M1 Dynamics and Moments Question Help

12

A wooden peg of mass 0.4 kg is driven vertically into the ground by a mallet of mass 2 kg moving vertically downwards. The speed of the mallet just prior to impact is 8 m/s. After impact the mallet and peg remain in contact. By modelling the peg and mallet as particles find the speed with which the peg begins to enter the ground. If the ground offers a resistance to motion of 1 kN find how far the peg is driven into the ground due to the impact.

I've been puzzling over this for a while, and still haven't gotten anywhere. The answers that are in the back of the book are Speed = 6.67ms^-1 and Distance = 0.0533m. Logic tells me that the equation to find the distance is v^2 = u^2 + 2as, with v=0, u=6.67 and a=9.8. However, I only arrive at that because I know the answer for speed, which I can't get.

Can anyone give me any help for working this out? The equations I think I'm supposed to use are:

m1u1 + m2u2 = m1v1 + m2v2
I = Ft
v^2 = u^2 + 2as
?F = ma?

Thanks in advance

Reply 1

BJack

19

• After the collision, you can treat the peg+mallet as a single particle with mass 2.4 kg.
• Use conservation of momentum to find the speed of this new particle.
• As you suggested, use F = ma to find the acceleration upwards due to the resistive force; don't forget to include g to calculate the resultant acceleration of the particle.
• Use the equation of motion you suggested, with the values of a and u that you found, to calculate the distance travelled by the new particle.

Reply 2

Kneechuh

OP

12

BJack

• After the collision, you can treat the peg+mallet as a single particle with mass 2.4 kg.
• Use conservation of momentum to find the speed of this new particle.
• As you suggested, use F = ma to find the acceleration upwards due to the resistive force; don't forget to include g to calculate the resultant acceleration of the particle.
• Use the equation of motion you suggested, with the values of a and u that you found, to calculate the distance travelled by the new particle.

Thankyou!

I did just like you said, and got:
(0.4 * 0) + (2 * 8) = 2.4v
This gave v = 6.6666.... success!

Then, to get the distance travelled, I needed to find A, so used F = ma
1000 = 2.4a
a = 416.66...
Then I just put that into v^2 = u^2 + 2as and out came s!

Thanks a bunch BJack!

Reply 3

AsianPersuasion9

Why did you use 1000N as the F? Surely the F is the resultant force so you would do the force that the peg and the mallet exert on to the ground take away the resistive force of the ground to give you the resultant force. And then use that to work out the acceleration etc

Reply 4

lizard54142

6

Original post

by AsianPersuasion9

Why did you use 1000N as the F? Surely the F is the resultant force so you would do the force that the peg and the mallet exert on to the ground take away the resistive force of the ground to give you the resultant force. And then use that to work out the acceleration etc

This is from 2009.

Reply 5

Zeeoniyan

Original post

by AsianPersuasion9

Why did you use 1000N as the F? Surely the F is the resultant force so you would do the force that the peg and the mallet exert on to the ground take away the resistive force of the ground to give you the resultant force. And then use that to work out the acceleration etc

If anyone gets this answer, even in the distant future, please do tell me

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