Question

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

(a) What length of pendulum has a period of 1.8 s on Earth?
____________________ cm

(b) What length of pendulum would have a 1.8-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 period of 1.8 s on Earth.
__________________ kg

(d) Find the mass suspended from this spring that would result in a period of 1.8 s on Mars.
__________________ kg

Answer 1

a) Use formula for time period of the pendulum:

T = 2?*sqrt(L/g)

Make L the subject of formula:

L = g* (T/2?)^2

At earth, g=9.8m/s^2; you want T=1.8 so substituting it in the formula above:

L = 9.8*(1.8/2?)^2 = 0.8051 m
b) For Mars, do the same as above, just put g=3.7 instead of 9.8.

L = 3.7*(3/2?)^2 = 0.3039 m

c,d) Use spring formula:

T = 2?*SQRT(m/k)

Make m the subject of formula:

m = k*(T/2?)^2

For both earth and mars, k=10 so the answer will the same for both planets.

m = 10 * (1.8/2?)^2 = .8215 Kg