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Chapter 1: Q20E (page 230)

A 1.20-kg piece of cheese is placed on a vertical spring of negligible mass and force constant k = 1800 N/m that is compressed 15.0 cm. When the spring is released, how high does the cheese rise from this initial position? (The cheese and the spring are not attached.).

Short Answer

Expert verified

The piece of cheese rises to 3.44 m .

Step by step solution

01

Determine the expression for height raised by cheese from its initial positionGiven Data:

The mass of the piece of cheese is m = 1.20 kg

The force constant of spring is: k = 1800 N/m

The compression of spring is:x=15cm1m100cm=0.15cm

Height raised by cheese piece:

The elastic potential energy of the spring is equated to the gravitational potential energy of the piece of cheese due to the rise.

The height raised by a piece of cheese is given as:

mgh=12kx2

Here, m is the mass of cheese, g is the gravitational acceleration, h the height raised by cheese k is spring constant and x is compression of spring.

02

Determine the height raised by the cheese piece

Substitute all the values in the above equation and we get,

1.20kg9.8m/s2h=121800N/m0.15m2

h = 3.44 m

Therefore, the piece of cheese rises to 3.44 cm .

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