# Magnitude of velocity and impulse

In one of MSU’s seven sacks, MSU linebacker Denicos Allen sacked UM quarterback Devin Gardner. Just prior to being sacked, the quarterback was at rest. Just after they collided, the two players were momentarily stuck together and both slide a distance of 1.5 m before coming to a stop. In addition, assume this motion was purely horizontal. Denico Allen’s mass was 103.3 kg and Devin Gardner’s mass was 92.8 kg.

(a) Draw a free-body diagram of Denicos Allen and Devin Gardner as they slide as one body along the field surface of Spartan Stadium.

(b) The acceleration of the two players due to the frictional force is 2.45 m/s2. What was the magnitude of the velocity of the two players immediately after their collision?

(c) What was the total impulse delivered to the two players during their slide?

(d) What was the magnitude of the velocity of Denicos Allen just before he sacked the quarterback?

(e) In answer (d), what assumption did you make?

p=mv
F=ma
F= p/t
v=d/t
a= v/t
Ffriction=uN

## The Attempt at a Solution

(a) Draw a free-body diagram of Denicos Allen and Devin Gardner as they slide as one body along the field surface of Spartan Stadium.

Force going down: mass*gravity
Force going up: force of players
Force going to left: friction
Force going to right: Force of Denicos Allen

If you assume the motion is purely horizontal, then would you disregard frictional force?****

(b) The acceleration of the two players due to the frictional force is 2.45 m/s2. What was the magnitude of the velocity of the two players immediately after their collision?

v=sqrt((m1v1/(m1+2))^2+(m2v2/(m1+v2))^2)
v=sqrt((103.3*2.45/196.1)^2+(92.8*2.45/196.1)^2) = 1.735m/s

(c) What was the total impulse delivered to the two players during their slide?

p=mv
p= 196.1*1.735= 340.2335 kg*m/s

(d) What was the magnitude of the velocity of Denicos Allen just before he sacked the quarterback?

vf=vi+(Fnet/m)*time

Im not sure how to find time

(e) In answer (d), what assumption did you make?

No air resistance, gravity 9.81m/s^2, constant force
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Simon Bridge
Homework Helper
Responding to the following (arrows indicate points)
Force going down: mass*gravity
Force going up: force of players <<<1
Force going to left: friction
Force going to right: Force of Denicos Allen

If you assume the motion is purely horizontal, then would you disregard frictional force? <<<2
1> What does "force of players" mean?
2> s Spartan Stadium playing field really a frictionless playing surface?

I'm not sure how to find time
You may not need it ... is there another approach to the problem?

haruspex
Homework Helper
Gold Member
... and what is "force of Denicos Allen"?

1)I think you wouldn't consider friction because it says "If you assume the motion is purely horizontal"
2)force of players would just be their masses
3)How does my work look for the other parts?

haruspex
Homework Helper
Gold Member
1)I think you wouldn't consider friction because it says "If you assume the motion is purely horizontal"
I have no idea what logic leads you to that conclusion. If there were no friction, the players would slide forever.
2)force of players would just be their masses
A mass is not a force. If you mean the gravitational force resulting from their masses, you've already covered that:
Force going down: mass*gravity
Force going up: force of players
They'd be the same thing, right? Both acting downwards.

Simon Bridge