Question

On a given planet, the weight of an object varies directly with the mass of the object. Suppose that an object whose mass is 5 kg weighs 15 N. Find the weight of an object whose mass is 9 kg.

Answer 1

To find the weight of a 9 kg object on a given planet, we first calculate the constant of proportionality (3 N/kg) using the weight-to-mass ratio of a 5 kg object that weighs 15 N. Then, we use this constant to multiply by the mass of the 9 kg object, resulting in a weight of 27 N.

Step-by-step explanation:

The weight of an object is dependent on its mass and the acceleration due to gravity (g) of the location where the object is.

Since the question states that weight varies directly with mass and gives an example on a given planet that a 5 kg object weighs 15 N, we can use this information to calculate the weight of another object with a different mass on the same planet.

First, we determine the constant of proportionality (which is the equivalent of g on this planet). Using the data given:

w = mg
= (5 kg)(g) = 15 N
g = 15 N / 5 kg = 3 N/kg

Now, we use the value of g to find the weight of a 9 kg object:

w = mg
= (9 kg)(3 N/kg) = 27 N

Therefore, a 9 kg object on this planet would weigh 27 N.