# Football tackle force

1. Nov 28, 2007

### theredlight

1. The problem statement, all variables and given/known data
A 110 kg football linebacker moving at 2 m/s tackles head-on a 70 kg halfback running 4 m/s. If they have an inelastic collision, and neglecting the effects due to digging in of cleats:
a)If the collision takes .5 sec, what is the force imparted on the halfback?
b) what is the force imparted on the linebacker?

2. Relevant equations
Ft=$$\Delta$$p

3. The attempt at a solution

110(2) + 70(-4) = 110v + 70v
v= 1/3 m/s in halfback's direction

when i solve, I get a negative force. Is this possible?
For both a and b, i get -513.34 N, is this correct?

a)F=(70)(.333 - 4)/.5
F=-513.4 N

b)F=(110)(-.333 - 2)/.5
F=-513.4 N

Last edited: Nov 28, 2007
2. Nov 29, 2007

### Bill Foster

I'm not going to calculate the numbers, but using variables:

$$m_1 v_1 + m_2 v_2 = (m_1 + m_2)v$$

Solve for $$v$$:

$$\frac{m_1 v_1 + m_2 v_2}{m_1 + m_2}=v$$

Using v, you can get change in momentum:

$$\Delta p_1=m_1(v_1 - v)$$
$$\Delta p_2=m_2(v_2 - v)$$

Then you can calulate the force in each case.

$$F_1=\frac{m_1(v_1 - v)}{t}$$
$$F_2=\frac{m_2(v_2 - v)}{t}$$

Yes, you can get a negative value for force. Force is a vector, as is velocity.

So initially, assume the halfback is running in the positive x direction, his velocity is positive. The linebacker will be running in the negative x direction with a negative velocity.