My Math Forum Help with conservation of momentum question

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 March 19th, 2017, 01:30 AM #1 Member   Joined: Mar 2017 From: Tasmania Posts: 36 Thanks: 2 Help with conservation of momentum question Q1) Tiny Tim of mass 72kg is playing in the super bowl against the Arizona Cardinals. Tiny Tim is running at 4ms-1 when he collides with Alan Branch, with mass 165kg, running in the opposite direction with a speed of 5ms-1. Momentarily after the collision Alan Branch’s velocity was 0ms-1. ii. Calculate Tiny Tim’s speed after the collision iii. If the collision took place over a time of 0.3 seconds, what was the force experienced by Tiny Tim during the collision? iv. Hence or otherwise, what was the force experienced by Alan Branch during the collision? Thanks from agentredlum
 March 19th, 2017, 06:17 AM #2 Math Team   Joined: Jul 2011 From: Texas Posts: 2,693 Thanks: 1351 Show what you have attempted ...
 March 19th, 2017, 01:51 PM #3 Member   Joined: Mar 2017 From: Tasmania Posts: 36 Thanks: 2 I got the final velocity of Tiny Tim, which was -7.46ms^-1 I am stuck on question iii and iv as I'm not quite sure how to go about it. Last edited by skipjack; March 19th, 2017 at 11:45 PM.
March 19th, 2017, 03:12 PM   #4
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Quote:
 Originally Posted by Posher I got the final velocity of Tiny Tim, which was -7.46ms^-1
correct

Quote:
 iii. If the collision took place over a time of 0.3 seconds, what was the force experienced by Tiny Tim during the collision?
impulse equation ...

$F \cdot \Delta t = m \cdot \Delta v$

Quote:
 iv. Hence or otherwise, what was the force experienced by Alan Branch during the collision?
Apply Newton's 3rd law.

Last edited by skipjack; March 19th, 2017 at 11:45 PM.

 March 19th, 2017, 10:08 PM #5 Member   Joined: Mar 2017 From: Tasmania Posts: 36 Thanks: 2 Also, for iv, wouldn't the force received from Alan be 0 since the final velocity is 0? Edit: for iii, I got -1790.4N Last edited by skipjack; March 19th, 2017 at 11:41 PM.
March 20th, 2017, 08:23 AM   #6
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(ii) Tiny Tim's speed is $|v| = |-7.46 \, m/s| = 7.46 \, m/s$

(iii) $F \Delta t = m \Delta v \implies F = \dfrac{m(v_f-v_0)}{\Delta t} = \dfrac{72(-7.46 - 4)}{0.3} = -2750 \, N$

(iv) same equation for impulse on the larger player ...

$F \Delta t = M \Delta v \implies F = \dfrac{M(v_f-v_0)}{\Delta t} = 2750 \, N$

Quote:
 wouldn't the force received from Alan be 0 since the final velocity is 0?
No. This is a common misconception related to another misconception ... "if acceleration = 0 then velocity = 0", or the converse of that statement.

Force is the agent of change. That force acting on an object for a defined period of time yields an impulse, which by another name is change in momentum.

The force on the larger player is equal and opposite in direction to the force acting on the smaller player. Heard that before?

Just because velocity = 0 does not imply that force = 0.
An example ... think about a ball thrown straight up under the influence of gravity. At the top of its trajectory, the velocity is 0, but the force of gravity acts on it the entire time it moves as a projectile in the gravitational field.

Another example ... a car drives at high speed and hits a wall bringing it to rest in minimal time. Did the wall exert a force on the car causing it to stop? Did the car exert an equal and oppositely directed force on the car?

Last edited by skeeter; March 20th, 2017 at 08:30 AM.

 March 20th, 2017, 02:35 PM #7 Member   Joined: Mar 2017 From: Tasmania Posts: 36 Thanks: 2 (iii) $F \Delta t = m \Delta v \implies F = \dfrac{m(v_f-v_0)}{\Delta t} = \dfrac{72(-7.46 - 4)}{0.3} = -2750 \, N$ shouldn't the -4 be positive since Tim is traveling in opposite directions
 March 20th, 2017, 04:29 PM #8 Math Team   Joined: Jul 2011 From: Texas Posts: 2,693 Thanks: 1351 Tim ... $v_0 = +4 \, m/s$, $v_f = -7.46 \, m/s$ $\Delta v = v_f - v_0 = -7.46 - (+4) = -11.46 \, m/s$ Branch ... $v_0 = -5 \, m/s$, $v_f = 0$ $\Delta v = v_f - v_0 = 0 - (-5) = 5 \, m/s$ kapish? Thanks from agentredlum and Posher
 March 20th, 2017, 08:58 PM #9 Member   Joined: Mar 2017 From: Tasmania Posts: 36 Thanks: 2 I already it figured that out like 10 minutes after posting the reply. I'm sorry I wasted your time in posting another reply :/
March 21st, 2017, 04:09 AM   #10
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Quote:
 Originally Posted by Posher I already it figured that out like 10 minutes after posting the reply. I'm sorry I wasted your time in posting another reply :/

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