4. +-14 points My Notes Ask Your Teacher An electron and a proton are each relea

Question

4. +-14 points My Notes Ask Your Teacher An electron and a proton are each released from rest in a uniform electric field that has a magnitude of 600 N/C. The energy and speed of each particle is measured after it has moved through a distance of 40.0 crn. Assume the particles do not influence one another but are influence onl, y the electri field. Without doing any calculations, determine which particle has more kinetic energy, has a higher speed, and takes more time to cover 25 cm (a) Comparing the particles after they have each traveled 40.0 cm, which of the following statements are true? Select all that apply. O The electron has more kinetic energy. O The proton has more kinetic energy O The two particles have the same kinetic energy. O The electron has a higher speed O The proton has a higher speed. O The two particles have the same speed O It takes the electron more time to cover the given distance. O It takes the proton more time to cover the given distance. O The two particles take the same time to cover the given distance. Now, we'll do the calculations for the proton. (b) What is the proton's kinetic energy after it has traveled 40.0 cm through the field? (c) What is the proton's speed after it has traveled 40.0 cm through the field? m/s (d) How much time does it take the proton to travel 40.0 cm through the field, after being released from rest?

Explanation / Answer

a)

E = electric field

d = distance travelled

q = magnitude of charge on each electron and proton

kinetic energy gained is the change in electrical potential energy which is given as

U = q E d  

since for both electron and proton , "q" , E and "d" are same , they gain equal kinetic energy

The two particles have same kinetic energy

kinetic energy is given as

KE = (0.5) m v2

Since kinetic energy gained is same for both electron and proton. hence the one with smaller mass , travels at greater speed. Since mass of electron< mass or proton , Electron has higher speed.

acceleration is given as

a = F/m

force due to electric field is same on both electron and proton. Since proton has greater mass . the acceleration of proton is smaller.

distance travelled is given as

d = (0.5) a t2 since they both started from rest

so t = sqrt(2d/a)

clearly , greater acceleration will result in smaller time . hence proton will take more time.

b)

KE = qE d = (1.6 x 10-19) (600) (0.40) = 3.84 x 10-17 J

c)

KE = (0.5) m v2

3.84 x 10-17 = (0.5) (1.67 x 10-27) v2

v = 2.1 x 105 m/s

d)

acceleration is given as

a = F/m = qE/m = (1.6 x 10-19) (600)/(1.67 x 10-27) = 5.75 x 1010 m/s2

X = displacement = 40 cm = 0.40 m

Vo = initial velocity = 0 m/s

t = time taken = ?

Using the equation

X = Vo t + (0.5) a t2

0.40 = 0 (t) + (0.5) (5.75 x 1010) t2

t = 3.7 x 10-6 sec

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