Help Solve Physics Problem Now: String Unwound from Wheel

[joecocobo]

Need Help Now

A string wound on the rim of a wheel 20 cm in diameter is pulled out at a rate of 75 cm/s. Through how many revolutions will the wheel have turned by the time that 9.0m of string has been unwound? Also how long did it take?

I really need help with this. If you post, please show all work so I can learn how to do this type of problem.

 

[gneill]

joecocobo, welcome to PF.

You'll have to follow the posting template and show your attempt at working on the problem before help/hints/guidance can be offered.

 

[joecocobo]

Homework Statement

A string wound on the rim of a wheel 20 cm in diameter is pulled out at a rate of 75 cm/s. Through how many revolutions will the wheel have turned by the time that 9.0m of string has been unwound? Also how long did it take?

Homework Equations

I don't know any equations to use

The Attempt at a Solution

I honestly don't know where to start, to even make an attempt

 

[DaveC426913]

You may be overthinking it. For starters, separate the question into its two components. They are not related.1] A 9.0m string is wound on the rim of a wheel 20 cm in diameter. How many times is the string wrapped around the wheel?
Do you know the relationship between the diameter of a circle and its circumference?

2] How long will a point on the string take, moving at 75cm/s, to travel 9.0m?
Do you know how to calculate time, given a distance and a velocity?

 

[rwisz]

I am happy to assist you with this physics problem. Let's break it down step by step.

First, we need to identify the given information and what we are looking for. The given information is the diameter of the wheel (20 cm), the speed at which the string is being pulled out (75 cm/s), and the amount of string that has been unwound (9.0 m). We are looking for the number of revolutions the wheel will have turned and the time it takes for this to happen.

Next, we need to use the formula for the circumference of a circle, which is C = 2πr, where C is the circumference, π is the mathematical constant pi, and r is the radius of the circle. In this case, the radius of the wheel is half of its diameter, so r = 10 cm.

To find the number of revolutions, we can use the formula N = d/C, where N is the number of revolutions, d is the distance traveled, and C is the circumference. In this problem, d = 9.0 m and C = 2πr = 2π(10 cm) = 20π cm.

Substituting these values into the formula, we get N = (9.0 m)/(20π cm) = 0.1436 revolutions.

To find the time it takes for this to happen, we can use the formula t = d/v, where t is the time, d is the distance traveled, and v is the speed. In this problem, d = 9.0 m and v = 75 cm/s.

Substituting these values into the formula, we get t = (9.0 m)/(75 cm/s) = 0.12 seconds.

Therefore, the wheel will have turned approximately 0.1436 revolutions and it will take 0.12 seconds for this to happen.

I hope this explanation helps you understand how to approach and solve this type of physics problem. If you have any further questions, please feel free to ask. Good luck!