Why does the man on a horse get thrown forward when the horse stops?

[nilic1]

Homework Statement

A man of mass 50kg is riding a horse of mass 450kg at a steady speed of 10m/s. The horse stops suddenly and the man is thrown forwards. Find the speed with which the man is thrown forwards.

Applying law of conservation of momentum, the resulting speed is 100m/s. Poor man.
However, I checked whether K.E. is conserved or not in such a situation. To my surprise, the K.E. after is greater than that before!

Homework Equations

K.E = 1/2 m v^2

The Attempt at a Solution

According to the law of conservation of energy... energy can neither be created nor destroyed, so what is wrong here?

 

[aim1732]

How does the horse stop? If there is an external force on the horse how can you conserve the momentum of system ?

 

[ehild]

Not counting the interaction between the horse and the ground, you can model the horse-man system as a cart with a spring on it and a ball attached to the end of the spring. You keep the spring compressed with some thread and let the cart go with a certain speed. Suddenly you burn off the thread, so the spring is released. The impulse of the spring is just enough to stop the cart, and the ball will take away all the momentum. The KE of the ball will be greater than the original KE of the whole system, as the elastic energy of the spring is added.
I do not know what exactly the horse does with the man and with the ground but some kind of elastic energy can transform into the KE of the man.

ehild

 

[nilic1]

How does the horse stop? If there is an external force on the horse how can you conserve the momentum of system ?

Thanks for answering. This was an exam question and there is no further information. There is no other way of finding the resulting speed anyway. The horse just decides to stop abruptly lol. Does the K.E. calculation show that this an impossible situation in practice?

 

[nilic1]

Not counting the interaction between the horse and the ground, you can model the horse-man system as a cart with a spring on it and a ball attached to the end of the spring. You keep the spring compressed with some thread and let the cart go with a certain speed. Suddenly you burn off the thread, so the spring is released. The impulse of the spring is just enough to stop the cart, and the ball will take away all the momentum. The KE of the ball will be greater than the original KE of the whole system, as the elastic energy of the spring is added.
I do not know what exactly the horse does with the man and with the ground but some kind of elastic energy can transform into the KE of the man.

ehild

Thanks for your reply. So speaking about conservation of K.E does not make sense then? Does it make sense to speak about conservation of momentum because there are external forces involved here?

 

[aim1732]

If the horse stops by pressing against the ground(and there is no slipping) then energy and momentum will be conserved because although there is an external friction force it does not perform any work. This however is assuming the horse's back is smooth.

 

[ehild]

Well, the horse would stop even without the man and then all the momentum and KE would be lost. During the stopping process, its hovers press against the ground and deform it, so there is some displacement and some time during this interaction: neither the momentum nor the energy is conserved when the interaction with Earth is not taken into account. The momentum is conserved if that scenario holds which I outlined in my previous post: that the man is attached with a compressed spring to the back of the horse, and this spring is suddenly released. :)

 

[nilic1]

Thanks ehild very interesting observation. After some more research I learned that total K.E. can actually increase and is called a super-elastic collision, where energy as you suggested might come from some stored potential or elastic energy.

 

[ehild]

Well, it is true, but this is certainly not the case when a horse stops. I think, with a slippery back, with no horizontal interaction force between horse and man, the man just would keep its initial 10 m/s velocity while the horse stops.

ehild