An electron of mass 9.11 10-31 kg has an initial speed of 2.60 105 m/s. It travels in a straight line, and its speed increases to 6.00 105 m/s in a distance of 4.40 cm. Assume its acceleration is constant.
(a) Determine the magnitude of the force exerted on the electron.
...N
(b) Compare this force (F) with the weight of the electron (Fg), which we ignored.
F/Fg =
force = change in momentum / time
average speed = s = 10^5(6+2.6)/2
so
time = t = .044/s
F = 9.11*10^-31 (6-2.6)10^5 / t
compare to m g
how to get time
To find the magnitude of the force exerted on the electron, we can use Newton's second law of motion:
F = ma
where F is the force, m is the mass, and a is the acceleration.
We can find the acceleration by using the following equation:
a = (vf - vi) / d
where a is the acceleration, vf is the final velocity, vi is the initial velocity, and d is the distance.
From the given information,
initial velocity (vi) = 2.60 × 10^5 m/s
final velocity (vf) = 6.00 × 10^5 m/s
distance (d) = 4.40 cm = 4.40 × 10^-2 m
First, let's find the acceleration:
a = (6.00 × 10^5 - 2.60 × 10^5) / (4.40 × 10^-2)
= 3.40 × 10^5 / (4.40 × 10^-2)
= 3.40 × 10^7 m/s^2
Next, we can calculate the force:
F = (9.11 × 10^-31 kg) × (3.40 × 10^7 m/s^2)
= 3.09 × 10^-23 N
Therefore, the magnitude of the force exerted on the electron is 3.09 × 10^-23 N.
Now, let's compare this force (F) with the weight of the electron (Fg).
The weight of an object can be calculated by multiplying its mass (m) with the acceleration due to gravity (g). The weight formula can be written as:
Fg = mg
where Fg is the weight, m is the mass, and g is the acceleration due to gravity near Earth's surface (approximately 9.8 m/s^2).
Given the mass of the electron (m) = 9.11 × 10^-31 kg, we can calculate the weight:
Fg = (9.11 × 10^-31 kg) × (9.8 m/s^2)
= 8.94 × 10^-30 N
Finally, we can compare the force (F) and the weight (Fg):
F/Fg = (3.09 × 10^-23 N) / (8.94 × 10^-30 N)
Using scientific notation, this can be written as:
F/Fg = 3.46 × 10^6
Therefore, the force (F) is approximately 3.46 million times larger than the weight of the electron (Fg).