Final answer:
To calculate the speed of an electron and proton in a 520 N/C electric field after 48 ns, we use the force from the field and apply Newton's second law to find acceleration and then speed. For an object to float in a 610 N/C electric field with a 24μC charge, we equate the electric force to the gravitational force and solve for the mass.
Step-by-step explanation:
To calculate the speed of an electron and a proton placed at rest in an electric field of 520 N/C after 48 ns, we can use the formula F = qE to calculate the force on each particle, where q is the charge and E is the electric field strength. Given that the charge of an electron is -1.60 x 10-19 C and that of a proton is +1.60 x 10-19 C, we find that the magnitude of the force is the same for both particles but in opposite directions. The acceleration a of each particle can be calculated using Newton's second law F = ma. Since an electron and a proton have different masses, their accelerations will differ. Acceleration can then be used to find the speed v using the equation v = at, where t is the time. For the second part, to calculate the mass of an object that "floats" in a uniform electric field of 610 N/C with a net charge of 24μC, we can use the balance between the electric force Fe = qE and the gravitational force Fg = mg, where m is the mass and g is the acceleration due to gravity. Solving for m, we find the mass that allows the electric and gravitational forces to balance, resulting in the object floating.