Two identical balls of 29.5 g are suspended from threads of length 1.1 m and carry equal charges as shown in the figure. Each ball is 1.5 cm from the centerline. a) Assume that the angle Θ is so small that its tangent can be replaced by its sine. This is called the small angle approximation and means that for small angles sin(Θ)=tan(Θ). Find the magnitude of charge on one of the balls. b) Now, assume the two balls are losing charge to the air very slowly. That means they'll be slowly approaching each other. If a ball is moving at an instantaneous speed of 2.50E−05 m/s, at what rate is the ball losing charge? Start by writing the speed of the ball and the rate of change of the charge as symbolic derivatives, and then relate those derivatives. Give your answer in Coulombs per second (C/s). Note that because the balls are losing charge so slowly, we can still use our results from the previous part, as the system is almost in equilibrium. Give your answer as a magnitude.
Two identical balls of 29.5 g are suspended from threads of length 1.1 m and carry equal charges as shown in the figure. Each ball is 1.5 cm from the centerline.
a)
Assume that the angle Θ is so small that its tangent can be replaced by its sine. This is called the small angle approximation and means that for small angles sin(Θ)=tan(Θ). Find the magnitude of charge on one of the balls.
b)
Now, assume the two balls are losing charge to the air very slowly. That means they'll be slowly approaching each other. If a ball is moving at an instantaneous speed of 2.50E−05 m/s, at what rate is the ball losing charge? Start by writing the speed of the ball and the rate of change of the charge as symbolic derivatives, and then relate those derivatives. Give your answer in Coulombs per second (C/s). Note that because the balls are losing charge so slowly, we can still use our results from the previous part, as the system is almost in equilibrium. Give your answer as a magnitude.
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