Two blocks are connected with the massless, non-stretchable rope, and connected

Question

Two blocks are connected with the massless, non-stretchable rope, and connected to the spring that is fixed to the wall as shown. One of the blocks is hanging from the side of the table, while the other lies on the table. Mass of each block m = 0.5 kg, spring stiffness k=40 N/m, friction coefficient between the block and the table mu = 0.2. The spring is originally unstretched while the blocks are held at rest. Find maximum velocity (v max) of the blocks once the system is released (i.e. the hanging block starts to go down).

Explanation / Answer

now coside m which is on the table

T-mu*m*g-kx=m*a

T=mg

mg*(1-mu)-kx=m*dv/dt

(g*(1-mu)-kx)dx=vdv

integrate it we get

v(x)=2*sqrt(g(1-mu)x-kx^2/2)

For V max. Dv/dx=0

1-mu-(kx)=0

x=1-mu/k

x=0.02 m

Max V=2*sqrt(g(1-mu)x-kx^2/2)

=0.77 m/s ans

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.