. Glider 1 has mass m1 = 0.240 kg and moves to the right with speed 0.740 m/s. It will have a rear-end collision with glider 2, of mass m2 = 0.360 kg, which initially moves to the right with speed 0.120 m/s. A light spring of force constant 45.0 N/m is attached to the back end of glider 2 as shown in Figure P9.41. When glider 1 touches the spring, superglue instantly and permanently makes it stick to its end of the spring. (a) Find the common speed the two gliders have when the spring is at maximum compression. (b) Find the maximum spring compression distance. The motion after the gliders become attached consists of a combination of (1) the constant-velocity motion of the center of mass of the two-glider system found in part (a) and (2) simple harmonic motion of the gliders relative to the center of mass. (c) Find the energy of the center-of-mass motion. (d) Find the energy of the oscillation.arrow_forwardPendulum bob 1 has mass m1. It is displaced to height h1 and released. Pendulum bob 1 elastically collides with pendulum bob 2 of mass m2 (Fig. P11.43). FIGURE P11.43 a. Find an expression for the maximum height h2 of pendulum bob 2. b. If m2 = 2.5m1 and h1 = 5.46 m, what is h2?arrow_forward
- A 6 000-kg freight car rolls along rails with negligible friction. The car is brought to rest by a combination of two coiled springs as illustrated in Figure P6.27 (page 188). Both springs are described by Hookes law and have spring constants k1 = 1 600 N/m and k2, = 3 400 N/m. After the first spring compresses a distance of 30.0 cm, the second spring acts with the first to increase the force as additional compression occurs as shown in the graph. The car comes to rest 50.0 cm after first contacting the two-spring system. Find the cars initial speed.arrow_forwardConsider an undamped linear oscillator with a natural frequency ω0 = 0.5 rad/s and the step function a = 1 m/s2. Calculate and sketch the response function for an impulse forcing function acting for a time τ = 2π/ω0. Give a physical interpretation of the results.arrow_forwardTwo blocks of masses m and 3m are placed on a frictionless, horizontal surface. A light spring is attached to the more massive block, and the blocks are pushed together with the spring between them (Fig. P8.7). A cord initially holding the blocks together is burned; after that happens, the block of mass 3m moves to the right with a speed of 2.00 m/s. (a) What is the velocity of the block of mass m? (b) Find the systems original elastic potential energy, taking 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 beforehand and plenty of motion afterward? Figure P8.7arrow_forward
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