- #1

PhysicsCanuck

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- 1

- Homework Statement
- Suppose in the same Atwood setup another string is attached to the bottom of m1 and a constant force f is applied, retarding the upward motion of m1.

If m1 = 5.00 kg and m2 = 10.00 kg, what value of f will reduce the acceleration of the system by 50%?

- Relevant Equations
- T = m1*a1 + m1*g

T = m2*a2 + m2*g

-a1 = a2

and

T = m1*a1 + m1*g

T = m2*a2 + m2*g <--substitute -a1 = a2, multiply everything by -1, add the two equations in order to solve for a1 (and thus also a2)

T = m1*a1 + m1*g

-T = m2*a1 - m2*g

0 = m1*a1 + m1*g + m2*a1 - m2*g <-- substitute known values (m1 = 5.00kg, m2 = 10.00kg, g=9.8m/s^2), solve for a1

a1 = +3.266 m/s^2 (and thus a2 = -3.266 m/s^2)

The question then states a 50% reduction, so 3.266/2 = 1.633 m/s^2 for the following equations.

After grinding through this for hours (and knowing the final solution to be 24.5N), I was able to determine the following:

T' = m1*a1 + m1*g + F

T' = m2*a2 + m2*g

Since we know m1, m2, a1, a2, and g, we can solve for F, where F = 24.5NMy question is as follows: Since a force (and thus a tension) is being added to m1 (and thereby increasing the tension experienced in the line/rope/cable, wouldn't I also add that same force value to m2 since it is also experiencing more tension as they are connected and inextensible.

Can anyone explain this and help me better understand?

Thank you very much.