Suppose a 100-gram mass when attached to a spring causes the spring to stretch 8 cm
what would you expect a 25-gram mass to do when attached to the same spring
stretch the spring 8 cm
stretch the spring 32 cm
stretch the spring 4 cm
stretch the spring 2 cm
To determine the effect of a 25-gram mass on the spring, we need to consider the relationship between mass and the amount of stretch in the spring.
In this case, we know that a 100-gram mass stretches the spring by 8 cm. From this information, we can infer that the increase in stretch is directly proportional to the increase in mass.
Using this relationship, we can set up a proportion to solve for the expected stretch when a 25-gram mass is attached.
(100 g) / (8 cm) = (25 g) / (x cm)
Simplifying the proportion:
(100 g)(x cm) = (25 g)(8 cm)
Cross-multiplying:
100x = 200
Dividing both sides by 100:
x = 2 cm
Therefore, we expect the 25-gram mass to stretch the spring by 2 cm.
To determine how a 25-gram mass would affect the spring, we can use the concept of proportionality. Assuming the extension of the spring is directly proportional to the mass attached, we can set up a proportion:
(100 g) / (8 cm) = (25 g) / x
where x represents the extension caused by the 25-gram mass.
Simplifying the equation, we have:
(100 * x) = (25 * 8)
(x) = (25 * 8) / (100)
(x) = 2 cm
Therefore, when a 25-gram mass is attached to the same spring, it would stretch the spring by 2 cm.
To determine how a 25-gram mass would affect the same spring, we need to understand the relationship between the mass and the amount the spring stretches.
In this case, the mass is directly proportional to the amount the spring stretches. This means that if the mass is doubled, the amount of stretch will also double.
Given that a 100-gram mass causes the spring to stretch 8 cm, we can set up a proportion to solve for the stretch caused by a 25-gram mass.
Let's set it up:
(100 grams / 8 cm) = (25 grams / x cm)
Now we can cross multiply and solve for x:
100x = 8 * 25
100x = 200
x = 200 / 100
x = 2 cm
Therefore, a 25-gram mass, when attached to the same spring, would cause the spring to stretch 2 cm. So the correct answer is to stretch the spring 2 cm.