Combine the expressions for tension and solve for acceleration

  • Thread starter asusal
  • Start date
  • #1
1
0
1. Derive an equation for the acceleration of both the cart and suspended mass in
terms of both masses (Mc and Ms ), the angle of the incline (θ), and the acceleration due to gravity (g).


Homework Equations


Fx=
T - Mgsin θ = Ma

T = Mgsin θ + Ma
Fy
T = mg - ma

Combine the expressions for Tension and solve for the acceleration.

A= (mg - Mg sin θ / M + m )

https://imgur.com/a/Okk79t9 (I know in the picture it's already derived in the correct form I just want to know how they got that correctly.)[/B]


The Attempt at a Solution



So I combined the equations

T= (ms*g-mc*g*sin(θ) ) / ( mc + mg)

T= ms (g- (ms*g-mc*g*sin θ/ mc+ms) )

[/B]
I'm assuming I factor MS and common denom but it doesn't seem like i'm doing this correctly.



Any help would be appreciated!

Thanks.
 

Answers and Replies

  • #2
CWatters
Science Advisor
Homework Helper
Gold Member
10,532
2,298
Uploaded the image for future readers..
cart.jpg
 

Attachments

  • #3
CWatters
Science Advisor
Homework Helper
Gold Member
10,532
2,298
So I combined the equations
T= (ms*g-mc*g*sin(θ) ) / ( mc + mg)
T= ms (g- (ms*g-mc*g*sin θ/ mc+ms) )

I'm assuming I factor MS and common denom but it doesn't seem like i'm doing this correctly.
Any help would be appreciated!
Can you show more of your working?

Why introduce ms and mc ? In the image they use "M" for the mass of the cart and "m" for the suspended mass. I suggest you stick to that notation.
 
  • #4
CWatters
Science Advisor
Homework Helper
Gold Member
10,532
2,298
Hint: When you combine two equations you can frequently eliminate one unknown variable. Which unknown doesn't appear in the final equation given to you?
 

Related Threads on Combine the expressions for tension and solve for acceleration

Replies
4
Views
6K
Replies
1
Views
3K
Replies
2
Views
5K
Replies
7
Views
3K
Replies
2
Views
2K
Replies
5
Views
18K
Replies
1
Views
1K
Replies
1
Views
443
Top