Question

The free-fall acceleration on Mars is 3.7 m/s2.

(a) What length pendulum has a period of 2.4-s on Earth? cm
(b) What length pendulum would have a 2.4-s period on Mars? cm An object is suspended from a spring with force constant 10 N/m.
(c) Find the mass suspended from this spring that would result in a 2.4 s period on Earth.
(d) Find the mass suspended from this spring that would result in a 2.4 s period on Mars.

Answer 1

a) 142.98 cm b) 53.98 cm c) 1.46 kg d) 1.46 kg

Step-by-step explanation:

Using the equation for the period of a simple pendulum we can answer the first 2 questions.

a)
`T=2\pi\sqrt(l)/(g)\\T^2=4\pi^2(l)/(g)\\l=(T^2g)/(4\pi^2)=((2.4s)^29.8m/s)/(4\pi^2)\\l=1.42 m= 142.98 cm`

b)
`l=(T^2g)/(4\pi^2)=((2.4s)^23.7m/s)/(4\pi^2)\\l=0.53 m= 53.98 cm`

Using the equation for the period of a mass-spring system we can answer the last 2 questions.

c)
`T=2\pi\sqrt(m)/(k)\\T^2=4\pi^2(m)/(k)\\m=(T^2k)/(4\pi^2)=((2.4s)^210N/m)/(4\pi^2)\\l=1.46 kg`

d)
`T=2\pi\sqrt(m)/(k)\\T^2=4\pi^2(m)/(k)\\m=(T^2k)/(4\pi^2)=((2.4s)^210N/m)/(4\pi^2)\\l=1.46 kg`

we can observe that the period of this system does not depend on the value of gravity.