CALC Proton Bombardment.? A proton with mass 1.67 X 10-27 kg is propelled at an initial speed of 3.00 X 105 m/s directly toward a uranium nucleus 5.00 m away. The proton is repelled by the uranium nucleus with a force of magnitude F = ?/x2, where x is the separation between the two objects and ? = 2.12 X 10-26 N.m2. Assume that the uranium nucleus remains at rest. (a) What is the speed of the proton when it is 8.00 X 10-10 m from the uranium nucleus? (b) As the proton approaches the uranium nucleus, the repulsive force slows down the proton until it comes momentarily to rest, after which the pro-ton moves away from the uranium nucleus. How close to the uranium nucleus does the proton get? (c) What is the speed of the proton when it is again 5.00 m away from the uranium nucleus?

Solution 76 P Step 1: Mass of proton m = 1.67 × 10 27kg Initial speed v = 3.00 × 10 m/s i Distance x = 5m 2 Repelling force F = /x 26 = 2.12 × 10 Nm 2 We need to find the speed of the proton when it is distance x = 8.00 × 10 10m 2 v 2= v + 2ax f i Step 2 : Let us find repelling force It is given as F = /x 2 Substituting values we get F = 2.12 × 10 26 Nm /5 2 28 F = 8.48 × 10 N 28 Thus we have force as 8.48 × 10 N