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Chapter 1: Q16E (page 125)

An astronaut鈥檚 pack weighs 17.5 N when she is on the earth but only 3.24 N when she is at the surface of a moon.

(a) What is the acceleration due to gravity on this moon?

(b) What is the mass of the pack on this moon?

Short Answer

Expert verified

(a) The acceleration due to gravity on the surface of the moon where the astronaut's pack weighs 3.24 N is 1.81m/s2.

(b) The mass of the astronaut's pack on the moon is 1.79 kg.

Step by step solution

01

Given data

The weight of the astronaut's pack on Earth is

WE=17.5N

The weight of the astronaut's pack on the moon is

Wm=3.24N

The acceleration due to gravity on Earth is

g=9.8m/s2

02

Gravitational force

The downward gravitational force on a body of mass mis

Fg=mg.....(1)

03

The acceleration due to gravity on the moon

From equation (1), the ratio of weights of the astronaut's pack on the moon and on Earth is

WmWE=mgmmggm=WmWE脳ggm=3.24N17.5N脳9.8m/s2gm=1.81m/s2

Thus, the acceleration due to gravity on the moon is1.81m/s2

04

Mass of the astronaut's pack

From equation (1), the mass of the astronaut's pack is

m=Wmgm=3.24N1.81m/s2=1.79路1m/s2路1N脳1kg路m/s21N=1.79kg

Thus, the mass of the pack is 1.79 kg.

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