The Ballistic Pendulum
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The Ballistic Pendulum | Determining the initial speed of a projectile | | | | |
THE BALLISTIC PENDULUM
ABSTRACT
The experiment was carried out to determine the initial speed of a projectile: i) by means of a ballistic pendulum. ii) by measurements of the range and vertical distance of fall during its flight.
The initial speed for the ballistic pendulum was found to be 5.0551±0.0008m/s and the initial speed for the pendulum was found to be 4.72±0.02 m/s.
INTRODUCTION: i) Ballistic pendulum
A ball of mass m and velocity v₀ nets a pendulum bob of mass M. The total mass (M + m) acquires a velocity v₀ just after impact, and subsequently rises by a height h. Using the law of conversion of momentum, mv₀ = (M + m)v velocity v₀ (when neglecting friction) is given by: v₀ = (M+mm)2gl (1-cosθ
θ θ l - h l - h
l l
h h 12mv2= mgh (by law of conversion of energy) mv2= 2mgh cosθ= adjacenthypotenuse v2= 2gh lcosθ=l-hl*l v=±2gh lcosθ=l-h l-lcosθ=h l1-cosθ=h * h=l1-cosθ * v=±2gh = ±2gl(1-cosθ) ………..(1)
mv₀ = (M + m)v ……….(2)
Subtracting 1 into 2 we get: mv₀ = (M + m) ± 2gl1-cosθ v₀ = (M+mm) ± 2gl (1-cosθ
ii) Projectile
The projectile with initial horizontal velocity v₀ is projected in such a way that its vertical distance of fall is H and the range is R. The trajectory is illustrated in the diagram below.
V₀
V₀
H
H
R
R
Using the kinematic equation s = ut + ½ at2 we get x = v₀t along the horizontal direction. sina-u= v₀ then: x=v₀(t)+12(0)t2 a=0 x=v₀t+02 x=v₀t and along vertical direction: y=12gt2 u=g=0
When t is time of flight, then x = 2 and y = 1
Giving v₀ = lg2h 1=12gt2; t = 2Hg v₀ = xt=l2Hg=l2Hg12 =lg2h
IMAGE OF A BALLISTIC PENDULUM
METHODS AND MATERIALS:
MATERIALS
Assembled ballistic pendulum, steel ball, ramrod, metre rule, electronic balance, tape measure, 2 plain papers,
The Ballistic Pendulum | Determining the initial speed of a projectile | | | | |
THE BALLISTIC PENDULUM
ABSTRACT
The experiment was carried out to determine the initial speed of a projectile: i) by means of a ballistic pendulum. ii) by measurements of the range and vertical distance of fall during its flight.
The initial speed for the ballistic pendulum was found to be 5.0551±0.0008m/s and the initial speed for the pendulum was found to be 4.72±0.02 m/s.
INTRODUCTION: i) Ballistic pendulum
A ball of mass m and velocity v₀ nets a pendulum bob of mass M. The total mass (M + m) acquires a velocity v₀ just after impact, and subsequently rises by a height h. Using the law of conversion of momentum, mv₀ = (M + m)v velocity v₀ (when neglecting friction) is given by: v₀ = (M+mm)2gl (1-cosθ
θ θ l - h l - h
l l
h h 12mv2= mgh (by law of conversion of energy) mv2= 2mgh cosθ= adjacenthypotenuse v2= 2gh lcosθ=l-hl*l v=±2gh lcosθ=l-h l-lcosθ=h l1-cosθ=h * h=l1-cosθ * v=±2gh = ±2gl(1-cosθ) ………..(1)
mv₀ = (M + m)v ……….(2)
Subtracting 1 into 2 we get: mv₀ = (M + m) ± 2gl1-cosθ v₀ = (M+mm) ± 2gl (1-cosθ
ii) Projectile
The projectile with initial horizontal velocity v₀ is projected in such a way that its vertical distance of fall is H and the range is R. The trajectory is illustrated in the diagram below.
V₀
V₀
H
H
R
R
Using the kinematic equation s = ut + ½ at2 we get x = v₀t along the horizontal direction. sina-u= v₀ then: x=v₀(t)+12(0)t2 a=0 x=v₀t+02 x=v₀t and along vertical direction: y=12gt2 u=g=0
When t is time of flight, then x = 2 and y = 1
Giving v₀ = lg2h 1=12gt2; t = 2Hg v₀ = xt=l2Hg=l2Hg12 =lg2h
IMAGE OF A BALLISTIC PENDULUM
METHODS AND MATERIALS:
MATERIALS
Assembled ballistic pendulum, steel ball, ramrod, metre rule, electronic balance, tape measure, 2 plain papers,
References: (n.d.). Retrieved October 27, 2012, from http://www.bing.com/images/search?q=ballistic+pendulum&qs=n&form=QBIR&pq=ballistic+pendulum&sc=0-0&sp=-1&sk= Dr.S, C. (2012/2013). Mechanics and Geometrical Optics. Gaborone: University of Botswana. Giancoli, D. C. (2009). Physics for scientists and engineers with modern physics. New Jersey: Pearson Education, Inc.