Average force in totally inelastic collision

[uk9999]

Homework Statement

Two bodies A and B collide in a totally inelastic collision. Using the relevant equations and given that the mass of body A is 1200kg and the collision lasts for 0.2s, determine the average force vectors acting on each body during the collision.

Homework Equations

v_A=5i+3j m/s
v_B=-i+4j m/s
m_A=(3/2)m_B
Common velocity after collision v=2.6i+3.4j m/s

The Attempt at a Solution

attempt 1
Ft = (m_A+m_B)v - (m_Av_A+m_Bv_B)
calculation checked and rechecked... leads to wrong answer
attempt 2
Ft = (m_A+m_B)v - (m_Av_A-m_Bv_B)
calculation checked and rechecked... leads to wrong answer
attempt 3
F_At=0.5(m_A+m_B)v - m_Av_A
F_Bt=0.5(m_A+m_B)v - m_Bv_B
calculation checked and rechecked... leads to wrong answer

Answer is stated as "F_A= -F_B= (-14400i+2400j) N in the mark scheme

 

[Galadirith]

Hi there uk9999. Well i think you need to rethink the way you looking at the question. First let's have a look back at how we define impulse and momentum:

$$\textbf{I} = \textbf{F}t = m\textbf{v} - m\textbf{u}$$

now I, F, v and u can all be vectors as we have in this question, but in order to solve a problem involving vectors we should brake it down into its components, in this scenario in 2D so well equate the x comonets and the y comonents seperatly.

Now in actual fact the question gives you far more information than you actually need, and it is not nessesary to consider both bodies, as the question tells us the initial and final velocity of both, and Impulse is described for a single body, so you can take you pick as to which one you want to use. so looking back at the first equation we need to modify this so that we can consider componets:

$$I_x = F_x t = mv_x - mu_x$$
$$I_y = F_y t = mv_y - mu_y$$

now i decided to use body A, no reason just was the first one I came to :D, so if wee input those values into you componentised Impluse equations we get:

$$I_x = F_x t = 1200(2.6) - 1200(5)$$
$$I_y = F_y t = 1200(3.4) - 1200(3)$$

now have a go from there, I think there is enough info there for you to finish off the question :D have fun

 

[Doc Al]

The Attempt at a Solution

attempt 1
Ft = (m_A+m_B)v - (m_Av_A+m_Bv_B)
calculation checked and rechecked... leads to wrong answer
attempt 2
Ft = (m_A+m_B)v - (m_Av_A-m_Bv_B)
calculation checked and rechecked... leads to wrong answer
attempt 3
F_At=0.5(m_A+m_B)v - m_Av_A
F_Bt=0.5(m_A+m_B)v - m_Bv_B
calculation checked and rechecked... leads to wrong answer

In all of your attempts you have tried to use the combined momentum of both masses. Don't!

To find the average force on mass A, you need the change in momentum of mass A. Similarly, to find the average force on mass B, you need the change in momentum of mass B. (Of course, you don't have to calculate the force twice. Use Newton's 3rd law.)

 

[uk9999]

Ah thank you knew I was doing something wrong