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.

 

[asteriatic]

No need to apologize, it's completely understandable to feel overwhelmed or confused by a question at first. Let's break it down step by step.

First, we need to understand what the question is asking. It is asking for the acceleration of a car, given the deflection of a fuzzy die hanging from a string attached to the roof of the car. This means that the car is moving and the die is hanging from the string, and we want to find out the acceleration of the car.

Now, let's look at the given information. We know that the mass of the die is 250 g, and it is deflected 15 degrees to the vertical. This means that the string attached to the roof of the car is at an angle of 15 degrees from the vertical, and the die is hanging from it.

Next, let's think about what forces are acting on the die. There are two main forces: the tension force from the string and the force of gravity (Fg). The tension force is pulling the die towards the roof of the car, while the force of gravity is pulling it towards the ground. These two forces are in opposite directions, so we can use Newton's Second Law (F=ma) to find the acceleration of the car.

We can also use Newton's Third Law, which states that for every action, there is an equal and opposite reaction. This means that the tension force from the string is equal in magnitude to the force of gravity on the die (Ftension = Fg).

Now, let's put this all together. We know that the net force on the die is equal to the tension force minus the force of gravity (Fnet = Ftension - Fg). We can also rewrite this as ma = Ftension - Fg, since F=ma.

Since we know that Ftension = Fg, we can substitute this into our equation to get ma = Fg - Fg = 0. This means that the net force on the die is 0, and therefore the acceleration of the car is also 0. This makes sense, since the die is hanging straight down and not moving, so the car must also be at a constant velocity.

In summary, the acceleration of the car is 0, given the fuzzy die hanging from a string attached to the roof of the car is deflected 15 degrees to the vertical. This is because the net force on