Time left 0:04:11 Question 5 Incorrect Marked out of 1.00 Flag question Tips Question text Two point charges, q1 and q2 are separated by a distance d. For convenience, we will say that q1 is at the origin (0,0) on a coordinate system, q2 is at (d,0) and a reference point p is directly above q2 at a distance h at point (d,h). q1 has value 1μ C and q2 has value 8μ C. Take d= 1.1m and h= 0.7m. Note k=9×109Nm2/C2 q1 and q2 both have mass 0.1 kg. If they are released, what will be the final speed of q1 (when the charges collide or when they are far enough apart that they no longer interact)? Give your answer in m/s but do not include the units in your response. Include three significant digits in your answer.
Question
Time left 0:04:11 Question 5 Incorrect Marked out of 1.00 Flag question Tips Question text Two point charges, q1 and q2 are separated by a distance d. For convenience, we will say that q1 is at the origin (0,0) on a coordinate system, q2 is at (d,0) and a reference point p is directly above q2 at a distance h at point (d,h). q1 has value 1μ C and q2 has value 8μ C. Take d= 1.1m and h= 0.7m.
Note k=9×109Nm2/C2 q1 and q2 both have mass 0.1 kg. If they are released, what will be the final speed of q1 (when the charges collide or when they are far enough apart that they no longer interact)? Give your answer in m/s but do not include the units in your response. Include three significant digits in your answer.
Solution
To solve this problem, we need to use the principles of conservation of energy and conservation of momentum.
First, we calculate the initial potential energy of the system. The potential energy (U) between two charges is given by the formula U = kq1q2/d, where k is Coulomb's constant (9x10^9 Nm^2/C^2), q1 and q2 are the charges, and d is the distance between them.
Substituting the given values, we get U = 9x10^9 * 1x10^-6 * 8x10^-6 / 1.1 = 0.06545 Joules.
Since the charges are initially at rest, the initial kinetic energy of the system is 0. Therefore, the total initial energy of the system is just the potential energy, which is 0.06545 Joules.
When the charges are far apart, the potential energy between them is negligible. Therefore, the final energy of the system is just the kinetic energy of the charges.
By conservation of energy, the total initial energy equals the total final energy. Therefore, the final kinetic energy of the charges is also 0.06545 Joules.
The kinetic energy (K) of a moving object is given by the formula K = 1/2 * m * v^2, where m is the mass of the object and v is its speed.
Since both charges have the same mass (0.1 kg), we can set up the equation 0.06545 = 1/2 * 0.1 * v1^2 + 1/2 * 0.1 * v2^2, where v1 and v2 are the final speeds of q1 and q2, respectively.
By conservation of momentum, the total initial momentum equals the total final momentum. Since the charges are initially at rest, the total initial momentum is 0. Therefore, the final momentum of q1 is equal and opposite to the final momentum of q2. This gives us the equation 0.1 * v1 = -0.1 * v2, or v1 = -v2.
Substituting v1 = -v2 into the energy conservation equation, we get 0.06545 = 1/2 * 0.1 * v1^2 + 1/2 * 0.1 * (-v1)^2 = 0.1 * v1^2. Solving for v1, we get v1 = sqrt(0.06545 / 0.1) = 0.808 m/s.
Therefore, the final speed of q1 is 0.808 m/s.
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