Suppose you lay a spring with k = 200 N/m on the floor against a wall. A3 kg mas

Question

Suppose you lay a spring with k = 200 N/m on the floor against a wall. A3 kg mass is placed on an 5 meter high frictionless ramp. The mass is released from rest and slides down the ramp into the spring. a) What is the maximum acceleration the mass will experience as it compresses the spring? (It's pretty large.) b) Suppose we increased the mass of the box. Would the new box compress the spring more, less, or (he same amount as the 3 kg box? Justify your answer in words or math. c) Suppose we increased the mass of the box. Would the new box experience a maximum acceleration that is larger, smaller, or the same as the acceleration m part a. Justify your answer with math.

Explanation / Answer

here,

k = 200 N/m

mass , m = 3 kg

the angular speed , w = sqrt(k/m)

w = 8.16 rad/s

a)

let the spring compresses x m

using conservation of energy

0.5 * k * x^2 = m * g * h

0.5 * 200 * x^2 = 3 * 9.81 * 5

x = 1.21 m

the maximum accelration , am = x * w^2 = 80.8 m/s^2

b)

using conservation of energy

0.5 * k * x^2 = m * g * h

x = sqrt(2 * m * g * h /k)

when we incresed the mass

the value of x increases

so the compression of mass increases

c)

the angular speed (w = sqrt(k/m)) decreases

so, the maximum accelration , am = A * w^2

am = sqrt(2 * m * g * h /k) * ( k/m)

am = ( 2 * m * g * h * k /m)

so when mass increases

the maximum accelration is smaller

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