You're squeezing a springy rubber ball in your hand. If you push inward on it with a force of 1 N, it dents inward 2 mm. How far must you dent it before it pushes outward with a force of 3 N?
27
To determine how far you must dent the springy rubber ball before it pushes outward with a force of 3 N, you need to consider Hooke's Law. Hooke's Law states that the force exerted by a spring is directly proportional to the distance it is stretched or compressed.
In this case, let's assume that the spring follows Hooke's Law and is a linear spring (meaning it obeys Hooke's Law within its elastic limit).
From the given information:
- When you push inward with a force of 1 N, the ball dents inward by 2 mm.
- We want to find the distance the ball will dent when you push inward with a force of 3 N.
Using Hooke's Law, we can set up a proportion:
Force1 / Distance1 = Force2 / Distance2
Substituting the values:
1 N / 2 mm = 3 N / x
To solve for x, the distance the ball will dent when you push inward with a force of 3 N:
1 N / 2 mm = 3 N / x
Cross-multiplying, we get:
1 N * x = 3 N * 2 mm
Simplifying:
x = (3 N * 2 mm) / 1 N
x = 6 mm
Therefore, you must dent the springy rubber ball by 6 mm before it pushes outward with a force of 3 N.
To find out how far you must dent the rubber ball before it pushes outward with a force of 3 N, we can use Hooke's Law. Hooke's Law states that the force exerted by a spring or elastic material is directly proportional to the displacement from its equilibrium position.
First, we need to determine the spring constant (k) of the rubber ball. The spring constant represents the stiffness of the springy material and is specific to each material. It can be calculated using the formula:
k = F / x
where
k is the spring constant,
F is the force applied,
and x is the displacement.
In this case, when you pushed on the ball with a force of 1 N, it dented inward by 2 mm, which is equivalent to 0.002 m. Therefore, the spring constant can be calculated as:
k = 1 N / 0.002 m = 500 N/m
Now that we have the spring constant, we can use it to find the displacement needed for a force of 3 N. Rearranging Hooke's Law formula, we get:
x = F / k
Substituting the values, we have:
x = 3 N / 500 N/m = 0.006 m
Therefore, you would need to dent the rubber ball inward by 0.006 meters, or 6 mm, for it to push outward with a force of 3 N.