# Collision Force and Collision Time by pengxuebo

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• pg 1
```									COLLISION TIME
AND
COLLISION FORCE
Just before collision                 obstacle fixed to
initial velocity         the runway
(force sensor)

trolley
0.505 kg

A trolley is moving towards a force sensor fixed
to the runway. The force sensor serves as an
obstacle hit by the trolley.

The velocity of the trolley is measured with a
motion sensor.
During collision                       obstacle fixed to
the runway
(force sensor)

trolley
0.505 kg

collision force
acting on the trolley
by the obstacle
The collision force is measured by the force sensor.
The period during which the collision force is acting is known
as collision time.
The collision force is not uniform.
Just after collision                  obstacle fixed to
final velocity     the runway
(force sensor)

trolley
0.505 kg

The front of the trolley and the force sensor are made of
very strong material. There is negligible permanent
deformation produced by the collision.
The collision force - time graph and the velocity - time graph
are to be shown.

The positive direction is taken as the direction of motion of the
trolley before collision.

Therefore the collision force is negative. The initial velocity is
positive and the final velocity is negative.
collision time = 0.03 s

maximum magnitude of
collision force
= 30 N

final velocity
initial velocity
= -0.22 m s-1
= 0.44 m s-1
The collision time is short and the collision force is large.

Average collision force on the trolley
= mass of the trolley  average acceleration of the trolley

(-0.22) - (0.44)
 0.505
0.03
= -11 N

Note that the maximum magnitude of the collision force is
much larger than the magnitude of the average collision
force.
What if the front of the trolley is so
designed that it deforms slowly and
permanently during collision ?
Just before collision                 obstacle fixed to
initial velocity         the runway
(force sensor)

trolley
0.505 kg

Bumper (made of paper)
Just after collision                   obstacle fixed to
final velocity              the runway
(force sensor)

trolley
0.505 kg

Bumper deformed permanently after the collision. This
absorbs part of the initial kinetic energy of the trolley.
The collision force - time graph and the velocity - time graph
are to be shown.
collision time = 0.31 s

maximum magnitude of
collision force
= 2.6 N

initial velocity
final velocity
= 0.46 m   s-1
= -0.22 m s-1
The collision time is much longer and the collision force is
considerably smaller.

Average collision force on the trolley
= mass of the trolley  average acceleration of the trolley

(-0.22) - (0.46)
 0.505
0.31
= -1 N
That’s why the front and back of a car is so designed that
it is collapsible during collision. This increases the time
of collision and hence reduces the collision force.
However the middle portion of the car is still made of
strong material so as to protect the passengers inside.
velocity
Summary
u
u is the speed before
collision.
0                  time
-v                         v is the speed after
collision.

collision force               t is the collision time.
Fmax is the maximum
0                 time   magnitude of the
collision force.
-Favg
Favg is the magnitude of
the average collision
-Fmax                        force.
t
velocity
Summary
u
( -v ) - ( u )
- Favg  m 
time                        t
0
(-mv) - ( mu)
-v                                 
t
collision force                            m(u  v)
Favg   
t
0                 time
The collision force increases for
-Favg
• larger mass of the object

-Fmax                        • higher speed of the object
just before collision
t
• shorter collision time
velocity
Summary
u

0             time
-v

collision force

0            time
Collision force decreases
with increase of collision
time for the same change
in momentum.
velocity
Summary
u

0                  time
-v
v cannot be greater than u.
Why ?
collision force

0                 time
-Favg

-Fmax
t
velocity
Summary
u
If there is no kinetic energy
loss during collision,
0                  time
-v                                    v=u
This is the case when a gas
collision force               molecule collides with the
wall of the container. The
magnitude of the average
0                 time   collision force is given by
-Favg
2mu
Favg   
t
-Fmax
t
Favg a u
The fate of a passenger without wearing
a safety belt in a car accident
Just before the collision between the car and the wall, the car and
the passenger moves with the same velocity u. The passenger is
at rest relative to the car.
u
The car hits the wall. Fc is the collision force acting on the
car. Fc does not act on the passenger !
There is no horizontal force acting on the passenger to stop him
from moving. The friction provided by the seat is negligible.

>>
Fc

Newton’s First Law states that, due to its inertia, an object will
maintain its original state of motion unless a resultant force acts
on it. Thus the passenger continues to move with the original
velocity u towards the front panel of the car.
The passenger finally hits the front panel of the car. Fp is the
collision force acting on the passenger by the car. Fp is large
and stops the passenger in a short period of time !

Fp

The area of contact between the passenger and the front panel
is small and hence the pressure is very large. This imposes
serious injury on the passenger.
velocity-time of the car
velocity
velocity-time of the passenger

u

0                 time
velocity-time of the car
velocity
velocity-time of the passenger

u

0                            time

The car hits the
wall and stops in
a short time.
velocity-time of the car
velocity
velocity-time of the passenger

u

0                                          time

The passenger continues
to move forward after the
car stops.
velocity-time of the car
velocity
velocity-time of the passenger

u

0                    time

The passenger hits the front
panel and finally stops.
Safety Belt
Fp           safety belt

The force exerted by the safety belt on the passenger will
depend on the speed with which the safety belt is pulled out.
Fp          safety belt

Functions of safety belt :
Provide a force Fp to stop the passenger so that he will not hit
the front panel of the car.
Achieve a longer collision time between the belt and the
passenger so that Fp will be small enough to prevent injury to
the passenger.
velocity-time of the car
velocity
velocity-time of the passenger

u

0                 time
Fp

An air bag exploded during the collision between the car and
the wall serves a similar purpose as a safety belt.

What are the disadvantages of using an air bag instead of a
safety belt ?

```
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