A proton with mass 1.23*10 -27 kg is propelled atan initial speed of 3.95*10 5 m

Question

A proton with mass 1.23*10-27 kg is propelled atan initial speed of 3.95*105 m/s directly toward auranium nucleus 5.42 m away. The proton is repelled by the uraniumnucleus with a force of magnitude F = a/x2 where xis the separation between the two objects and a = 2.55*10-26 Nm2. Assume that the uraniumnucleus remains at rest. What is the speed of the proton when it is8.66 *10-10 m from the nucleus?

Give your answer in m/s in scientific notation to threesignificant digits (i.e. 1.15*10^2)

Note: The numbers given in this problem do not represent actualfigures, instead this is to be thought of as a theoreticalcalculation.

A proton with mass 1.23*10-27 kg is propelled atan initial speed of 3.95*105 m/s directly toward auranium nucleus 5.42 m away. The proton is repelled by the uraniumnucleus with a force of magnitude F = a/x2 where xis the separation between the two objects and a = 2.55*10-26 Nm2. Assume that the uraniumnucleus remains at rest. What is the speed of the proton when it is8.66 *10-10 m from the nucleus?

Give your answer in m/s in scientific notation to threesignificant digits (i.e. 1.15*10^2)

Note: The numbers given in this problem do not represent actualfigures, instead this is to be thought of as a theoreticalcalculation.

Explanation / Answer

it is moving directly toward the nucleus conservation of energy m*v2/2 =a/x +m*v'2/2 the work of the nucleus to proton with respect to x W(x)=- a/x2dx =a/x, at the infinity(W()=0) mass 1.23*10-27 kg v= 3.95*105 m/s x=8.66 *10-10 m => v'=3.29*105 m/s

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