Challenge
The weight of an object is calculated using the formula [tex]W=m g[/tex], where:
[tex]W[/tex] is the weight, in newtons (N)
[tex]m[/tex] is the mass, in kg
[tex]g[/tex] is the acceleration due to gravity, in [tex]m / s ^2[/tex]
On Earth [tex]g=10 m / s ^2[/tex], and on the Moon [tex]g=2 m / s ^2[/tex].
The mass of a man is 75 kg and the mass of a lunar landing module is 10344 kg.
a. Work out the weight of the:
i. man on Earth
ii. lunar landing module on Earth.
b. Work out the weight of the:
i. man on the Moon
ii. lunar landing module on the Moon.
Answer (1)
Calculate the weight of the man on Earth: W = 75 × 10 = 750 N.
Calculate the weight of the lunar landing module on Earth: W = 10344 × 10 = 103440 N.
Calculate the weight of the man on the Moon: W = 75 × 2 = 150 N.
Calculate the weight of the lunar landing module on the Moon: W = 10344 × 2 = 20688 N.
The weight of the man on Earth is 750 N , the weight of the lunar landing module on Earth is 103440 N , the weight of the man on the Moon is 150 N , and the weight of the lunar landing module on the Moon is 20688 N .
Explanation
Understanding the Problem We are given the formula to calculate the weight of an object: W = m g , where W is the weight in Newtons (N), m is the mass in kg, and g is the acceleration due to gravity in m / s 2 . We are also given that on Earth, g = 10 m / s 2 , and on the Moon, g = 2 m / s 2 . The mass of the man is 75 kg, and the mass of the lunar landing module is 10344 kg. Our objective is to calculate the weights of the man and the lunar landing module on both Earth and the Moon.
Man's Weight on Earth First, we calculate the weight of the man on Earth. Using the formula W = m g , we have m = 75 kg and g = 10 m / s 2 . Therefore, the weight of the man on Earth is: W = 75 × 10 = 750 N
Lunar Landing Module's Weight on Earth Next, we calculate the weight of the lunar landing module on Earth. Using the formula W = m g , we have m = 10344 kg and g = 10 m / s 2 . Therefore, the weight of the lunar landing module on Earth is: W = 10344 × 10 = 103440 N
Man's Weight on the Moon Now, we calculate the weight of the man on the Moon. Using the formula W = m g , we have m = 75 kg and g = 2 m / s 2 . Therefore, the weight of the man on the Moon is: W = 75 × 2 = 150 N
Lunar Landing Module's Weight on the Moon Finally, we calculate the weight of the lunar landing module on the Moon. Using the formula W = m g , we have m = 10344 kg and g = 2 m / s 2 . Therefore, the weight of the lunar landing module on the Moon is: W = 10344 × 2 = 20688 N
Final Answer Therefore, the weight of the man on Earth is 750 N, the weight of the lunar landing module on Earth is 103440 N, the weight of the man on the Moon is 150 N, and the weight of the lunar landing module on the Moon is 20688 N.
Examples
Understanding weight calculations is crucial in space exploration. For instance, knowing the weight of equipment on the Moon helps engineers design lunar vehicles that can efficiently carry payloads. Similarly, calculating the weight of astronauts and their gear on different celestial bodies is essential for mission planning and ensuring the safety and success of space missions. These calculations are also important in everyday life, such as determining the appropriate load capacity for bridges and elevators.
