PEARSON ETEXT ENGINEERING MECH & STATS
15th Edition
ISBN: 9780137514724
Author: HIBBELER
Publisher: PEARSON
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Chapter 15, Problem 38P
A ballistic pendulum consists of a 4-kg wooden block originally at rest, θ = 0°. When a 2-g bullet strikes and becomes embedded in it, it is observed that the block swings upward to a maximum angle of u = 6°. Estimate the initial speed of the bullet.
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Ballistic Pendulum
To apply conservation of energy and momentum.
As shown, an object of mass m is fired with an initial speed v0 at a ballistic pendulum’s bob. The bob has mass M and is suspended by a massless rod of length L. After the collision, the pendulum’s bob and object stick together and swing to a maximum angular displacement θ.
Find an expression for v0, the initial speed of the object fired.
Express your answer in terms of some or all of the variables m, M, L, and θ and g, the acceleration due to gravity.
2. A block of mass m=3 kg is sliding along a frictionless inclined surface that makes an angle
of o = 30°with respect to the horizontal surface.
At the lowest points of the inclined surface, a projectile is fired at a speed of v, = 12 m/s that
makes an angle 8, = 45° with respect to the horizontal. Our aim of this problem is to find the
time when the projectile will hit the block.
e = 450
h = ?
Ro= 10 m
P= 30°
x= ?
(a) Find the time when the projectile hits the block. (Given, the initial distance between the block
and the projectile along the inclined surface at t=0 is R, = 10 m as shown in the figure)
Page 1 of 3
(b) Find the height h, where the projectile will hit the block.
(c) Now assume that the projectile hits the block at its maximum range R along the inclined
surface and the block is not sliding at all. Then find the maximum range along the inclined
surface, Rmax = ?
1. A crate with mass 32.0 kg initially at rest on a warehouse floor is acted on by a net horizontal force
of 130 N. (a) What acceleration is produced? (b) How far does the crate travel in 13.0 s?
2. A spring of stiffness k = 500 N/m is mounted against the 10-kg block. If the block is subjected to the
force of F = 500N, determine its velocity at s = 0.45 m. When s = 0, the block is at rest and the
spring is uncompressed. The contact surface is smooth.
Chapter 15 Solutions
PEARSON ETEXT ENGINEERING MECH & STATS
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