(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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/s^{2}? 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

2. Relevant equations

Newton's Laws

3. The attempt at a solution

(Viewed as a system)

F = (m_{A}+ m_{B}+ m_{C})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)

m_{A}a_{a}= T - m_{A}g [itex]\leftarrow[/itex] Here, I am using a_{a}as the 3 m/s^{2}acceleration of the two smaller blocks

T = m_{A}a_{a}+ m_{A}g

T = (1 kg)(3 m/s^{2}) + (1 kg)(9.8 m/s^{2})

T = 12.8 N

(From FBD of Block B - choosing RIGHT as the positive direction)

m_{B}(a - a_{a}) = T

a = (T + m_{B}a_{a}) / m_{B}

a = (12.8 N + 6 N) / 2 kg

a = 9.4 m/s^{2}

... Finally, plugging the acceleration into our first equation to find the force:

F = (7 kg)(9.4 m/s^{2})

F = 65.8 N

If 65.8 is not actually the correct answer, what am I doing wrong in my solution?

Thank you.

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# Dynamics: 3 Masses (blocks), one pulley, find acceleration and force to push blocks

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