A 2.0 g plastic bead charged to −4.0 nC and a 4.0 g glass bead ch...

Question

A 2.0 g plastic bead charged to −4.0 nC and a 4.0 g glass bead charged to +8.0 nC are 2.0 cm apart and free to move. What are the accelerations of (a) the plastic bead and

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 1.5 g charged silicone block with a charge of negative 2.5 nano columns and a 0.5 g charged acrylic block with a charge of positive 4.2 nano columns are initially set 3.0 centimeters apart and permitted to move unimpeded, compute the acceleration experienced by the silicone block. So that is our end goal is to determine the acceleration experienced by the silicone block. OK. So we're given some multiple choice answers and they're all in the same units of meters per second squared. So let's read them off to see what our final answer might be. A is 0.08 B is 0.07 C is 0.03 and D is 0.04. OK. So in order to find the acceleration experienced by the silicon block, we need to recall and use Kums Law to find the force between the two charged blocks and we also need to recall and use Newton's second law to find the acceleration of the silicon block. So to begin, let us start by using Coolum Law first to determine the force between the blocks. So that's so Kums Law states that the force is equal to Kums constant multiplied by the absolute value of charge, one multiplied by the absolute value of charge two divided by R squared where R is the distance between the blocks. So now we can plug in our known variables the sol for the force. So let's do that. We know that Kums constant, the numerical value for that is 9.0 multiplied by 10 to the power of nine. It's in new, in units of newtons multiplied by meters squared per Coolum square multiplied by the first charge. So the charge on the silicone block was negative 2.5 nano columns. But since it's the absolute value, any absolute value of a negative number will give us a positive number. We should get 2.5 nano columns, but we need to convert nano columns to Coolum. So all we have to do is just multiply 2.5 by 10 to the power of negative nine and it's gonna be positive. Now, a set of negative, these are the absolute value signs and we need to multiply it by the charge of the acrylic block which was 4.2 multiplied by to the power of negative nine columns means we also need to convert the nano columns to columns. OK? And the distance between the blocks was 3.0 centimeters, but we need to convert centimeters to meters. So all we have to do is take 3.0 and then multiply it by 10 to the power of negative two and square it. So when you plug it into a calculator, we should get that the force is equal to 1.05 multiplied by 10 to the power of negative four newtons. So now we can recall and use Newton's second law to find the acceleration of the silicone block. So let's say that the acceleration of the silicone block, let's denote it as a subscript lowercase S is equal to the force divided by the mass of the silicone block. So let's plug in our known variables to solve for the acceleration. So the acceleration is equal to the force value which we just found, which was 1.05 multiplied by 10 to the power of negative four newtons divided by the mass of the silicone block, which was given to us as 1.5 kg. Actually, I should say 1.5 g, but we need to convert it to kilograms. So 1.5 multiplied by 10 to the power of negative kg. So all we have to do is to convert grams of kilograms when we take our gram value, which was 1.5 and multiply it by 10 to the power of negative three. So when we plug into a calculator, we should find that our acceleration of the silicone block is 0.07 m per second squared, which is our final answer. So the acceleration experienced by the silicone block is 0.07 m per second squared. So let's make a quick note here in case you're curious like how in the world do we get the units in meters per second squared? Let's note that and one Newton is equal to one kilogram multiplied by meter divided by seconds squared. So that's how our units turn out the way that they do. Ok. So going back to look at our multiple choice answers, the correct answer has to be the letter B 0.07 m per second squared. Thank you so much for watching. Hopefully that helps and I can't wait to see you in the next video. Bye.

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A 2.0 g plastic bead charged to −4.0 nC and a 4.0 g glass bead charged to +8.0 nC are 2.0 cm apart and free to move. What are the accelerations of (a) the plastic bead and

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