Question

Two blocks are attached to one another, as shown, by means of a massless cord that passes over a massless frictionless pulley. Block 1 (mass 10 .0 kg ) is connected to a spring with spring constant
100 N/m, and block 2 (mass 20 .0 kg ) sits on a frictionless ramp that makes an angle 30 .0

Answer 1

Can you provide the figure please?

Answer 2

a)

gravitational potential energy of the blocks-earth-spring-ramp system to be zero when the spring is relaxed.

now,

let the extention in the spring is x m

the

displacement of block 1 in vertical directional will be zero so no gravitational potential Energy change only PE change due to Frictional force.. and

displacement of block 2 in vertical direction = x*sin(30 degree)

so,

PE of system(x)= PE of spring + PE of Block 1 + PE of Block 2

PE(x) = 1/2*k*x^2+F*d+m2*g*h

PE(x) = 1/2*100*x^2 - 10*10*0.1*x +20*10*(-x*sin(30 degree)

PE(x) = 50*x^2-10x - 100*x = 50x^2-110x

Graph

b)

E(x) = PE(X)+KE(x)

= 50x^2-110x + 1/2*m1*v1^2+1/2*m2*v2^2

at max. x, v1=v2=0

so,

E(x) =  50x^2-110x

dE/dx = 100*x-110 = 0

x= 110/100 = 1.1

so max. x=1.1m