I need help with part b... I found in part a that delta L is .29568m and I think I might be doing something wrong with the units because I can't get the right answer.

A 156 g hockey puck is attached to a rubber band and rotated with an angular speed of 12.8 rad/s on frictionless horizontal ice. It takes a force of 1.12 N to stretch the rubber band by 1 cm.

(a) If the original length L of the rubber band is 1 m, by how much (in m) will it be stretched by the rotation?

Delta L = .29568m

(b) How much energy do you need to start the stone from rest and rotate as in part (a) with an angular speed of 12.8 rad/s? Neglect the mass of the rubber band.

Etotal = J

HELP: Add up the kinetic energy and the elastic potential energy.

HELP: Ekin = 1/2*m*v2, with v = length*omega.

Remember again to use the stretched length:

Eelast = 1/2*k*(Delta L)2

To solve part (b), we need to calculate the total energy required to start the stone from rest and rotate it with an angular speed of 12.8 rad/s.

We can use the formulas given in the question to calculate the kinetic energy (Ekin) and the elastic potential energy (Eelast).

1. Kinetic energy (Ekin):
The formula for kinetic energy is Ekin = 1/2 * m * v^2, where m is the mass and v is the velocity.

Here, the mass of the hockey puck is given as 156 g, which can be converted to kilograms by dividing by 1000 (1 g = 0.001 kg). So, the mass (m) is 0.156 kg.

The velocity (v) can be calculated using the formula v = length * omega, where length is the stretched length of the rubber band and omega is the angular speed.

From part (a), we found that the stretched length (Delta L) is 0.29568 m, so the length is 1.29568 m (1 m original length + 0.29568 m stretched length).

Now, calculate the velocity: v = 1.29568 m * 12.8 rad/s = 16.589824 m/s.

Next, plug these values into the kinetic energy formula: Ekin = 1/2 * 0.156 kg * (16.589824 m/s)^2.

Calculate Ekin to get the value of kinetic energy.

2. Elastic potential energy (Eelast):
The formula for elastic potential energy is Eelast = 1/2 * k * (Delta L)^2, where k is the spring constant and Delta L is the change in length of the rubber band.

The force required to stretch the rubber band by 1 cm is given as 1.12 N.

We can use Hooke's Law, F = k * Delta L, to find the spring constant (k).
Rearrange the formula to solve for k: k = F / Delta L.

Convert 1 cm to meters: Delta L = 0.01 m.

Now, calculate the spring constant: k = 1.12 N / 0.01 m.

Finally, calculate the elastic potential energy using the formula: Eelast = 1/2 * (k) * (Delta L)^2.

Calculate Eelast to get the value of elastic potential energy.

3. Total energy (Etotal):
To find the total energy required, we need to add up the kinetic energy and elastic potential energy.

Etotal = Ekin + Eelast.

Add the calculated values of Ekin and Eelast to find the total energy (Etotal).

The final answer should be in joules (J), which is the unit for energy.