Rigid body kinetics -- force on ankle joint

[mastermechanic]

Homework Statement

Rigid body kinetics problem involving Impulse-Momentum application

Relevant Equations

G = m.v and H = m.v.r

PROBLEM

Here from the conservation of angular momentum I found angular velocity just before impact,
$$ H_1 = 0 $$
$$ H_2 = I_0\omega + mV_0d $$
$$ H_2 = 66\omega + 76.(1.2).(0.87)$$
$$ H_1 = H_2 $$
$$ \omega = 1.202 rad/s $$

But I couldn't solve it to find joint force.

Thanks in advance,

 

[kuruman]

$$ H = I_0\omega + mV_0d $$

What is H in this equation? If it is supposed to express angular momentum conservation, the equation does not look like it. Angular momentum conservation is expressed as $$L_{\text{before}}=L_{\text{after}}.$$Is your $d$ the same as $h$ in the figure? How are you going to use the information that the collision lasts 20 msec? Hint: Think "impulse".

 

[mastermechanic]

You're right I just wrote it fast, the angular momentum is zero before the impact and is the expression I wrote above after the impact. So I found $$ \omega = 1.202 rad/s $$

I found a way but I appreciate if you confirm it's validity,

V of the ankle joint,

$$ V = \omega.r $$
$$V = 1.202 * 0.87 = 1.05 m/s $$
$$ \frac {m.(V_f - V_i)} {t} = \frac {76.(1.05 - 1.2)} {0.02} = - 585 N $$

Is this correct?

 

[jbriggs444]

You're right I just wrote it fast, the angular momentum is zero before the impact

The angular momentum about what axis is zero before the impact?

 

[mastermechanic]

The angular momentum about what axis is zero before the impact?

To the page

 

[kuruman]

Is this correct?

It's what I got. Nevertheless, think about the answer you gave to @jbriggs444. If the angular momentum is zero before the impact and non-zero after the impact, it cannot be conserved through the collision, can it?

 

[jbriggs444]

To the page

The page? I do not understand. The page is a plane. An axis is a line. If you draw a normal rising out of the page, that still does not define an axis because no location for the line is defined.

The problem statement gives a large hint about what axis to use. The problem is that you've not correctly used it.