Mechanics question

Did you have no luck on Rudolf's forum?

I think the attachment is correct.

Reply 2

OP

For part A, I (and my tutor) got -gm(cos a)(sin a)/M

However, I also was made aware of the correct answers; and they aren't the same as any of yours (or mine :frown:

).

Reply 3

Rudo says that the solutions to this problem sheet will be available next week, after your examples class.

My Mechanics is extremely rusty (this is the first problem I've done for the course), but I don't understand how you could get an answer involving

m

for the first part, as the only force acting on the block is gravity and the strength of the gravitational force is independent of the mass of the object upon which it is acting.
.

Reply 4

Square

13

Scrap that acually, I'll give it a bash see where I end up.

Reply 5

OP

The first question asks for the acceleration of the wedge. so the force acting on it is a function of the mass of the block; but the acceleration it imparts on the wedge will also be a function of the mass of the wedge.

Reply 6

estel

The first question asks for the acceleration of the wedge. so the force acting on it is a function of the mass of the block; but the acceleration it imparts on the wedge will also be a function of the mass of the wedge.

I have completely misread the question; many apologies for that.

Diagram?

OP

*scrounges around*

Lusus Naturae

Rudo says that the solutions to this problem sheet will be available next week, after your examples class.

My Mechanics is extremely rusty (this is the first problem I've done for the course), but I don't understand how you could get an answer involving

m

for the first part, as the only force acting on the block is gravity and the strength of the gravitational force is independent of the mass of the object upon which it is acting.
.

Start with if the wedge is fixed, it may help with the understanding part.

Reply 10

Doing this by newtonian mechanics is going to eb hard work, your best of using a lagrangian formalism. But I'd say use a lagrangian formalism for any such problem, less room for error.

Reply 11

Heres my answer for Q1:

\ddot{x}_1 = \frac{\ddot{x}_2 + g \sin \theta}{\cos \theta} = \frac{m_2}{m_1 + m_2} \cos \theta \ddot{x}_2

\ddot{x}_1

~ Acceleration of Wedge

\ddot{x}_2

~ Acceleration of block on Wedge

m_1 , m_2

~ masses of wedge, block

Solving for the acceleration of the block gives:

\ddot{x}_2 = \frac{g \sin \theta}{\mu (\cos \theta)^2 - 1}

where:

\mu = \frac{m_2}{m_1 + m_2}

Acceleration of the wedge:

\ddot{x}_1 = \mu \cos \theta \frac{g \sin \theta}{\mu (\cos \theta)^2 - 1}

Rearranging gives:

\ddot{x}_1 = \frac{m_2 g}{(m_1 + m_2) \tan \theta + \frac{m_1}{\tan \theta}}

BTW: Do you know the answers to these questions?

All of this above is starting from the Lagrangian of:

L = \frac{1}{2} m_1 \dot{x}_1^2 + \frac{1}{2} m_2 ( \dot{x}_2^2 + \dot{x}_1^2 - 2 \dot{x}_1 \dot{x}_2 \cos \theta ) - m_2 g x_2 \sin \theta

Reply 12

OP

Yes, I do know the answers, but I can't find a rearrangement from that one to the answer that I have. The answer is not given in terms of x''_2.

Reply 13

0 div curl F

BTW: Do you know the answers to these questions?

The answer to (E) is

(M+m)g \tan a

Reply 14

Hopping Mad Kangaroo

15

estel

Yes, I do know the answers, but I can't find a rearrangement from that one to the answer that I have. The answer is not given in terms of x''_2.

x" means acceleration, it should be replaced with a1 and a2.

Reply 15

estel

Yes, I do know the answers, but I can't find a rearrangement from that one to the answer that I have. The answer is not given in terms of x''_2.

Ignoring differences in notation, are the answers in my post anywhere near the solutions you have?

Reply 16

OP

Closish, but not exactly.

Spoiler

Reply 17

estel

Closish, but not exactly.

Spoiler

This is infact the same as my answer, just a fair bit of manipulation and trig identities, just been through it on paper, will double check it in 5 mins

Yep, just checked my solution and it is identical to your solution, just in a different form (I think my form is neater and easily releases its information but thats the way the lagrangian works out)

Reply 18

OP

Grr, I'm checking it numerically and getting different results for the two -.-

Edit: Scrap that, looks like I was probably reading from the wrong line

Reply 19