You throw a metal block of mass 0.19 kg into the air, and it leaves your hand at time t= 0 at location <0, 2, 0> m with velocity <3.5, 4.5, 0> m/s. At this low velocity air resistance is negligible. Using the iterative method shown in Section 2.4 with a time step of 0.05 s, calculate step by step the position and velocity of the block at t= 0.05 s, t= 0.10 s, and t= 0.15 s. (Express your answers in vector form.)
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- A 22-gg bullet traveling 245 m/s penetrates a 2.0 kg block of wood and emerges going 135 m/s. a)If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?A bullet of mass mm = 0.0010 kg embeds itself in a wooden block with mass M = 0.999 kg which then compresses a spring (k = 130 N/m ) by a distance x = 0.053 m before coming to rest. The coefficient of kinetic friction between the block and table is μ = 0.50. A. What is the initial velocity (assumed horizontal) of the bullet? 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?(a).A body of weight 640 N body is at rest. Another body of weight 310 N moving to the left with a velocity of 15 m/s collides with body which is at rest. After impact the body which is moving before impact comes to rest. Find the final velocity of body after impact and the coefficient of restitution . (b).A truck of mass 19 tonnes runs into a buffer stop having two buffer springs connected in series each of 1250 kN/cm and 2250 kN/cm stiffness respectively. Find the maximum compression of the springs, if the truck is travelling at 60 km/hr. Also calculate the load acting on the spring. (a)Solution The final velocity of body after impact in m/s is The coefficient of restitution is (b)Solution The maximum compression of the spring in mm is The load acting on the spring in kN is
- Use the approximation that vavg = pf/m for each time step.A spring with a relaxed length of 25 cm and a stiffness of 13 N/m stands vertically on a table. A block of mass 79 g is attached to the top of the spring. You pull the block upward, stretching the spring until its length is now 28.4 cm, hold the block at rest for a moment, and then release it. Using a time step of 0.1 s, predict the position and momentum of the block at a time 0.2 s after you release the block. (Assume the +y direction is upward. Express your answers in vector form.) r = m p = kg · m/sA block of mass M = 5.4 kg, capable of sliding with negligible friction over pad, is attached to a spring of negligible mass and elastic constant k = 6000 N.m-1, which is at the other end attached to wall. initially relaxed. A projectile with mass m = 9.5 g and horizontal velocity v = 630 m.s-1, hits the block at t=0 enters the body velocity.The projectile remains trapped in the body.(a) Determine the velocity of the body just after impact. (b)Calculate the amplitude of the resulting harmonic motion.A spring with a spring constant of 335 N/m is initially compressed by a distance of 0.045 m from its equilibrium position. A mass of 0.045 kg is then held against the compressed spring and released from rest while upon a horizontal, frictionless surface. Assuming that the spring then pushes the mass across the surface, with speed does the mass leave the spring? Assume proper SI Units.
- A 10.0 g bullet is fired into and embeds itself in a 1.60 kg block attached to a spring with a spring constant of 23.7 N/m and whose mass is negligible. How far is the spring compressed if the bullet has a speed of 300 m/s just before it strikes the block, and the block slides on a frictionless surface? (Note: You must use conservation of momentum in this problem.) mA bullet with a mass m(b)=13.1 g is fired into a block of wood at velocity v(b)=261 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 cmbefore the whole system momentarily comes to a stop. Assuming that the surface on which the block is resting is frictionless, determine the mass m(w) of the wooden block.A 0.180 kg billiard ball that is moving at 4.60 m/s strikes the bumper of a pool table and bounces straight back at 3.68 m/s (80% of its original speed). The collision lasts 0.0190 s. (Assume that the ball moves in the positive direction initially.) c)What percent of the original energy is left?
- In the figure, block 2 (mass 1.70 kg) is at rest on a frictionless surface and touching the end of an unstretched spring of spring constant 218 N/m. The other end of the spring is fixed to a wall. Block 1 (mass 1.70 kg), traveling at speed v1 = 3.40 m/s, collides with block 2, and the two blocks stick together. When the blocks momentarily stop, by what distance is the spring compressed?A 2 kg object moving at 3 m/s collides with a 4 kg object that is stationary. If the collision is perfectly inelastic, what is the speed of the 2 kg object after the collision? and how much is KE lost? speed = −0.5 m/s and KE lost = 9J speed = −1 m/s and KE lost = 3J No answer speed = 1 m/s and KE lost = 6J speed = 1.5 m/s and KE lost = 12JA bullet of mass 4 g moving with an initialspeed 300 m/s is fired into and passes througha block of mass 7 kg. The block, initially at rest on a frictionless,horizontal surface, is connected to a spring offorce constant 440 N/m. If the block moves a distance 1.5 cm to theright after the bullet passed through it, findthe speed v at which the bullet emerges fromthe block. Answer in units of m/s. Additionally, find the magnitude of the energy lost in thecollision. Answer in units of J.