1) the weight of an object at Earth's surface is given by \(F=mg\), where m is the mass of the object and \(g=9.81 m/s^2\) is the gravitational acceleration at Earth's surface. The book in this problem has a mass of m=2.2 kg, therefore its weight is
\(F=mg=(2.2 kg)(9.81 m/s^2)=21.6 N\)
2) On Mars, the value of the gravitational acceleration is different:\(g=3.7 m/s^2\). The formula to calculate the weight of the object on Mars is still the same, but we have to use this value of g instead of the one on Earth: \(F=mg=(2.2 kg)(3.7 m/s^2)=8.1 N\)
3) The weight of the textbook on Venus is F=19.6 N. We already know its mass (m=2.2 kg), therefore by re-arranging the usual equation F=mg, we can find the value of the gravitational acceleration g on Venus:
\(g= \frac{F}{m}= \frac{ 19.6 N}{2.2 kg}=8.9 m/s^2\)
4) The mass of the pair of running shoes is m=0.5 kg. Their weight is F=11.55 N, therefore we can find the value of the gravitational acceleration g on Jupiter by re-arranging the usual equation F=mg:
\(g= \frac{F}{m} = \frac{11.55 N}{0.5 kg} =23.1 m/s^2\)
5) The weight of the pair of shoes of m=0.5 kg on Pluto is F=0.3 N. As in the previous step, we can calculate the strength of the gravity g on Pluto as
\(g= \frac{F}{m} = \frac{0.3 N}{0.5 kg} =0.6 m/s^2\)
6) On Earth, the gravity acceleration is \(g=9.81 m/s^2\). The mass of the pair of shoes is m=0.5 kg, therefore their weight on Earth is
\(F=mg=(0.5 kg)(9.81 m/s^2)=4.9 N\)
