Question

A 2.7-kg block slides with a speed of 1.1 m/s on a frictionless, horizontal surface until it encounters a spring.

(a) If the block compresses the spring 6.0 cm before coming to rest, what is the force constant of the spring?
(b) What initial speed should the block have to compress the spring by 1.5 cm?

Answer 1

given,

mass of block = 2.7 kg

speed of block = 1.1 m/s

a) spring compressed to distance of 6 cm or 0.06 m

using conservation of energy

kinetic energy is converted into spring energy

`(1)/(2)mv^2= (1)/(2)kx^2`

`k =( mv^2)/(x^2)`

`k =(2.7* 1.1^2)/(0.06^2)`

k= 907.5 N/m

b) again using conservation of energy

kinetic energy is converted into spring energy

`(1)/(2)mv^2= (1)/(2)kx^2`

`v =\sqrt{(kx^2)/(m)}`

`v=\sqrt{(907.5* 0.015^2)/(2.7)}`

`v=√(0.075625)`

v= 0.275 m/s