Question

PROBLEM (a) Find the speed of the proton at x 0.0500 m if s released from rest at x -2.00 cm in a constant electric field with magnitude 1.50 x 103 N/C, pointing in the positive direction. (b) Find the initial speed of an electron fired from x 2.00 cm given that its speed has fallen by half when it reaches x 0.120 m STRATEGY Apply conservation of energy, solving for the unknown speeds. Part (b) involves two equations: the conservation of energy equation and the condition vf vi for the unknown nitial and final speeds SOLUTION (a) Calculate the proton's speed at x 0.050 m with a potential energy of 1.68 x 10 17 J. Assume the potential energy at the point of release is zero.) Use conservation of energy, with an o JAKE APE PE initial speed of zero Solve for v and substitute the change APE in potential energy. APE 1.68 x 10 J) (1.67 x 10 27 kg) 1.42 x 105 m/s (b) Find the electron's initial speed (at x 2.00 cm) given that its speed has fallen by half at x 0.120 m, a change in potential energy of 3.36 x 10 17 J Apply conservation of energy once again, substituting expressions for the AKE APE initial and final kinetic energies APE meV Substitute the condition vf Vi and APE meVi subtract the change in potential energy from both sides Combine terms and solve for vi the APE m V initial speed, and substitute the change 8 (3.36 x 10 17 J) 8APE in potential energy. 3m 3 (9.11 x 10 kg 9.92 x 106 m/s LEARN MORE REMARKS Although the changes in potential energy associated with the proton and electron were similar in magnitude, the effect on their speeds differed dramatically. The change in potential energy had a far greater effect on the much lighter electron than the proton QUESTION If a proto d electron both ove throug the same dis electric field, is placement in an n an the change in potential energy associated with the proton equal in magnitude and opposite in sign to the change in potential energy associated with the electron? (Select all that apply. The signs of the two changes in potential energy are opposite. They are equal in magnitude The magnitude of the change is larger for the proton U The signs of the two changes in potential energy are the same The magnitude of the change is smaller for the proton

Answer 1

2 C-2.64x16 0.83 /0-2