- #1
Eclair_de_XII
- 1,083
- 91
Homework Statement
"When the three blocks in Fig. 6-29 are released from rest, they accelerate with a magnitude of ##0.500 \frac{m}{s^2}##. Block 1 has mass M, Block 2 has mass 2M, and Block 3 has mass 3M. What is the coefficient of static friction between Block 2 and the table?"
Homework Equations
##f_s=(μ_k)(F_N)##
Answer from book: 0.37
The Attempt at a Solution
Okay, so I attempted this by beginning with the sum of all the forces at work, relative to the force on Block 3. There's the gravitational force on Block 1 negating half of Block 3's force, and then there's the static friction between Block 2 and the table also slowing the motion of Block 3. So:
##ΣF = ma = (-9.8\frac{m}{s^2})(M) + (μ_k)(-9.8\frac{m}{s^2})(2M) + (9.8\frac{m}{s^2})(2M)##
##ΣF = (μ_k)(-9.8\frac{m}{s^2})(2M) + (9.8\frac{m}{s^2})(M)##
##\frac{ΣF}{m} = a = (9.8\frac{m}{s^2})(-2μ_k + 1)##
##a = \frac{1}{2}\frac{m}{s^2}##
##\frac{1}{2}\frac{m}{s^2} = (9.8\frac{m}{s^2})(-2μ_k + 1)##
##\frac{1}{19.6}=-2μ_k + 1##
##-\frac{18.6}{19.6}=-2μ_k##
##μ_k=\frac{93}{196}##
I have a feeling I messed up on the third step, in calculating acceleration and equating it to ##\frac{1}{2}##. Are there any other forces at work here, that are slowing Block 3's descent? Thank you for anyone who is willing to help me.