Find Accel. of Cart from Mass m & Theta

In summary, the student is trying to solve an equation to find the acceleration of the cart based upon theta. They are confused by all the subscripts and are at a loss of even just identifying all the forces exactly. They are assuming the cart is moving to the right, but there is no force causing it to move forward.
  • #1
greenskyy
17
0

Homework Statement


http://img188.imageshack.us/img188/9897/73266226.png [Broken]

The problem is to create an equation to find the acceleration of the cart based upon theta. All that is given is the ball hanging is known as mass m.

Homework Equations


[tex]f=ma[/tex]
[tex]f=\frac{mv^{2}}{r}[/tex]

The Attempt at a Solution


I am assuming that the car is moving to the right, since the hanging mass is tilted backwards. I am really at a loss of even just identifying all the forces exactly. What confuses me the most is that we are assuming the cart is accelerating forward, but there is no force causing it to move forward.


So far, this is what I have:
m being the mass, c being the cart
[tex]F_{mx}=Tsin\theta[/tex]

[tex]F_{my}=Tcos\theta - mg[/tex]

[tex]F_{cx}=m_{c}a - Tsin\theta[/tex]

[tex]F_{cy}=-Tcos\theta = 0[/tex]

I know that these are probably wrong, but can someone please tell me why?
 
Last edited by a moderator:
Physics news on Phys.org
  • #2


I'm a little confused by all the subscripts! And can't make thetas here.
Vertical: Tcos(A) - mg = 0
Horizontal: Tsin(A) = ma
If you solve one for T and sub in the other, you'll get something that makes sense.

How do you make a theta?

PS it is accelerating to the right because theta > 0. If it wasn't accelerating, it would hang straight. So no need to think about what is making it accelerate.
 
  • #3


Haha, well you make a theta using latex code. For the theta symbol, it would be [ t e x ] \ t h e t a [ \ t e x ] (minus the spaces)
 
  • #4


Thank you greenskyy. I fear that is too awkward for me.
I have seen someone with a whole bunch of symbols (theta, pi, etc.) in his signature. I wonder if that is so he can copy a theta whenever he wants it? Do you know how I can have a signature here?
 
  • #5


Nope, I looked around and couldn't find it anywhere in the user control panel =\
 
  • #6


What is the net force on the ball-cart system? What quantity is conserved, then?
 

1. What is the formula for finding the acceleration of a cart from mass and theta?

The formula for finding the acceleration of a cart from mass and theta is a = m * g * sin(theta), where a is the acceleration, m is the mass of the cart, g is the gravitational constant, and theta is the angle of incline.

2. How do I determine the value of g in the equation?

The value of g can be determined by using the standard gravitational constant of 9.8 m/s^2, or by using the gravitational acceleration specific to your location if it is known.

3. Can this formula be used for any object on an incline?

Yes, this formula can be used for any object on an incline as long as the mass and angle of incline are known.

4. What units should be used for the mass and angle in the formula?

The mass should be in kilograms (kg) and the angle should be in radians (rad). If the angle is given in degrees (°), it must be converted to radians by multiplying it by π/180.

5. Is there a specific direction for the acceleration in this formula?

Yes, the direction of the acceleration will be in the direction of the incline, which is determined by the angle theta. If the incline is uphill, the acceleration will be positive, and if the incline is downhill, the acceleration will be negative.

Similar threads

Replies
44
Views
1K
  • Introductory Physics Homework Help
Replies
30
Views
1K
  • Introductory Physics Homework Help
Replies
24
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
3K
  • Introductory Physics Homework Help
Replies
15
Views
3K
  • Introductory Physics Homework Help
Replies
2
Views
793
  • Introductory Physics Homework Help
Replies
7
Views
4K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
3K
Back
Top