Physics 2. I'd really appreciate any help.

Question

Three blocks move on a surface with μs = 0.6 and μk = 0.4 as shown below. Jennifer, another

honor chemistry student, applied 34 N of force to move the system of three blocks, but she

failed. Assume that the string is massless.

(a) Michael asked why. Can you answer to Michael?

(b) Now, the determined Jennifer applied 50 N of force to the system. Draw free‐body diagrams

for each of blocks.

(c) Write down the equations of motions for all three blocks. What are net forces?

(d) Find the acceleration.

(e) Find the tension and the contact force between the first and second block.

Answer 1

There's a book way to solve these problems, but there is a much better way if you don't care about any of the tensions...

Treat all 3 bodies as a system (as long as they all interact completely (no slack in ropes and no detachments pushing) and the ropes are massless), you need only consider forces that are external to the three blocks.

For the forces acting on the system we have F to the right and to the left we have m₁μg + m₂gμ + m₃gμ

Static: F_max = μ_s(m1+m2+m3)g So, F_Max = (6kg)(9.8N/kg)(.6) = 35.28 N (anything F less won't budge anything)

Dynamic: F - μ_km_Tg = m_Ta m_T is the total mass (solve for a)

Now that you have a you can do a force balance around individual masses in order to find a Tension or interactive compressive force (like F₁₂ , force of 1 on 2)

The net forces for m₁, m₂, m₃ are m₁a, m₂a, m₃a respectively.

The tension can be found by the net force on mass 3:

F-T-m₃gμ_k = m₃a (solve for T using the a which is the same for all the crates.

You should work out the force balances for m₁ and m₂ yourself. I will list them here for completeness. Note that textbooks usually want you to write these out, add them up (which results in the equation that I started with as all internal forces cancel for the system of 3 masses), and solve for a. You then solve for T and F₁₂ the same way.

m2: F₁₂ - m₂gμ_k = m₂a

m₁: T - F₂₁ - m₁gμ_k = m₁a

I'll leave you to answer the particular questions.