A 3.5 kg block slides with a speed of1.1 m/s on a frictionless, horizontal surfa

Question

A 3.5 kg block slides with a speed of1.1 m/s on a frictionless, horizontal surface until it encounters aspring. (a) If the block compresses the spring7.5 cm before coming to rest, what isthe force constant of the spring?
1 N/m
(b) What initial speed should the block have to compress the springby 1.8 cm?
2 m/s (a) If the block compresses the spring7.5 cm before coming to rest, what isthe force constant of the spring?
1 N/m
(b) What initial speed should the block have to compress the springby 1.8 cm?
2 m/s

Explanation / Answer

mass of the block m = 3.5 kg speed v = 1.1 m / s compression x = 7.5 cm = 0.075 m (a). kinetic energy of the block = potential energy of thespring                              ( 1/ 2) m v ^ 2 = ( 1/ 2) k x ^ 2 from this force constant   k = m ( v / x ) ^ 2                                         = 752.88 N / m (b). compression x ' = 1.8 cm = 0.018 m we know kinetic energy of the block = potential energy of thespring                                 ( 1/ 2) m v ^ 2 = ( 1/ 2) k x ' ^ 2 from this initial speed of the block v = x ' [ k/ m ]                                                       = 0.264 m / s                                 ( 1/ 2) m v ^ 2 = ( 1/ 2) k x ' ^ 2 from this initial speed of the block v = x ' [ k/ m ]                                                       = 0.264 m / s

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