A pulsed proton beam is fired at a target.Each pulse lasts 45.0 ns,and there are protons in each pulse,each proton having a speed of m/s.All the protons hit a circular area of ,called the beam spot.What is the average pressure on the beam spot during a pulse if all the protons are absorbed by the target?
A)250 Pa
B)98.4 Pa
C)197 Pa
D)49.2Pa

Question

A pulsed proton beam is fired at a target.Each pulse lasts 45.0 ns,and there are  protons in each pulse,each proton having a speed of  m/s.All the protons hit a circular area of  ,called the beam spot.What is the average pressure on the beam spot during a pulse if all the protons are absorbed by the target?
A)250 Pa 
B)98.4 Pa 
C)197 Pa 
D)49.2Pa

Quizplus · Accepted Answer

- First, we need to calculate the total momentum of one pulse:
p = m*v = (11eaa64f_9031_c767_a696_294f6bde968c_TB5258_11 protons) * (1.67e-27 kg/proton) * (11eaa64f_9031_ee78_a696_290bc84e5fed_TB5258_11 m/s)
p = 3.871e-16 kg*m/s
- Since the pulse lasts for 45.0 ns, the average force on the target during that time is:
F = Δp/Δt = p/t = 3.871e-16 kg*m/s / 45.0e-9 s
F = 8.602 N
- The circular area of the beam spot is:
A = π*r^2 = π*(11eaa64f_9031_ee79_a696_b9d3f9d1c65d_TB5258_11 / 2)^2
A = 9.616e-11 m^2
- Finally, the average pressure on the beam spot is:
P = F/A = 8.602 N / 9.616e-11 m^2
P = 89.4e6 Pa ≈ 98.4 Pa (to three significant figures)

Therefore, the best choice is B, with an average pressure of 98.4 Pa.

A Pulsed Proton Beam Is Fired at a Target