GOAL Combine the concepts of conservation of energy and conservation of momentum in inelasticcollisions.PROBLEM The ballistic pendulum (Figure a) is a device used to measure the speed of a fast-movingprojectile such as a bullet. The bullet is fired into a large block of wood suspended from some light wires.The bullet is stopped by the block, and the entire system swings up to a height h. It is possible to obtainthe initial speed of the bullet by measuring h and the two masses. As an example of the technique,assume that the mass of the bullet, m₁, is 5.00 g, the mass of the pendulum, m2, is 1.000 kg, and h is5.00 cm. (a) Find the velocity of the system after the bullet embeds in the block. (b) Calculate the initialspeed of the bullet.STRATEGY Use conservation of energy to find the initial velocity of the block-bullet system, labeling itVsys. Part (b) requires the conservation of momentum equation, which can be solved for the initial velocityof the bullet, V₁i.SOLUTION(A) Find the velocity of the system after the bullet embeds in the block.(KE+ PE) after collisionApply conservation of energy to theblock-bullet system after the collision.Substitute expressions for the kineticand potential energies. Note that boththe potential energy at the bottom andthe kinetic energy at the top are zero.Solve for the final velocity of theblock-bullet system, vsys(B) Calculate the initial speed of the bullet.Write the conservation of momentumequation and substitute expressions.Solve for the initial velocity of thebullet, and substitute values.2(m₁ + m₂) v sys² + 0 = 0 + (m₁ + m₂)ghV sysVsysV sys===V1i =V₁; =2gh=m₁v₁i + m₂V2i ==✓ 2gh 2(9.80 m/s²) (5.00 × 10-² m)0.990 m/sPi Pf(KE + PE) top(m₁ + m₂) v sys(m₁ + m₂) v sysm₁(1.005 kg)(0.990 m/s)= 199 m/s PRACTICE ITUse the worked example above to help you solve this problem. The ballistic pendulum (Figure a) is adevice used to measure the speed of a fast-moving projectile such as a bullet. The bullet is fired into alarge block of wood suspended from some light wires. The bullet is stopped by the block, and the entiresystem swings up to a height h. It is possible to obtain the initial speed of the bullet by measuring h andthe two masses. As an example of the technique, assume that the mass of the bullet, m₁, is 5.35 g, themass of the pendulum, m2, is 1.097 kg, and h is 4.54 cm.(a) Find the velocity of the system after the bullet embeds in the block.m/s(b) Calculate the initial speed of the bullet.m/sHINTS: GETTING STARTED I I'M STUCK!A bullet with mass 5.06 g is fired horizontally into a 1.981-kg block attached to a horizontal spring. Thespring has a constant 5.84 x 10² N/m and reaches a maximum compression of 6.19 cm.EXERCISE(a) Find the initial speed of the bullet-block system.m/s(b) Find the speed of the bullet.m/s

Name: GOAL Combine the concepts of conservation of energy and conservation
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Description: GOAL Combine the concepts of conservation of energy and conservation of momentum in inelasticcollisions.PROBLEM The ballistic pendulum (Figure a) is a device used to measure the speed of a fast-movingprojectile such as a bullet. The bullet is fired

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Physics

PRACTICE IT Use the worked example above to help you solve this problem. The ballistic pendulum (Figure a) is a device used to measure the speed of a fast-moving projectile such as a bullet. The bullet is fired into a large block of wood suspended from some light wires. The bullet is stopped by the block, and the entire system swings up to a height h. It is possible to obtain the initial speed of the bullet by measuring h and the two masses. As an example of the technique, assume that the mass of the bullet, m₁, is 5.35 g, the mass of the pendulum, m2, is 1.097 kg, and h is 4.54 cm. (a) Find the velocity of the system after the bullet embeds in the block. m/s (b) Calculate the initial speed of the bullet. m/s EXERCISE HINTS: GETTING STARTED I'M STUCK! A bullet with mass 5.06 g is fired horizontally into a 1.981-kg block attached to a horizontal spring. The spring has a constant 5.84 x 10² N/m and reaches a maximum compression of 6.19 cm. (a) Find the initial speed of the bullet-block system. m/s (b) Find the speed of the bullet. m/s

PRACTICE IT Use the worked example above to help you solve this problem. The ballistic pendulum (Figure a) is a device used to measure the speed of a fast-moving projectile such as a bullet. The bullet is fired into a large block of wood suspended from some light wires. The bullet is stopped by the block, and the entire system swings up to a height h. It is possible to obtain the initial speed of the bullet by measuring h and the two masses. As an example of the technique, assume that the mass of the bullet, m₁, is 5.35 g, the mass of the pendulum, m2, is 1.097 kg, and h is 4.54 cm. (a) Find the velocity of the system after the bullet embeds in the block. m/s (b) Calculate the initial speed of the bullet. m/s EXERCISE HINTS: GETTING STARTED I'M STUCK! A bullet with mass 5.06 g is fired horizontally into a 1.981-kg block attached to a horizontal spring. The spring has a constant 5.84 x 10² N/m and reaches a maximum compression of 6.19 cm. (a) Find the initial speed of the bullet-block system. m/s (b) Find the speed of the bullet. m/s

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Use the worked example above to help you solve this problem. A block of mass m1 = 1.72 kg, initially moving to the right with a velocity of +3.95 m/s on a frictionless horizontal track, collides with a massless spring attached to a second block of mass m2 = 2.01 kg moving to the left with a velocity of −2.83 m/s. The spring has a spring constant of 6.33 x102 N/m. (a) Determine the velocity of block 2 at the instant when block 1 is moving to the right with a velocity of +3.00 m/s. (Indicate the direction with the sign of your answer.) (b) Find the compression of the spring.