A bullet with a mass of 0.01 kg is tired horizontally into a block of wood hanging on a string. The bullet sticks in the wood and causes it to swing upward to a height of 0.1 m. If the mass of the wood block is 2 kg, what was the initial speed of the bullet?
The initial speed of the bullet.
Answer to Problem 2C
The initial speed of the bullet is
Explanation of Solution
Given:
Given that a bullet with a mass of
Formula used:
According to the law of conservation of momentum, when the two objects collide in an isolated system, the total momentum before and after the collision is same.
Calculation:
Given that the bullet sticks in the wood and swing upward to a height of
Thus, kinetic energy of bullet is converted into the potential energy
Now, kinetic energy of combined mass just after the impact is calculated as
We have
Substituting the value in above formula, we get
Also, potential energy of wood and bullet together is calculated as
We have
Substituting the value in above formula, we get
Equating Eq(1) and Eq(2), we get
The impact of bullet on wooden block is an inelastic collision, thus momentum is conserved.
Using the conservation of momentum, we have
We have
Substituting the values, we have
Conclusion:
Hence, the initial speed of the bullet is
Want to see more full solutions like this?
Chapter 3 Solutions
Inquiry into Physics
- You hold a slingshot at arms length, pull the light elastic band back to your chin, and release it to launch a pebble horizontally with speed 200 cm/s. With the same procedure, you fire a bean with speed 600 cm/s. What is the ratio of the mass of the bean to the mass of the pebble? (a) 19 (b) 13 (c) 1 (d) 3 (e) 9arrow_forwardA particle is suspended from a post on top of a can by a light string of length L. as shown in Figure P9.57a. The can and particle are initially moving to the right at constant speed the with the string vertical. The can suddenly comes to rest when it runs into and sticks to a bumper as shown in Figure P9.57b. The suspended panicle swings through an angle . (a) Show that the original speed of the cart can be computed from. vi=2gL(1cos) (b) If the bumper is still exerting a horizontal force on the cart when the hanging panicle is at its maximum angle forward from the vertical. at what moment does the bumper stop exerting a horizontal force?arrow_forwardTwo gliders are set in motion on a horizontal air track. A spring of force constant k is attached to the back end of the second glider. As shown in Figure P8.48, the first glider, of mass m1, moves to the right with speed v1, and the second glider, of mass m2, moves more slowly to the right with speed v2. When m1 collides with the spring attached to m2, the spring compresses by a distance xmax, and the gliders then move apart again. In terms of v1, v2, m1, m2, and k, find (a) the speed rat maximum compression, (b) the maximum compression xmax, and (c) the velocity of each glider after m1 has lost contact with the spring.arrow_forward
- A block of mass m1 = 20.0 kg is connected to a block of mass m2 = 30.0 kg by a massless string that passes over a light, frictionless pulley. The 30.0-kg block is connected to a spring that has negligible mass and a force constant of k = 250 N/m as shown in Figure P7.73. The spring is un-stretched when the system is as shown in the figure, and the incline is frictionless. The 20.0-kg block is pulled a distance h = 20.0 cm down the incline of angle = 40.0 (so that the 30.0-kg block is 40.0 cm above the floor) and released from rest. Find the speed of each block when the 30.0-kg block is 20.0 cm above the floor (that is, when the spring is unstretched). Figure P7.73arrow_forwardThe coefficient of friction between the block of mass ml = 3.00 kg and the surface in Figure P7.22 is k = 0.400. The system starts from rest. What is the speed of the ball of mass, m2 = 5.00 kg when it has fallen a distance h = 1.50 m? Figure P7.22arrow_forwardThree runaway train cars are moving on a frictionless, horizontal track in a railroad yard as shown in Figure P11.73. The first car, with mass m1 = 1.50 103 kg, is moving to the right with speed v1 = 10.0 m /s; the second car, with mass m2 = 2.50 103 kg, is moving to the left with speed v2 = 5.00 m/s, and the third car, with mass m3 = 1.20 103 kg, is moving to the left with speed v3 = 8.00 m /s. The three railroad cars collide at the same instant and couple, forming a train of three cars. a. What is the final velocity of the train cars immediately after the collision? b. Would the answer to part (a) change if the three cars did not collide at the same instant? Explain. FIGURE P11.73arrow_forward
- A block of mass m1 = 4.00 kg initially at rest on top of a frictionless, horizontal table is attached by a lightweight string to a second block of mass m2 = 3.00 kg hanging vertically from the edge of the table and a distance h = 0.450 m above the floor (Fig. P8.77). If the edge of the table is assumed to be frictionless, what is the speed with which the first block leaves the edge of the table?arrow_forwardA massive tractor is rolling down a country road. In a perfectly inelastic collision, a small sports car runs into the machine from behind. (i) Which vehicle experiences a change in momentum of larger magnitude? (a) The car does. (b) The tractor does. (c) Their momentum changes are the same size. (d) It could be either vehicle. (ii) Which vehicle experiences a larger change in kinetic energy? (a) The car does. (b) The tractor does. (c) Their kinetic energy changes are the same size. (d) It could be either vehicle.arrow_forwardTwo objects are connected by a light string passing over a light, frictionless pulley as shown in Figure P7.7. The object of mass m1 = 5.00 kg is released from rest at a height h = 4.00 m above the table. Using the isolated system model, (a) determine the speed of the object of mass m2 = 3.00 kg just as the 5.00-kg object hits the table and (b) find the maximum height above the table to which the 3.00-kg object rises.arrow_forward
- Two gold hangers with masses 2 kg and 4 kg are attached to a string over a pulley. The mass of the pulley and the string is neglected and the pulley is considered frictionless. The two gold hangers are released from rest at the same level. Find the speed of the 2 kg gold hanger after it has risen 3 meters?arrow_forwardA arrow of mass 0.01 kg moving horizontal suddenly strikes a block of wood of mass 8.6 kg that is suspended by a light string, like a pendulum. The arrow passes through the wood, then the wood swings upward and momentarily stops when the string is horizontal. The length of the string is 2.0 cm. How long did it take the arrow to go through the wood if the friction force between the bullies and the wood is 100 N?arrow_forwardAs shown in the figure, a bullet of mass 0.010 kg moving horizontally suddenly strikes a block of wood of mass 1.5 kg that is suspended as a pendulum. The bullet lodges in the wood, and together they swing upward a vertical distance of 0.40 m. The length of the string is 2.0 m. What was the speed of the bullet just before it struck the wooden block?arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning