football helmet project. there are some questions you will need yo answer them. I have uploaded the power point about this project it has everything you need for this project.please if you find this hard do not do it coz you do it wrong.
lecture_15___football_helmet_project_mar_13_2019.pptx
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ENGR 214B: Dynamics
Dr. Dave Poling
Mechanical Engineering
Office: 164 Kirkbride Hall
E-mail: [email protected]
Project on Impact –
Football Helmet Collision
March 13, 2019
Dynamics, Fourteenth Edition
R.C. Hibbeler
Copyright ©2016 by Pearson Education, Inc.
All rights reserved.
Consider the Football Helmets as two particles coming together
Dynamics, Fourteenth Edition
R.C. Hibbeler
Copyright ©2016 by Pearson Education, Inc.
All rights reserved.
Y – Plane of Contact
X – Line of Impact
Oblique Impact
Dynamics, Fourteenth Edition
R.C. Hibbeler
Copyright ©2016 by Pearson Education, Inc.
All rights reserved.
Project on Impact – Football Helmet Collision
Problem Statement
1.
The football player with helmet “A” has a velocity of vA = 6 ft/sec in the direction
shown and his helmet collides with a stationary football player’s helmet, “B”, with a
helmet of equal mass and diameter and same material. If e=0.6, determine the
resulting magnitude of velocity of each football player’s helmet following impact.
2.
What approx. force is exerted on helmet B if the delta time of impact is 0.01 sec?
3.
What recommendations would you provide to lessen the impact of head injuries?
Consider the Football Helmets as two particles
vB
=0
Line of Impact
x
vA = 6 ft/sec
B
y Plane of Impact
B
Oblique Impact
WA = WB = 5 lb
30o
A
A
Before Impact
Dynamics, Fourteenth Edition
R.C. Hibbeler
During
Impact
Copyright ©2016
by Pearson Education, Inc.
All rights reserved.
Backup Material
Dynamics, Fourteenth Edition
R.C. Hibbeler
Copyright ©2016 by Pearson Education, Inc.
All rights reserved.
IMPACT (Section 15.4)
Impact occurs when two bodies collide during a very short time
period, causing large impulsive forces to be exerted between the
bodies. Common examples of impact are a hammer striking a
nail or a bat striking a ball. The line of impact is a line through
the mass centers of the colliding particles. In general, there are
two types of impact:
Central impact occurs when the
directions of motion of the two colliding
particles are along the line of impact.
Oblique impact occurs when the direction
of motion of one or both of the particles is
at an angle to the line of impact.
Dynamics, Fourteenth Edition
R.C. Hibbeler
Copyright ©2016 by Pearson Education, Inc.
All rights reserved.
CENTRAL IMPACT
Central impact happens when the velocities of the two objects
are along the line of impact (recall that the line of impact is a
line through the particles’ mass centers).
vA
vB
Line of impact
Once the particles contact, they may
deform if they are non-rigid. In any
case, energy is transferred between the
two particles.
There are two primary equations used when solving impact
problems. The textbook provides extensive detail on their
derivation.
Dynamics, Fourteenth Edition
R.C. Hibbeler
Copyright ©2016 by Pearson Education, Inc.
All rights reserved.
CENTRAL IMPACT (continued)
In most problems, the initial velocities of the particles, (vA)1 and
(vB)1, are known, and it is necessary to determine the final
velocities, (vA)2 and (vB)2. So the first equation used is the
conservation of linear momentum, applied along the line of impact.
(mA vA)1 + (mB vB)1 = (mA vA)2 + (mB vB)2
This provides one equation, but there are usually two unknowns,
(vA)2 and (vB)2. So another equation is needed. The principle of
impulse and momentum is used to develop this equation, which
involves the coefficient of restitution, or e.
Dynamics, Fourteenth Edition
R.C. Hibbeler
Copyright ©2016 by Pearson Education, Inc.
All rights reserved.
CENTRAL IMPACT (continued)
The coefficient of restitution, e, is the ratio of the particles’
relative separation velocity after impact, (vB)2 – (vA)2, to the
particles’ relative approach velocity before impact, (vA)1 – (vB)1.
The coefficient of restitution is also an indicator of the energy
lost during the impact.
The equation defining the coefficient of restitution, e, is
e =
(vB)2 – (vA)2
(vA)1 – (vB)1
If a value for e is specified, this relation provides the second
equation necessary to solve for (vA)2 and (vB)2.
Dynamics, Fourteenth Edition
R.C. Hibbeler
Copyright ©2016 by Pearson Education, Inc.
All rights reserved.
COEFFICIENT OF RESTITUTION
In general, e has a value between zero and one.
The two limiting conditions can be considered:
• Elastic impact (e = 1): In a perfectly elastic collision, no
energy is lost and the relative separation velocity equals the
relative approach velocity of the particles. In practical
situations, this condition cannot be achieved.
• Plastic impact (e = 0): In a plastic impact, the relative
separation velocity is zero. The particles stick together and
move with a common velocity after the impact.
Some typical values of e are:
Steel on steel: 0.5 – 0.8
Wood on wood: 0.4 – 0.6
Lead on lead: 0.12 – 0.18
Glass on glass: 0.93 – 0.95
Dynamics, Fourteenth Edition
R.C. Hibbeler
Copyright ©2016 by Pearson Education, Inc.
All rights reserved.
IMPACT: ENERGY LOSSES
Once the particles’ velocities before and after the collision
have been determined, the energy loss during the collision
can be calculated on the basis of the difference in the
particles’ kinetic energy. The energy loss is
U1-2 = T2 − T1 where Ti = 0.5mi (vi)2
During a collision, some of the particles’ initial kinetic
energy will be lost in the form of heat, sound, or due to
localized deformation.
In a plastic collision (e = 0), the energy lost is a maximum,
although the energy of the combined masses does not
necessarily go to zero. Why?
Dynamics, Fourteenth Edition
R.C. Hibbeler
Copyright ©2016 by Pearson Education, Inc.
All rights reserved.
OBLIQUE IMPACT
In an oblique impact, one or both of the
particles’ motion is at an angle to the line of
impact. Typically, there will be four
unknowns: the magnitudes and directions of
the final velocities.
The four equations required to solve for the unknowns are:
Conservation of momentum and the coefficient
of restitution equation are applied along the line
of impact (x-axis):
mA(vAx)1 + mB(vBx)1 = mA(vAx)2 + mB(vBx)2
e = [(vBx)2 – (vAx)2]/[(vAx)1 – (vBx)1]
Momentum of each particle is conserved in the direction perpendicular to
the line of impact (y-axis):
mA(vAy)1 = mA(vAy)2 and mB(vBy)1 = mB(vBy)2
Dynamics, Fourteenth Edition
R.C. Hibbeler
Copyright ©2016 by Pearson Education, Inc.
All rights reserved.
PROCEDURE FOR ANALYSIS
• In most impact problems, the initial velocities of the particles
and the coefficient of restitution, e, are known, with the final
velocities to be determined.
• Define the x-y axes. Typically, the x-axis is defined along the
line of impact and the y-axis is in the plane of contact
perpendicular to the x-axis.
• For both central and oblique impact problems, the following
equations apply along the line of impact (x-dir.):
m(vx)1 = m(vx)2 and e = [(vBx)2 – (vAx)2]/[(vAx)1 – (vBx)1]
• For oblique impact problems, the following equations are also
required, applied perpendicular to the line of impact (y-dir.):
mA(vAy)1 = mA(vAy)2 and mB(vBy)1 = mB(vBy)2
Dynamics, Fourteenth Edition
R.C. Hibbeler
Copyright ©2016 by Pearson Education, Inc.
All rights reserved.
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