- #1
KatrineRav
- 13
- 1
- Homework Statement
- Two objects are suspended in a pulley system. Their masses are identical (but I've called them m1 and m2 through most of the calculations). A force is applied to one of the objects. What is the resulting acceleration of that object?
- Relevant Equations
- F=ma
Fg=mg
SOLUTION ATTEMPT
Newtons 2nd law states that F=ma (eq. 1). When a force is applied to a mass m it results in an acceleration a=F/m (eq. 2). If a vertical force is applied to one of the objects in this system, acceleration of both objects will occur. Assuming the length of the rope is constant, a vertical acceleration of object 1 will result in a vertical acceleration of object 2 of equal magnitude but opposite direction, that is a1= - a2 (eq. 3). To calculate the acceleration resulting from a vertical force applied to one of the objects, equation 2 is substituted into equation 3 and then equation 1 is substituted in, giving
The acceleration a is then isolated giving
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SOLUTION ATTEMPT 2:
Not really an attempt, but I've looked into acceleration problems, where the objects suspended under the pulley has different masses (m1 and m2, m2>m1).
There the acceleration is calculated by
I guess the extra force applied could be expressed as a mass equivalent m_eq=F/g. I could then substitute m2 for m1+m_eq. But that seems like an odd way to go around it...
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SOLUTION ATTEMPT 3:
I've also tried to look at the forces applied to each object.
Object 1: gravity (down, -mg), tension (up, T), "the extra force" (down, -F)
Object 2: gravity (down, -mg), tension (up, T)
I tried some different ways of juggling that around but with no luck.
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My intuitive understanding is that the answer will be
a=F/(m1+m2)
In this case m1 = m2 and I substitute them for m:
a=F/2m
That makes sense to me, because the two objects are connected, which means that if you apply a force to one of them you are in fact trying to accelerate both of them, which means you have to look at their combined mass to calculate the resulting acceleration.
I just can't seem to get their or any!
Please help :)
Newtons 2nd law states that F=ma (eq. 1). When a force is applied to a mass m it results in an acceleration a=F/m (eq. 2). If a vertical force is applied to one of the objects in this system, acceleration of both objects will occur. Assuming the length of the rope is constant, a vertical acceleration of object 1 will result in a vertical acceleration of object 2 of equal magnitude but opposite direction, that is a1= - a2 (eq. 3). To calculate the acceleration resulting from a vertical force applied to one of the objects, equation 2 is substituted into equation 3 and then equation 1 is substituted in, giving
The acceleration a is then isolated giving
--------------------------------
SOLUTION ATTEMPT 2:
Not really an attempt, but I've looked into acceleration problems, where the objects suspended under the pulley has different masses (m1 and m2, m2>m1).
There the acceleration is calculated by
I guess the extra force applied could be expressed as a mass equivalent m_eq=F/g. I could then substitute m2 for m1+m_eq. But that seems like an odd way to go around it...
---------------------------
SOLUTION ATTEMPT 3:
I've also tried to look at the forces applied to each object.
Object 1: gravity (down, -mg), tension (up, T), "the extra force" (down, -F)
Object 2: gravity (down, -mg), tension (up, T)
I tried some different ways of juggling that around but with no luck.
---------------------------
My intuitive understanding is that the answer will be
a=F/(m1+m2)
In this case m1 = m2 and I substitute them for m:
a=F/2m
That makes sense to me, because the two objects are connected, which means that if you apply a force to one of them you are in fact trying to accelerate both of them, which means you have to look at their combined mass to calculate the resulting acceleration.
I just can't seem to get their or any!
Please help :)