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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