Question

A bucket filled with water of mass m1 = 5 kg is tied to a rubber band and stretched. When the rubber band is released, it produces an acceleration of 197 inch/s2 on the bucket. An identical rubber band is stretched by the same amount on another bucket of water of mass m2, and when released, it produces an acceleration of 36 ft/s2. Show your work and all unit conversions for full credit (10 points)

What is the mass of the second bucket in grams

What is the magnitude of the force exerted by the rubber band on the water in Newtons?

Answer 1

When the rubberband is stretched, potential energy is stored in the rubberband and when it is released, the potential energy is converted to kinetic energy and causing acceleration of bucket.

Mass of water in bucket 1 = m1 =5kg

Mass of water in bucket 2 = m2 =?

1 inch = 0.0254m

1 ft = 0.305m

Acceleration in bucket1 = a1=197inch/s2 = 197*0.0254 = 5.0038 m/s2

Acceleration in bucket 2 = a2 = 36 ft/s2 = 36*0.305 = 10.98m/s2

Indentical rubberband implies same force constant = k

same force is applied on both bucket

force = mass*acceleration

m1*a1= m2*a2

5*5.0038 = m2*10.98

25.019 = m2*10.98

m2 = 2.278 kg

Mass of water in bucket 2 is 2.278kg = 2.2785*1000 = 2278.5 g

Force excerted by rubberband on water = m1*a1 =m2*a2 = 5*5.0038 = 25.019N.

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