# Solving the Puzzle: Forces & Acceleration

• jamesdubya
In summary, the tensions in the two sections of the string are not equal, so M1, M2, and M3 are not equal.
jamesdubya
I had just asked a question about boats going across a river but that question and this question really have me stumped.

## Homework Statement

http://img138.imageshack.us/img138/7910/68512243.png
A)Find the acceleration using Newtons laws
B)Find the velocity using Conservation of Total Mechanical Energy.

## Homework Equations

Idisk=1/2mR^2 (what is R?)
M1=T+Ff-MG=ma
M2=1/2mR^2-t+t=ma
M3=-T-Mg=ma
I doubt these are right but I tried, I'm terrible at summing forces.

## The Attempt at a Solution

A)FnMuk-1.1(9.8)+1/2mR^2-t+t-t-Mg=m(a)
I know I am way off but just so you can see I at least tried.

Last edited by a moderator:
Radius of the disc R is required to find the acceleration.
The tensions in the two sections of the string are not equal.
So rewrite the equations for M1, M2 and M3.

m1=T-MG-Fn-FF ?
m2= ?? My only guess would be the previous equation.
m3=T+MGH

jamesdubya said:
m1=T-MG-Fn-FF ?
m2= ?? My only guess would be the previous equation.
m3=T+MGH

No, you're ignoring what rl.bhat said …

there are two tensions, so call them T1 and T2.

(yes, I know the tension along a string is usually constant, but that's only if the pulley is frictionless … in this case, there is friction at the pulley, otherwise it wouldn't turn, so the tension is different on either side.)

ohh ok i see i see, thank you for your response... so
M1=Muk*M+T1
M2=M*.5mr^2+T1-T2
M3=T2-mg
any better?

jamesdubya said:
ohh ok i see i see, thank you for your response... so
M1=Muk*M+T1
M2=M*.5mr^2+T1-T2
M3=T2-mg
any better?

(have a mu: µ and try using the X2 tag just above the Reply box )

You're not writing these properly.

The first and third equations are F = ma.

The second equation is torque = Iα.

Start again (and be careful about the ±s).

M1=$$\mu$$*M-T1=ma
M2=I$$\beta$$
M3=-T2+MG=ma
any better?

jamesdubya said:
M1=$$\mu$$*M-T1=ma
M2=I$$\beta$$
M3=-T2+MG=ma
any better?

(what happened to that µ i gave you? )

The third equation is correct.

In the first equation, the signs are wrong.

The second equation isn't an equation (and what is ß anyway?)

I tried to use it! it came out goofy looking.. By the big B i ment to put$$\alpha$$.
M1=-µ*M+T1=ma
M2= I $$\alpha$$= M2G+T2
M3=-T2+MG=ma

jamesdubya said:
By the big B i ment to put$$\alpha$$.

M1=-µ*M+T1=ma
M2= I $$\alpha$$= M2G+T2
M3=-T2+MG=ma

The first equation is fine now (and easy to read ), except you need a g (why are you writing "G"?)

In the second equation, why do you have an Mg … that pulley isn't going anywhere, is it? Also, you need to change α into a function of a, you need to use T1, and you need torque on the RHS, not force.

ok so then
M2=M2+T1=I$$\alpha$$
I don't really understand what you mean change a to a function of a sorry. Does this look at least a little better

jamesdubya said:
ok so then
M2=M2+T1=I$$\alpha$$
I don't really understand what you mean change a to a function of a sorry. Does this look at least a little better

grrr … not much.

What is M2 doing there?

What happened to T2?

And, I repeat, T is a force, you need a torque

(and you need a in all three equations, or you won't be able to solve them , so you must write α in terms of a)

m2 is just a pulley it is just letting the rope go through it pretty much. So add a -T2 and set it = r x F which is =r x ma ?

jamesdubya said:
m2 is just a pulley it is just letting the rope go through it pretty much. So add a -T2 and set it = r x F which is =r x ma ?

I think you need to get some sleep. :zzz:

Start again in the morning.

I fell asleep at 6 and woke up super early, I am up for the day.Can you please just help me with this I just am not understanding how to do torque..

jamesdubya said:
I fell asleep at 6 and woke up super early, I am up for the day.Can you please just help me with this I just am not understanding how to do torque..

You've been making silly mistakes for the last three posts. If you're not normally like this, then you need more sleep.

torque is force times (perpendicular) distance, in this case tension times radius.

no i had about 8 slept from 6-230ish...anyway...I just don't understand it, they may be silly to you but this makes 0 sense to me, that's why I came here, I wouldn't be here if i knew how to do it well.. I do appreciate your attempts at help though.. ok so then M2=t2*radius ?

jamesdubya said:

ok, now what is α in terms of a?

a\R=$$\alpha$$?

jamesdubya said:
a\R=$$\alpha$$?

Yup!

ok, now put all the numbers into the three equations, and solve them.

M1=-µ*Mg+T1=ma
M3=-T2+Mg=ma

µ*M1g+T1-T2+M3g=ma
.36*1.1*9.81+5*9.81=1.6(a)
33.08=a
is that right?
I don't know how to find the radius for the disk

jamesdubya said:
µ*M1g+T1-T2+M3g=ma
.36*1.1*9.81+5*9.81=1.6(a)
33.08=a
is that right?

Is M3 5 kg or 0.5 kg?

And you left out a minus.
I don't know how to find the radius for the disk

You don't need it, it cancels.

You need to eliminate T1 and T2 (because you don't know them, and the question doesn't ask for them), so get two equations for T1 - T2.​

It's 5kg.
t1-t2=Iα
and then I had a t1-t2 in my other equation that would cancel these out.

## 1. What is the difference between force and acceleration?

Force is a push or pull on an object, while acceleration is the rate at which an object's velocity changes over time.

## 2. How are forces and acceleration related?

According to Newton's Second Law of Motion, the net force acting on an object is equal to its mass multiplied by its acceleration. This means that the larger the force applied to an object, the greater its acceleration will be.

## 3. What are the different types of forces that can affect acceleration?

The four main types of forces that can affect acceleration are frictional forces, gravitational forces, electrostatic forces, and magnetic forces. These forces can either increase or decrease an object's acceleration depending on their direction and magnitude.

## 4. How do you calculate acceleration using force?

To calculate acceleration using force, you can use the formula a = F/m, where a is acceleration in meters per second squared (m/s^2), F is the net force in Newtons (N), and m is the mass of the object in kilograms (kg).

## 5. How does mass affect acceleration?

The greater the mass of an object, the more force is needed to accelerate it at the same rate. This means that objects with larger masses have lower accelerations compared to objects with smaller masses when the same force is applied.

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