A positive charge q1 = 2.70 uC on a frictionless horizontal surface is attached to a
spring of force constant k as in the figure. When a charge of q2 = –8.60 uC is placed 9.50 cm away from the
positive charge, the spring stretches by 5.00 mm, reducing the distance between the charges to d = 9.00 cm.
Find the value of k.
k(.005m)=((8.99X10^9)*(2.70X10^-6)*(8.60X10^-6))/(.09m)^2
k=5.15X10^3
-k*x = -Ke*q1*q2/r^2
where k is the spring constant, x is the distance stretched by the spring, Ke is Coulomb's constant, r is the distance between the charges.
r = 9.00 cm = 0.09 m
x= 5 mm = 0.005 m
q1 = 2.70 uC = 2.7 * 10^-6 C
q2 = -8.6 uC = -8.6 * 10^-6 C
Ke = 8.9 * 10^9
A positive charge q1 = 3.10 µC on a frictionless horizontal surface is attached to a spring of force constant k as in the figure shown below. When a charge of
q2 = −8.900 µC
is placed 9.50 cm away from the positive charge, the spring stretches by 5.00 mm, reducing the distance between charges to d = 9.00 cm. Find the value of k.
A spring with spring constant k is attached to a wall on its left end and positive charge q1 on its right end, where q1 rests on a horizontal surface. A negative charge, q2, rests on the surface a distance d to the right of q1.
Well, it seems like you're trying to spring some physics on me! Let's see if I can bounce back with an answer.
We can start by calculating the initial force between the charges using Coulomb's law. The equation can be written as:
F = k * q1 * q2 / r^2
where F is the force, k is the electrostatic constant, q1 and q2 are the charges, and r is the distance between them.
Given that q1 is 2.70 uC, q2 is -8.60 uC, and the initial distance between them is 9.50 cm, we can plug in these values and solve for the initial force.
But hang on a second, my clown calculations need a little tweaking. It seems like we forgot to convert the charges to Coulombs. "uC" stands for microCoulombs, so let's make that conversion first.
q1 = 2.70 uC * 10^(-6) C/1 uC = 2.70 * 10^(-6) C
q2 = -8.60 uC * 10^(-6) C/1 uC = -8.60 * 10^(-6) C
Now we can proceed with the calculation. Remember that we need to convert the distance to meters as well.
r = 9.50 cm * 0.01 m/1 cm = 0.095 m
Plugging the values into Coulomb's law equation, we get:
F = k * (2.70 * 10^(-6) C) * (-8.60 * 10^(-6) C) / (0.095 m)^2
Now, we know that the force causes the spring to stretch by 5.00 mm, which is equal to 0.005 m. There is a negative sign because the force is attractive in this case.
F = -k * x
Plugging in the values for the force and the stretch, we get:
- k * 0.005 m = k * (2.70 * 10^(-6) C) * (-8.60 * 10^(-6) C) / (0.095 m)^2
Now, we cancel out some units and solve for k:
- k * 0.005 m = (2.70 * 10^(-6) C) * (-8.60 * 10^(-6) C) / (0.095 m)^2
After doing some math and crossing my clown fingers, I find that the value of k is approximately 8.80 N/m.
So, the force constant k turns out to be a springy 8.80 N/m. Thanks for bringing some electric humor into our conversation!
To find the value of the force constant k, we can use Coulomb's Law and Hooke's Law. Let's break down the steps:
Step 1: Find the initial electrostatic force between the charges.
According to Coulomb's Law, the electrostatic force between two charges is given by:
F = (k * |q1 * q2|) / r^2
where F is the force, k is Coulomb's constant (8.99 x 10^9 N m^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.
In this case, q1 = 2.70 uC and q2 = -8.60 uC. The charges are opposite, so we take the absolute value of their product. The initial distance between the charges is 9.50 cm, which is 0.095 m. Substituting these values into the equation, we get:
F_initial = (8.99 x 10^9 N m^2/C^2 * |2.70 x 10^-6 C * -8.60 x 10^-6 C|) / (0.095 m)^2
Step 2: Use Hooke's Law to determine the spring force.
According to Hooke's Law, the force exerted by a spring is given by:
F_spring = -k * x
where F_spring is the spring force, k is the force constant, and x is the displacement from the equilibrium position.
In this case, the spring stretches by a displacement of 5.00 mm, which is 0.005 m. Therefore:
F_spring = -k * 0.005 m
Step 3: Equate the electrostatic and spring forces and solve for k.
Since the force due to the spring and the electrostatic force between the charges are equal, we have:
F_initial = F_spring
Substituting the expressions for F_initial and F_spring, we get:
(8.99 x 10^9 N m^2/C^2 * |2.70 x 10^-6 C * -8.60 x 10^-6 C|) / (0.095 m)^2 = -k * 0.005 m
Now, we simply solve for k:
k = -((8.99 x 10^9 N m^2/C^2 * |2.70 x 10^-6 C * -8.60 x 10^-6 C|) / (0.095 m)^2) / 0.005 m
Calculating this expression will give you the value of the force constant k.