Solving for a force eliminating acceleration

  • Thread starter Thread starter cwbullivant
  • Start date Start date
  • Tags Tags
    Acceleration Force
AI Thread Summary
A worker applies a force of 210N to a box on a cart, which moves as one unit due to friction. The discussion centers on understanding how to eliminate acceleration (A) from two simultaneous equations derived from free-body diagrams of the box and cart. The key equation derived is FCB = (Mcart*FBW)/(Mcart+Mbox), which simplifies the problem by substituting values and eliminating A. Clarification was provided that "eliminating A" means solving for A in one equation and substituting it into the other. The conversation highlights common struggles in physics problem-solving and the importance of clear communication in understanding concepts.
cwbullivant
Messages
60
Reaction score
0

Homework Statement



A worker applies a force of 210N to a box attached to a cart, with sufficient frictional force such that the box and the cart move as one. What is the frictional force on the box?

Force 1: Force on box by worker, FBW
Force 2: Force on cart by box, FCB
Force 3: Force on box by cart, FBC

Homework Equations





The Attempt at a Solution



This is from the solution, but I can't understand how it was obtained, as it doesn't explain the process:

FCB = McartA (I knew this part)
FBW - FBC = MboxA

"Since we want to solve for the unknown FCB = FBC, we eliminate A from these two equations and obtain:"

FCB = (Mcart*FBW)/(Mcart+Mbox)

I don't quite understand what they mean by "eliminate A" (hold it constant?), nor can I seem to deduce the process they used here.

I've tried substituting in McartA for FBC (since they're equal), but all that does is solve for A, which I'm evidently supposed to eliminate to begin with.
 
Physics news on Phys.org
This is from the solution, but I can't understand how it was obtained, as it doesn't explain the process:
They have started by drawing free-body diagrams for the box and the cart, then, for each diagram, summed the forces and used Newton's law.
This gives two simultanious equations and two unknowns ... how would you solve them?

I don't quite understand what they mean by "eliminate A"
Then mean that you solve for A in one equation and substitute it into the other one.
 
Simon Bridge said:
They have started by drawing free-body diagrams for the box and the cart, then, for each diagram, summed the forces and used Newton's law.
This gives two simultanious equations and two unknowns ... how would you solve them?

Then mean that you solve for A in one equation and substitute it into the other one.

The first became immediately obvious when I read the second. I feel really, -really- dumb right now; I really have no excuse for not getting that. Thanks for the help, much appreciated.
 
We all do that from time to time - sometimes a change in wording can make the mind go blank.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Thread 'Egg Drop Challenge! Need ideas for winning designs'

I was thinking using 2 purple mattress samples, and taping them together, I do want other ideas though, the main guidelines are; Must have a volume LESS than 1600 cubic centimeters, and CAN'T exceed 25 cm in ANY direction. Must be LESS than 1 kg. NO parachutes. NO glue or Tape can touch the egg. MUST be able to take egg out in less than 1 minute. Grade A large eggs will be used.
View full post »

Similar threads

Solving Cart Force Question: Magnitude & Direction
Replies
21
Views
7K
Newton's Third Law: Acceleration of box and worker
Replies
2
Views
5K
What is the ranking of forces in a problem on ranking forces?
Replies
8
Views
2K
Minimum acceleration needed for box to not fall from accelerating cart
Replies
8
Views
6K
Calculating the frictional forces on a sliding box on a ramp
Replies
2
Views
3K
Acceleration of object with friction: Homework help
Replies
1
Views
2K
Direction of friction on two stacked boxes
Replies
9
Views
4K
Acceleration of a cart immediately after the system is released
Replies
15
Views
4K
Getting the init. velocity given G-force?
Replies
1
Views
1K
Finding Force by using the coefficient of friction and mass
Replies
16
Views
3K

Hot Threads

Recent Insights

Back
Top