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robkom
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Homework Statement
Block C (m = 4 kg) sits on a frictionless horizontal surface. Block B (of m = 2 kg) sits on top of block C, and is attached to a rope that runs over the massless
pulley as shown in the figure. Block A (m = 1 kg) hangs vertically from the rope. With
what horizontal force F must you push Block C so that block A rises with an upward
acceleration of a = 3 m/s2? All surfaces are frictionless.
(a) 12 N
(b) 47 N
(c) 59.8 N [itex]\leftarrow[/itex] This is apparently the correct answer
(d) 15.0 N
(e) None of the above
Figure:
http://www.freeimagehosting.net/t/28bdd.jpg
Homework Equations
Newton's Laws
The Attempt at a Solution
(Viewed as a system)
F = (mA + mB + mC)a
F = (1 kg + 2 kg + 4 kg)a
F = (7 kg)a [itex]\leftarrow[/itex] I must find this acceleration to calculate the force
(From FBD of Block A - choosing UP as the positive direction)
mAaa = T - mAg [itex]\leftarrow[/itex] Here, I am using aa as the 3 m/s2 acceleration of the two smaller blocks
T = mAaa + mAg
T = (1 kg)(3 m/s2) + (1 kg)(9.8 m/s2)
T = 12.8 N
(From FBD of Block B - choosing RIGHT as the positive direction)
mB(a - aa) = T
a = (T + mBaa) / mB
a = (12.8 N + 6 N) / 2 kg
a = 9.4 m/s2
... Finally, plugging the acceleration into our first equation to find the force:
F = (7 kg)(9.4 m/s2)
F = 65.8 N
If 65.8 is not actually the correct answer, what am I doing wrong in my solution?
Thank you.