Hey.. I don't know exactly how to get the solution for this one...
doubleudoubleudouble dot physikerboard.de/files/fahrzeug_223.jpg
(its a sketch i made with paint^^)
We assume there are no frictions at all and we only look at the masses M, m1 and m2.
I want to know how much force do i have to give to push M in such a way that it accelerates so fast that m1 and m2 wont move related to M?
No friction? then the inertia on m1 tending to move it back (m1*a) is pulling on the cord, equalling in tension m2*g
first, what is a:
F=(M+m1+m2)a solve for a.
then m1*a=m2*g
m1(F/(M+m1+m2))=m2g
solve for F, check my math.
Ah great thank you. I got problems with it because there are no frictions...i can hardly imagine how the masses behave but ill get an "eye" for it. Seems very right, big thanks!
To determine the force required to accelerate mass M while keeping masses m1 and m2 stationary relative to M, we need to consider the principles of Newton's second law of motion and the concept of the net force.
1. Define the forces acting on the system:
- F1: Force applied to mass M
- F2: Force acting on mass m1 due to the interaction with mass M
- F3: Force acting on mass m2 due to the interaction with mass M
2. Apply Newton's second law of motion:
Newton's second law states that the net force acting on an object is equal to the product of its mass and acceleration. In this case, we want to calculate the force required to give M an acceleration such that m1 and m2 remain stationary.
The net force acting on mass M is given by:
F_net = M * a
where F_net is the net force, M is the mass of M, and a is the desired acceleration.
Since the forces F2 and F3 are acting in the opposite direction to F1, the net force F_net is the difference between F1 and the sum of F2 and F3:
F_net = F1 - (F2 + F3)
3. Analyze the forces acting on m1 and m2:
Since m1 and m2 are stationary relative to M, the net force acting on each of them is zero. This means that F2 and F3 cancel each other out.
F_net = F1 - (F2 + F3) = F1 - (0 + 0) = F1
Therefore, the net force acting on mass M is equal to the force applied to push mass M.
To find the force required, we need to know the masses of M, m1, and m2, as well as the desired acceleration a. Once these values are known, we can plug them into the equation F_net = M * a to calculate the force needed to accelerate M.