A spring is used to launch a coffee mug. The 20cm long spring can be compressed by a maximum of 8cm. The mug has a mass of 350 g. What kind of spring do you need to launch the mug at least 2 stories high (7 m) - as measured from the relaxed spring position - using the maximum compression?

The kind of spring needed to launch the 0.35 kg mug to 7 m high from start is 7510.78 N/m.

Explanation:

To solve the question, we note that the

Mass m of the mug = 350 g

Height to which mug is to be launched to = 7 m

Length of spring = 20 cm

Therefore we look for the governing equations of motion as follows

Energy required to raise the mug to 7 m = Gravitational Potential of the mug at 7 m and

Gravitational Potential = m·g·h

Where m = mass = 350 g = 0.35 kg

h = height = 7 m

g = Acceleration due to gravity = 9.81  m/s²

Energy of spring to raise the height of the mug to 7 m =

Where:

K = Spring constant

x = Length of compression or expansion

Equating the Energy supplied to the energy gained we get

m·g·h =

Making k the subject of the formula gives

= = 7510.78 N/m.

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