Question

two threads of spring constant 100n/m each is connected to the two sides of a body of mass 1kg standing on a horizontal frictionless surface prepdoor

Answer 1

Two rubber threads of spring constant of 100 N/m each is connected to the two sides of a body of a mass of 1 kg standing on a horizontal frictionless surface. The rubber threads are stretched by a length of Δl = 1cm and their ends are fixed. Then the body is displaced by a distance of 2∆l towards one of the fixing points and it is released. Determine initial acceleration of the mass.

solution : here, one of the elastic becomes totally lose when it is displaced towards one fixed end that causes all the initial force of mass will be only due to elastic on other sides .

I mean, elastic force is balanced by Newtonian force acting on mass m and with acceleration a .

e.g., Kx = ma

here, K = 10N/m , m = 1kg and x = 1cm + 2cm = 3cm [ where 1 cm of initial stretched and 2cm of later displacement ]

now, 100N/m × 3/100 m = 1kg × a

3 m/s² = a

hence, initial acceleration of the mass is 3m/s²