Final answer:
Using the direct proportionality of weight to mass, the weight of an object with a mass of 9 kg on a given planet, where a mass of 8 kg weighs 40 N, is calculated to be 45 N.
Step-by-step explanation:
When we talk about the weight of an object, we are referring to the gravitational force acting on it. On Earth, this gravitational force is represented by the symbol g, and it has a standard value of approximately 9.80 m/s². The weight of an object can be calculated using the formula w = mg, where w denotes weight, m represents mass, and g is the acceleration due to gravity. It's also important to remember that g can take a positive or negative value, based on the chosen coordinate system.
In the given problem, we are told an object with a mass of 8 kg weighs 40 N. This information allows us to determine the gravitational force on the given planet.
To find the weight of an object with a mass of 9 kg, we use the fact that weight is directly proportional to mass.
Therefore, the weight w of the 9 kg object can be found using the ratio w9 / w8, where w9 is the weight of the 9 kg object and w8 is the weight of the 8 kg object, which is 40 N. Thus:
w9 / 40 N = 9 kg / 8 kg
w9 = (9 kg / 8 kg) × 40 N = 45 N
The weight of the 9 kg object on the given planet is therefore 45 N.