Acceleration of block B on top of wedge A on a ramp

[dkopchak]

Homework Statement

A 12-lb block B rests on the upper surface of a 30-lb wedge A on a 30° ramp. Neglecting friction, determine immediately after the system is released from frest (a) the acceleration of A, (b) the acceleration of B relative to A.

Homework Equations

ƩFx=m_A a_A
W=mg
a_B = a_A + a_B/A

The Attempt at a Solution

Attemp page 1
View attachment 30 lb wedge pg 1.pdf
Attemp page 2
View attachment 30 lb wedge pg 2.pdf
Attemp page 3
View attachment 30 lb wedge pg 3.pdf

 

[LightHero]

Let the x-axis be the ramp and the origin at the top of the ramp. The free body diagrams for wedge A and block B are shown below,A: ƩFx=0 W=mA aAB: ƩFx=0 W=mB(aA+aB/A)From wedge A, WA=30*9.8=294NFrom block B, WB=12*9.8=118NTherefore, 294=mA aA 118=mB(aA+aB/A) Substituting mA=30 and mB=12, 294=30 aA 118=12(aA+aB/A) Solving for aA, aA=9.8 m/s2 Solving for aB/A, aB/A=1.08 m/s2 Therefore, aB = aA + aB/A aB=9.8 + 1.08 aB=10.88 m/s2