Question

the block of mass 50 kg is projected horizontally on a rough horizontal floor the coefficient of fri

Answer 1

your complete question -> A block of m=50kg is projected horizontally on a rough horizontal floor. The co-efficent of friction between the block and d floor is 0.1.The block strikes a light spring of stiffness k=100N/m with a velocity 2m/s. The maximum compression of spring is

solution : from work energy theorem,

kinetic energy of block = workdone by friction + potential energy of spring.

or, 1/2 mv² = fr. x + 1/2 kx²

or, 1/2 mv² = umgx + 1/2 kx²

here, u = 0.1, m = 50kg, v = 2m/s, K = 100N/m and g = 10m/s²

so, 1/2 × 50 × (2)² = 0.1 × 50 × 10 × x + 1/2 × 100 × x²

or, 100 = 50x + 50x²

or, x² + x - 2 = 0

or, x² + 2x - x - 2 = 0

or, x(x + 2) - 1(x + 2) = 0

or, (x - 1)(x + 2) = 0

x = 1 , -2 but x ≠ -2

so, x = 1m

hence, maximum compression of spring is 1m