How Do You Calculate Acceleration from a Hanging Die's Deflection?

[shlurpie]

Homework Statement

Calculate the acceleration of a car given the fuzzy die hanging from a string attached to the roof of the car is deflected 15degrees to the vertical. The mass of the die is 250 g.

Homework Equations

F = ma
F_g = mg

and possibly many more!

The Attempt at a Solution

I don't even understand the question! Please, someone help! I'm desperate right now! I'm sorry if this is done wrongly, or in the wrong place. I'll be eternally grateful for some help.

Edit: Okay,I attempted something, but it doesn't look anywhere near right to me.

Fnet = Ftension - Fgy
ma = Ftension - (0.250cos15)
ma = Ftension - 0.2415
(0.250)a = Ftension - 0.2415

The only thing is, I don't know how to find FTension! D:

 

[shlurpie]

I attempted something. But I don't know if I did any of it right!

 

[PhanthomJay]

Hello shlurpie, at this time we welcome you to PF!

Okay,I attempted something, but it doesn't look anywhere near right to me.

nor to me, but at least you tried, which is a good thing.

Draw a sketch showing the object and string attached to the interior roof of the car and swinging out at a 15 degree angle to the vertical.

Now identify and show the forces acting on the object alone. Remember that the weight force, which is mg, always acts down, vertically down. That's one of the forces. The other force acting on the fuzzy die is the string tension, T. In what direction does the string tension point?

Once you show these 2 forces on your sketch, you need to correctly apply Newton's Laws in the vertical direction and then in the horizontal direction. Break up the forces into their vert and horiz components.There is no acceleration in the vertical direction . There is acceleration in the horizontal direction. Use the vert direction first to solve for T. Then use the horiz direction to solve for a. Give it a try.

 

[Ericv_91]

Shlurpie,

A piece of advice, unrelated to the solution to this problem, is that you need to look at the units of your calculations.

Fnet = Ftension - Fgy
ma = Ftension - (0.250cos15)
ma = Ftension - 0.2415

It looks to me as though you tried to calculate the force of gravity in the y direction, but your force would've had units of only Kg.

F=m*a= kg*m/s².

So at the very least you would've had to multiply by some acceleration (gravity in this case) to actually get a force.