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Quick M1 Question

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 1.6 m above the top of the post.

(a) Show that the speed of the pile-driver just before it hits the post is 5.6 m s–1.

The post has mass 6 kg and the pile-driver has mass 78 kg. When the pile-driver hits the top of the post, it is assumed that the 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 0.06 s. By modelling this force as constant throughout this time,
(c) find the magnitude of the resistive force,
(d) find, to 2 significant figures, the distance travelled by the post and the pile-driver before they come to rest.

I got a) and b) as 5.6 and 5.2 m/s respectively.

However for (c) and (d) I get 7820N and 0.16m, but the answers are supposed to be 8103.2N and 0.14m.

I did:

5.2 m/s to 0 m/s in 0.06s -> acceleration of 86.6 m/s^2 so, using F=ma, 86.6 x 84 = 7280.

For part d) I just did 5.2 x (0.06/2) = 0.16m

Where have I gone wrong?

Thanks.
Reply 1
Avatar for Hopple
Hopple
18
Don't forget gravity!
Reply 2
Avatar for raheem94
raheem94
13
Original post by Thrug
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 1.6 m above the top of the post.

(a) Show that the speed of the pile-driver just before it hits the post is 5.6 m s–1.

The post has mass 6 kg and the pile-driver has mass 78 kg. When the pile-driver hits the top of the post, it is assumed that the 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 0.06 s. By modelling this force as constant throughout this time,
(c) find the magnitude of the resistive force,
(d) find, to 2 significant figures, the distance travelled by the post and the pile-driver before they come to rest.

I got a) and b) as 5.6 and 5.2 m/s respectively.

However for (c) and (d) I get 7820N and 0.16m, but the answers are supposed to be 8103.2N and 0.14m.

I did:

5.2 m/s to 0 m/s in 0.06s -> acceleration of 86.6 m/s^2 so, using F=ma, 86.6 x 84 = 7280.

For part d) I just did 5.2 x (0.06/2) = 0.16m

Where have I gone wrong?

Thanks.


The part c will be done in this way:

v = u + at
0 = 5.2 + 0.06a
-5.2/0.06 = a = -86.666 ms-2

F - 84g = 84a
F - 823.2 = 7280
F = 7280 + 823.2 = 8103.2N

For part d my answer comes as 0.156m.
Reply 3
Avatar for Thrug
Thrug
OP
3
Original post by raheem94
The part c will be done in this way:

v = u + at
0 = 5.2 + 0.06a
-5.2/0.06 = a = -86.666 ms-2

F - 84g = 84a
F - 823.2 = 7280
F = 7280 + 823.2 = 8103.2N

For part d my answer comes as 0.156m.


Ah so I did forget gravity (I guess gravity applies to everything at all times :tongue:). Thanks for showing me how to do it. :smile:

And yes, that's what I got for part (d) :s-smilie:
Original post by raheem94
The part c will be done in this way:

v = u + at
0 = 5.2 + 0.06a
-5.2/0.06 = a = -86.666 ms-2

F - 84g = 84a
F - 823.2 = 7280
F = 7280 + 823.2 = 8103.2N

For part d my answer comes as 0.156m.

I don’t understand the part F-84g = 84a, why is 84g being subtracted from F

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