A slingshot consists of a light leather cup

attached between two rubber bands. It takes
a force of 25 N to stretch the bands 1.1 cm.

a) What is the equivalent spring constant
of the rubber bands?
Answer in units of N/m

b) How much force is required to pull the cup
of the slingshot 4.0 cm from its equilibrium
position?
Answer in units of N

a) k = 25 N/0.011 m = 2273 N/m

b) k*X= 2273 N/m * 0.040 m = 90.9 N

Xuseen

a) Well, you've got a slingshot and you're talking about spring constants? Are you sure you didn't mix up your toys? Anyway, let's calculate the spring constant of the rubber bands.

The formula for the spring constant (k) is given by k = F/x, where F is the force applied and x is the displacement. In this case, the force is 25 N and the displacement is 1.1 cm (or 0.011 m). Plugging these values into the formula gives us:

k = 25 N / 0.011 m ≈ 2272.73 N/m

So the equivalent spring constant of the rubber bands is approximately 2272.73 N/m.

b) Now, you want to know how much force is required to pull the cup of the slingshot 4.0 cm from its equilibrium position. Hold on tight, let's calculate that.

Using the same formula as before, F = k * x, where k is the spring constant and x is the displacement. In this case, the spring constant is 2272.73 N/m (as we calculated earlier) and the displacement is 4.0 cm (or 0.04 m). Plugging these values into the formula gives us:

F = 2272.73 N/m * 0.04 m ≈ 90.91 N

So, it would take approximately 90.91 N of force to pull the cup of the slingshot 4.0 cm from its equilibrium position. I hope you've been working out, because that's quite a pull!

To solve this problem, we can use Hooke's law, which states that the force required to stretch or compress a spring is directly proportional to the displacement.

a) To find the equivalent spring constant of the rubber bands, we can use the formula: F = k * x, where F is the force, k is the spring constant, and x is the displacement.

We are given that it takes a force of 25 N to stretch the bands 1.1 cm. Let's convert centimeters to meters: 1.1 cm = 0.011 m.

Using the formula, we can rearrange it to solve for k: k = F / x.

Therefore, k = 25 N / 0.011 m = 2273 N/m.

b) To determine the force required to pull the cup of the slingshot 4.0 cm from its equilibrium position, we can again use the formula F = k * x.

Given that x = 4.0 cm = 0.04 m, and k = 2273 N/m (from part a), we can now calculate the force required:

F = 2273 N/m * 0.04 m = 90.92 N.

The force required to pull the cup of the slingshot 4.0 cm from its equilibrium position is 90.92 N.

a) To find the equivalent spring constant of the rubber bands, we can use Hooke's Law, which states that the force required to stretch or compress a spring is directly proportional to the displacement from its equilibrium position.

Hooke's Law equation: F = k * x

Where:
- F is the force applied to the spring (in this case, 25 N)
- k is the spring constant (what we need to find)
- x is the displacement from the equilibrium position (1.1 cm)

To find k, we need to rearrange the equation as:
k = F / x

Substituting the given values:
k = 25 N / 0.011 m (1.1 cm is equivalent to 0.011 m)

k = 2273.0 N/m

So, the equivalent spring constant of the rubber bands is 2273.0 N/m.

b) To determine the force required to pull the cup of the slingshot 4.0 cm from its equilibrium position, we can use Hooke's Law again. We don't need to know the spring constant since we've already found it in part (a).

Using the same Hooke's Law equation: F = k * x

Where:
- F is the force applied to the spring (what we need to find)
- k is the spring constant (2273.0 N/m)
- x is the displacement from the equilibrium position (4.0 cm)

Substituting the given values:
F = 2273.0 N/m * 0.04 m (4.0 cm is equivalent to 0.04 m)

F = 90.92 N

So, the force required to pull the cup of the slingshot 4.0 cm from its equilibrium position is 90.92 N.