A 2.5 kg mass slides over a smooth surface at a speed of 6.4m/s. This mass colli

Question

A 2.5 kg mass slides over a smooth surface at a speed of 6.4m/s. This mass collides with a stationary spring of force constant 5000 N/m. The mass and spring stick together and then the mass oscillates back and forth.

a) What is the max distance the spring is compressed?

b) How long does it take the mass to complete one round trip after becoming attached to the spring?

c) What is the acc. of the mass when the spring is compressed by 0.064m?

d) What is the speed of the mass when the spring is compressed by 0.11m?

Explanation / Answer

Given that,

m = 2.5 kg

v = 6.4 m/s

k = 5000 N/m

(a)

From conservation of energy,

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

2.5*(6.4)^2 = 5000*x^2

x = 0.143 m

(b)

T = 2*pi*sqrt (m / k)

T = 2*pi*sqrt (2.5 / 5000)

T = 0.1404 s

(c)

ma = kx

a = kx / m = 5000*0.064 / 2.5

a = 128 m/s^2

(d)

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

2.5*v^2 = 5000*(0.11)^2

v = 4.919 m/s

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