A massless spring is attached to a support at one end and has a 2...

Question

A massless spring is attached to a support at one end and has a 2.0 μC charge glued to the other end. A −4.0 μC charge is slowly brought near. The spring has stretched 1.2 cm when the charges are 2.6 cm apart. What is the spring constant of the spring?

Accepted Answer

Hello, fellow physicists today, we're gonna solve the following practice problem together. So first off, let's read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A massless elastic band is fixed at one end and a 20 nano Coolum charged object is fastened to the other end. A negative 40 nano Coolum charged object is carefully moved closer. When the charged objects are 1.8 centimeters apart, the elastic band stretches by 0. centimeters from its original length, calculate the spring constant for the stretched elastic band. So that's our end goal is to calculate the spring constant for the stretched elastic band. OK. So we're given some multiple choice answers and they're all in the same units of newtons per meter. So let's read them off to see what our final answer might be. A is 3.48 B is 6.55 C is 2.47 and D is 4.98. OK. So to help us better visualize this problem, let us look at the following diagram on the right. So the diagram on the left shows are two particles, but the diagram on the right shows the path and it just shows, basically helps us break us down. It shows us what our delta X which will explain more in depth with that is and what our our value is, which is the distance between the two particles. So this is just like a more simpler version of the diagram that's given to us by the problem itself. OK. So our end goal like we mentioned above is to find the spring constant K for the stretched elastic band. So we need to recall and use the equations for Kim's law and the spring constant to help us find the net force. So the net force is equal to. So F net, the net force is equal to negative K where K is the spring constant multiplied by delta X and delta X is shown here in the diagram. It's the distance between this dotted line and Q one, the particle, the charge of particle one. OK plus Coolum is constant multiplied by the charge of the first object multiplied by the charge of the second object. And note that charge one and charge two are absolute values of. So anything that we take an absolute value of will give us a positive value all divided by R squared where R is the distance between the charged objects. So now we need to rearrange the net force equation to solve for K using a little bit of algebra. And we get that the spring constant is equal to one divided by delta X multiplied by Kums constant multiplied by the absolute value of charge one multiplied by the absolute value of charge two, all divided by R squared. So now we could plug in all of our known variables to solve for K. So let's do that our spring constant. So we're trying to solve for our spring constant, Haza. So delta X, our numerical value for delta X is 0.9 centimeters because that describes the elastic band stretch from its original length. So it's gonna be one divided by 0.9 centimeters, but we need to convert centimeters to meters. So all we do is take 0.9 multiply it by 10 to the power of negative two to convert it to meters multiplied by Kums constant, which the numerical value for that is 9.0 multiplied by 10 to the power of nine. And it's in U in units of newtons multiplied by meters squared per Coolum square multiplied by the charge of object one which was 20 nano columns, which we need to convert nano columns to columns. So all we have to do is just multiply it by 10 to the power of negative nine and it multiplied by the charge of the second object which was negative 40 nano cos so I remember the absolute value signs will make it positive and we need to convert that to Coolum. So like before, we just need to multiply it by 10 to the power of negative nine. OK. All divided by R squared, which our, our value was 1.8 centimeters, but we need to convert centimeters to meters. So all we have to do is just multiply it by 10 to the power of negative 2 m and don't forget to square it. So when we plug that into a calculator, we should get that. Our spring constant is 2.47 newtons per meter. So the spring constant for the stretched elastic band is approximately 2.47 newtons per meter. So looking at our multiple choice answers, the correct answer has to be the letter C 2. newtons per meter. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

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A massless spring is attached to a support at one end and has a 2.0 μC charge glued to the other end. A −4.0 μC charge is slowly brought near. The spring has stretched 1.2 cm when the charges are 2.6 cm apart. What is the spring constant of the spring?

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