Please answer these questions with appropriate explanations. More points will be
ID: 1274556 • Letter: P
Question
Please answer these questions with appropriate explanations. More points will be awarded to answers that match to solutions and explain.
3. An electron, traveling at 1000 ms 1 along the x-axis (in the +x direction) collides with a stationary electron located at the origin. After the collision, one of the electrons is observed to be traveling in a direction at +60.0° to +x, the other at -30°. (The mass of the electron is 9.11 x 10 31 kg.) a. After the collision, what is the velocity of each electron? (500 ms 1 and 866 ms 1 respectively) b. Was the collision elastic? (yes) 4. An electric drill bit starts from rest and accelerates with a constant angular acceleration of 120 rad s a. How long does it take to reach its maximum angular velocity of 8,000 revolutions per minute? (7.0 s) b. How many revolutions of the dill bit occur during this time? (465 rev)Explanation / Answer
Q1 )
Let mass of electron be denoted by m
Before collision, momentum along x-direction = m*v = m*1000
Before collision, momentum along y-direction = 0
Let velocity of electron travelling at +60' after collision be v1 and that of ther be v2
After collision, momentum along x-direction = m*v1cos60' + m*v2cos30'
Since momentum in this direction remains conserved, so :
m*v1cos60' + m*v2cos30' = m*1000 ---(1)
After collision, momentum along y-direction = m*v1sin60' - m*v2sin30'
Since momentum in this direction also remains conserved, so :
m*v1sin60' - m*v2sin30' = 0 ---(2)
The -ve sign shows that y-components are opposite to each other
Solving (1) and (2), we get :
v1*cos60' + 31/2*v1*cos30' = 1000
Thus, v1 = 500 m/s
and v2 = 31/2 * v1 = 866.025 m/s
Kinetic energy before collision, K1 = 1/2*m*(1000)2
Kinetic energy after collision, K2 = 1/2*m*(5002 + 866.0252) = 1/2*m*999.992 = 1/2*m*10002
Thus, K1 = K2 , so collision was elastic
Q2)
Using equation, v = u + at
Here, we assume that v denotes final rotational velocity, u denotes initial rotational velocity, a denotes angular acceleration
Given : a = 120 rads-2 , v = 8000 rev/min = 8000*2*pi/60 = 837.75 rads-1
Putting values, we get :
t = v-u/a = 837.75-0/120 = 6.98 s
Using equation, S = ut + 1/2at2 , where S denotes the total radians covered
Putting values we get :
S = 0 + 1/2*120*6.982 = 2940 rad = 2923.22/(2*pi) = 465.24 rev
because 1 rev = 2*pi rad