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M1 Mock Exam Paper Please Help

Has any one answered question 5) in the mock paper.

5)
A post is driven into the ground by means of a blow from a pile-driver. The pile-driver falls from rest from a height of 1.6m above the top of the post.

a) Show that the speed of the pile drive just before it hits the post is 5.6 ms-1

The post has a mass of 6kg and the pile-driver has mass 78kg. When the pile-driver hits the top of the post, it is assumed that there is no rebound and that both then move together with the same speed.

b) Find the speed of the pile-driver and the post immediately after the pile-driver has hit the post.

The post is brought to rest by the action of a resistive force from the ground acting for 0.06s.
By modeling this force as a constant throughout this time,

c) find the magnitude of the resistive force,

d) find, to 2 significant figures, the distance traveled by the post and the pile-driver before they come to rest.

The answers are:
Question 5
a) 5.6 ms-1 b) 5.2 ms-1 c) 8103.2 N d) 0.14 m

But i don't know why part C) is 8103.2 N (I got 14560 N :s-smilie:

) and why part d) is 0.14m (I got 0.156m )

Reply 1

phys981

Are the masses you've given here correct?

Reply 2

intellectualtourist

Sorry the masses are:

Post => 6 kg

Pile-Driver => 78 kg

Reply 3

phys981

Ok, Ft = change of momentum.

Change of momentum = (78+6) x 5.2 = 436.8

So F = 436.8/0.06 = 7280N

This is the RESULTANT force, so the resitance force = 7280 + W
= 7280 + (84x9.8) = 8103.2

Reply 4

intellectualtourist

How about part D), how do you do that?

Reply 5

phys981

Use work and energy

Find the ke of the post and driver - this is the same as the work done by the resistive force in stopping it.

Work = force x distance, so divide the work by the force.