The weight of an object exerts on a scale varies directly with the mass of an object. If a bowling ball has a mass of 6 kg, the scale reads 54.
If another object has a mass of 8kg, what would the scale read?
w = km, where w is weight, m is mass and k is a constant
given: when w = 54 , m = 6
54 = k(6)
k = 9
so w = 9m, so if m = 8, w = ...
or, just use a proportion:
x/54 = 8/6
x = 54(4/3) = ... same as above
To find out what the scale would read for an object with a mass of 8 kg, we need to determine the proportionality constant that relates the mass to the weight.
We know that the scale reads 54 when the mass is 6 kg. So, we can set up a proportion to solve for the scale reading when the mass is 8 kg:
Mass 1 / Scale 1 = Mass 2 / Scale 2
6 kg / 54 = 8 kg / Scale 2
Now, we can cross-multiply and solve for Scale 2:
6 kg * Scale 2 = 8 kg * 54
Scale 2 = (8 kg * 54) / 6 kg
Scale 2 = 432 kg / 6 kg
Scale 2 = 72
Therefore, if another object has a mass of 8 kg, the scale would read 72.
To find out what the scale would read for an object with a mass of 8 kg, we can use the concept of direct variation. In this scenario, the weight of an object is directly proportional to its mass. This means that as the mass increases, the weight will also increase in the same proportion.
To solve this problem, we can set up a proportion using the given information. Let's use "x" to represent the scale reading for the 8 kg object.
The given information tells us that when the mass is 6 kg, the scale reads 54. We can write this as a proportion:
6 kg / 54 = 8 kg / x
We can solve this proportion by cross-multiplying:
6 kg * x = 54 * 8 kg
Now, we can solve for x by dividing both sides of the equation by 6 kg:
x = (54 * 8 kg) / 6 kg
x = 432 kg / 6 kg
x = 72
Therefore, the scale would read 72 for an object with a mass of 8 kg.