The last page is always the most challenging. Help conceptually? Thanks! A proto

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The last page is always the most challenging. Help conceptually? Thanks!

A proton, coming from a long distance away, reaches a distance of 25.3 mu m from a stationary gold nucleus with charge +79e. Determine the initial velocity of the proton. There are two identical small metal spheres with charges 57.1 mu C and -95.8 mu C. The distance between them is 15.7. Cm. The spheres are placed in contact then set at their original distance. Calculate the magnitude of the force between the two spheres at the final position. Three charges are placed on a coordinate axis as shown in the figure. Q_1 is + 16.0 mu C and placed at the point (0.00 cm, 6.00cm) Q_2 is + 3.62 mu C and placed at the origin. Q_3 is 27.0 muC and placed at the point (9.00 cm, 0.00cm). Determine the magnitude of the force on Q_2.

Explanation / Answer

10)

) 928 m/s

let q is the charge of proton. so, q = 1.6*10^-19 C

charge of gold nucleus, Q = +79*1.6*10^-19

d = 25.3 micro m

Apply conservation of energy

K1 + U1 = K2 + U2

K1 + k*q*Q/d1 = k2 + k*q*Q/d2

k1 + 0 = 0 + k*q*Q/d2 (since d1 = infinite and k2 = 0)

k1 = 9*10^9*1.6*10^-19*79*1.6*10^-19/(25.3*10^-6)

= 7.19*10^-22 J

now Apply, k1 = 0.5*m*v1^2

==> v1 = sqrt(2*k1/m)

= sqrt(2*7.19*10^-22/(1.67*10^-27))

= 928 m/s

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