PROBLEM 1: A rifle bullet of mass m strikes and is embedded in a block of mass M which is resting on a frictionless, horizontal surface and is attached to a spring of force constant k. (a) Find the speed of the block (with embedded bullet) immediately after the impact. (b) If the spring is compressed a distance d, what was the initial velocity of the bullet?
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- Two objects of masses m, - 0.42 kg and m, = 0.90 kg are placed on a horizontal frictionless surface and a compressed spring of force constant k = 300 N/m is placed between them as in figure (a). Neglect the mass of the spring. The spring is not attached to either object and is compressed a distance of 9.6 cm. If the objects are released from rest, find the final velocity of each object as shown in figure (b). (Let the positive direction be to the right. Indicate the direction with the sign of your answer.) m/s V2 = m/s aA bullet of mass mm = 0.0010 kgkg embeds itself in a wooden block with mass MM = 0.999 kgkg, which then compresses a spring (kkk = 130 N/mN/m ) by a distance xxx = 0.048 mm before coming to rest. The coefficient of kinetic friction between the block and table is μμ = 0.50. a. What is the initial velocity (assumed horizontal) of the bullet? Express your answer using two significant figures. b. What fraction of the bullet's initial kinetic energy is dissipated (in damage to the wooden block, rising temperature, etc.) in the collision between the bullet and the block?Two objects of masses m, = 0.46 kg and m, = 0.90 kg are placed on a horizontal frictionless surface and a compressed spring of force constant k = 250 N/m is placed between them as in figure (a). Neglect the mass of the spring. The spring is not attached to either object and is compressed a distance of 9.6 cm. If the objects are released from rest, find the final velocity of each object as shown in figure (b). (Let the positive direction be to the right. Indicate the direction with the sign of your answer.) m/s m/s a m m2
- A 12.0-g bullet is fired horizontally into a 114-g wooden block that is initially at rest on a frictionless horizontal surface and connected to a spring having spring constant 141 N/m. The bullet becomes embedded in the block. If the bullet-block system compresses the spring by a maximum of 82.5 cm, what was the speed of the bullet at impact with the block?In the figure, block 2 (mass 1.20 kg) is at rest on a frictionless surface and touching the end of an unstretched spring of spring constant 208 N/m. The other end of the spring is fixed to a wall. Block 1 (mass 1.90 kg), traveling at speed v1 = 3.50 m/s, collides with block 2, and the two blocks stick together. When the blocks momentarily stop, by what distance is the spring compressed? eelle Number i UnitsA cart of mass 5 kg is held on the ramp at a height of 2.5 m. Another cart of mass 5 kg is on a frictionless surface sitting next to a spring with spring constant 158 N/m. At some instant, the first cart starts sliding down and hits the second cart. If the collision between the carts is elastic in nature, find the compression in the spring caused by the second cart. [limit your answers within one decimal places). m1 m2
- A golf ball of mass m = 0.11 kg is dropped from a height h. It interacts with the floor for t = 0.185 s, and applies a force of F = 10.5 N to the floor when it elastically collides with it. Part (a) Write an expression for the ball's velocity, v, in terms of the variables m, t, and F, just after it rebounds from the floor. (Hint: The fact that the collision is elastic is important when solving this problem.) Part (b) What is the magnitude of the ball's velocity v, in meters per second, right after it rebounds? Part (c) How high h, in meters, will the ball travel on the rebound?A bullet of mass m=5g moving with an initial speed 400m/s of 400 m/s is fired into and passes through a M=1 kg block, as in Figure. The block, initially at rest on frictionless, horizontal surface is connected to a 5.00cm! spring of force constant k=900 N/m. If the block moves d= 5 cm to the right after impact and the object stops. What is the speed of block at which the bullet emerges from it? 1,5 m/s 200 m/s 2 m/s 100 m/s 150 m/sTwo objects of masses m, = 0.44 kg and m, = 0.90 kg are placed on a horizontal frictionless surface and a compressed spring of force constant k = 270 N/m is placed between them as in figure (a). Neglect the mass of the spring. The spring is not attached to either object and is compressed a distance of 9.6 cm. If the objects are released from rest, find the final velocity of each object as shown in figure (b). (Let the positive direction be to the right. Indicate the direction with the sign of your answer.) 37983.18 V = The response you submitted has the wrong sign. m/s |-18569.55 V2 = The response you submitted has the wrong sign. m/s a k
- Problem 4. A 15.0-kg block is attached to a very light horizontal spring of force constant 500.0 N/m and is resting on a frictionless horizontal table (see figure below). Suddenly it is struck by a 3.00-kg stone traveling horizontally at 8.00 m/s to the right. The collision is totally inelastic. (a) Find the velocity of the stone-block just after collision. (b) Find the maximum distance that the stone-block will compress the spring after the collision. 15.0 kg 3.00 kg 8.00 m/sA force in the negative direction of an x axis is applied for 36 ms to a 0.28 kg ball initially moving at 22 m/s in the positive direction of the axis. The force varies in magnitude, and the impulse has magnitude 42.8 N s. (a) What is the ball's velocity (including sign for direction) just after the force is applied? (b) What is the average magnitude of the force on the ball? (a) Number i Units (b) Number i UnitsStarting with an initial speed of 4.80 m/s at a height of 0.264 m, a 2.16-kg ball swings downward and strikes a 4.93-kg ball that is at rest, as the drawing shows. (a) Using the principle of conservation of mechanical energy, find the speed of the 2.16-kg ball just before impact. (b) Assuming that the collision is elastic, find the velocity (magnitude and direction) of the 2.16-kg ball just after the collision. (c) Assuming that the collision is elastic, find the velocity (magnitude and direction) of the 4.93-kg ball just after the collision. (d) How high does the 2.16-kg ball swing after the collision, ignoring air resistance? (e) How high does the 4.93-kg ball swing after the collision, ignoring air resistance?