Question

Suppose that a stray neutron with an initial speed of 1.4 x 107 m/s is just barely captured by a nucleus with diameter d = 1.0 X 10-14 m. Assuming the strong force on the neutron isconstant, find the magnitude ofthat force. The neutron's mass is 1.67 X 10-27 kg.

Answer 1

Answer:

$F=16.366N$

Explanation:

Given data

Initial velocity of neutron v₀=1.4×10⁷m/s

Diameter of nucleus d=1×10⁻¹⁴m

Mass of neutron m=1.67×10⁻²⁷kg

The acceleration of neutron is given from equation :

$v^{2}=v_{o}^{2}+2ad\\ where\\v=0\\So\\a=\frac{v^{2}-v_{o}^{2} }{2d}\\ a=\frac{-v_{o}^{2}}{2d}\\ a=\frac{-(1.4*10^{7}m/s )^{2}}{2(1.0*10^{-14} m)}\\a=-9.81*10^{27}m/s^{2}$

So its magnitude is a=9.81×10²⁷m/s²

To find magnitude of force we use Newtons second law of motion

So

$F=ma\\F=(1.67*10^{-27} kg)(9.81*10^{27}m/s^{2} )\\F=16.366N$