Atwood's Machine with one side holding a variable mass

[coffeebird]

Homework Statement

Figure 5-47 shows Atwood's machine, in which two containers are connected by a cord (of negligible mass) passing over a frictionless pulley (also of negligible mass). At time t = 0, container 1 has mass 1.30 kg and container 2 has mass 2.80 kg, but container 1 is losing mass (through a leak) at the constant rate of 0.200 kg/s. At what rate is the acceleration magnitude of the containers changing at (a) t = 0 and (b) t = 3.00 s? (c) When does the acceleration reach its maximum value?

Homework Equations

Fnet=ma

The Attempt at a Solution

m1= 1.30-.200t m2=2.80

Fnet(at t=0) = Tension= m1g- m2g=27.44-12.74=14.7N

acceleration of system (at t=0)= Fnet/mass= 14.7/ 4.1= 3.59 ms^2

 

[gneill]

You've found the acceleration for time t=0, but they're looking for the rate of change of acceleration (with respect to time). What does 'rate of change of a function' suggest to you?

Why don't you begin by finding an expression for the acceleration assuming that m1 and m2 are constants (don't plug in any numbers yet, use symbols only). Then write an expression for m1 as function of time and plug it into the acceleration expression. What does that give you?

 

[coffeebird]

so, m1= 1.30-.200t, but i don't know how to figure out an acceleration expression really

 

[HallsofIvy]

gneill told you you don't want an "acceleration expression", you want the rate of change of acceleration. Have you taken Calculus?

 

[gneill]

gneill told you you don't want an "acceleration expression", you want the rate of change of acceleration. Have you taken Calculus?

Well to be fair, the OP will need to begin with an expression for acceleration with respect to time, and then proceed to find its rate of change with respect to time.

 

[gneill]

so, m1= 1.30-.200t, but i don't know how to figure out an acceleration expression really

Start by taking the work you did to find the acceleration at time t=0 and write it out symbolically (don't substitute any numbers). What the expression for a(t = 0) in terms of m1, m2, and g?

 

[coffeebird]

gneill told you you don't want an "acceleration expression", you want the rate of change of acceleration. Have you taken Calculus?

in response- yes i know that i am looking for the rate of change- and yes i have taken calc classes, but i don't really see how that clarifies anything in this case, because- i guess I'm going to be super duper specific here - i don't know how to find that rate of change without first finding an expression for the acceleration--and there's probably something I'm forgetting here.

so...would that be the Fnet/mass= a? where do i go from there though...find the derivative of this, but how if i have the two variables, because they're both going to be changing...i'm sorry if my questions seem too stupid. is there like a rule against against lowly questions on this site, because i'll leave no prob

 

[SammyS]

in response- yes i know that i am looking for the rate of change- and yes i have taken calc classes, but i don't really see how that clarifies anything in this case, because- i guess I'm going to be super duper specific here - i don't know how to find that rate of change without first finding an expression for the acceleration--and there's probably something I'm forgetting here.

so...would that be the Fnet/mass= a? where do i go from there though...find dF/dm?

i'm sorry if my questions seem too stupid to some people, is there like a rule against against lowly questions on this site, because i'll leave no prob

Here's a link for the Wikipedia entry for Atwood's machine. Link

It gives the acceleration in terms of m₁ & m₂ .

Just plug-in your values for m₁ & m₂, including m₁'s time dependence, then take the derivative w.r.t. time.

 

[gneill]

The only stupid question is the one that isn't asked. If you need help clarifying concepts then this is the place to be!

An Atwood machine is driven by gravity. So in general the idea behind finding the acceleration is to proceed to find the tension in the string and thus the net forces acting on the masses. But a shortcut of determining the net "unbalanced" force acting on the system is fine, too.

Going the traditional route, draw a Free Body Diagram for each mass and solve for the tension. Use the tension to find the overall acceleration.

-or-

Using the shortcut, determine what the unbalanced force is (i.e., m2*g - m1*g) and use that as the net force acting on the total mass.

Either way, write an expression for the acceleration in terms of g, m1, and m2.