Horizontal force due to tension from vertical wieght

[fatalphysics]

Homework Statement

Block C (m= 4 kg) sits on a frictionless horizontal surface. Block B of (m
= 2kg) 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 = 3m/s²? All surfaces are frictionless.

Diagram:

Homework Equations

F=ma

The Attempt at a Solution

Using free body diagrams came up with:

F=ma_c
T=2a_c
T/2=a_c

F=ma_a
T-mg=(3)(1)
T=3+(9.8)(1)
T=12.8 N

(12.8)/2=a_c
a_c=6.4 m/s²

F=(m_c+m_a)a_c
F=(6)(6.4)
F=38.4 N

Actual answer = 59.8N

 

[PeterO]

Homework Statement

Block C (m= 4 kg) sits on a frictionless horizontal surface. Block B of (m
= 2kg) 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 = 3m/s²? All surfaces are frictionless.

Diagram:
View attachment 40143

Homework Equations

F=ma

The Attempt at a Solution

Using free body diagrams came up with:

F=ma_c
T=2a_c
T/2=a_c

F=ma_a
T-mg=(3)(1)
T=3+(9.8)(1)
T=12.8 N

(12.8)/2=a_c
a_c=6.4 m/s²

F=(m_c+m_a)a_c
F=(6)(6.4)
F=38.4 N

Actual answer = 59.8N

It looks like you are mixing up the mass of A and B. A is 1 ; B is 2 not the other way.