Q. A hammer of mass M falls from a height h repeatedly to drive a pile of mass m into the ground. The hammer makes the pile penetrate in the ground to a distance d in single blow. Opposition to penetration is given by?
6i think it means the force imparted by the pile on to the hammer , rite??
so , its simple , find the impulse.........and then force can be found out...
1Well i guess.... work power energy gives a nice and convininet explaination....
now first...
initially taking 0 P.E. to be at the ground level....
initially total energy=Mgh
and finally total enrgy= -(M+m)gd
thereofre change=F.s where s= d
Assumption... The masses are point masses
(Ashish could u pls post problems by the proffesor who coaches the indian ipho team for our practises)
1Its not a perfectly elastic collision. Final total energy will contain energy produced due to vibration, sound etc...
1I am posting the solution which I rarely do :D
Just before and after the collision, momentum of the two masses is conserved (approximately).
Mv=(M+m)v'
v'=Mv/(M+m), where v=√2gh
Now applying work-energy theorem,
0.5(M+m)(0 - v'2)=-F*d, where F is the resistive force
F=M2/(M+m)d
Now the total opposing force on the system = F + (M+m)g = M2gh/(M+m)d + (M+m)g
Here I made an assumption that the hammer doesnot rebound before travelling a distance 'd' and comes to rest together with the pile.
30Varun , my approach was similar, but what Swordfish has done is right. The right answer is indeed M2gh(M+m)d + (M+m)g.
@Swordfish - One question, why is the term (M+m)g included in the total opposing force on the system? [7]
30And by the way, are you confusing me with Asish bhaiya (like most people out here do), who is currently in IIT-K? I don't know the professor who you are talking about! [3]
71@ashish
(M+m)g will also also because that's the gravitational force of attraction on the combined bodies. The ground has to oppose both the impulse and weight. That's all!
1i believe more in giving hints than solving each and evry prob!!!
I think it should be like - 'I believe more in giving hints to be on the safe side rather than solving each and evry prob wrongly!!!' [4]
No Offence
1Well nice answer
But on the question its very unclear actually confisuing ... I am dammn sure such confusing questions wont come.... in any exam . All the physics we study are based on the assumptions of idealism.... so it should have been clearly specifed that apart from the opp. force there can be enrgy losss. I beleive so.....
1Energy loss is certain. There is no need to specify it. You never see an elastic collision between a hammer and a nail.
While applying work energy theorem wouldn't v consider (m+M )g×d {work done by gravity}??