what force must be exerted on an electron to move it from a state of rest to a speed of 3.5 x 10^7 m/s in a distance of 0.75 m?
Look up the mass of the electron and call it m. Then compute the required acceleration a, using
V = sqrt(2 a X)
(Solve that for a)
For the force required, use
F = m a
what force must be exerted on an electron to move it from a state of rest to a speed of 3.5 x 10^7 m/s in a distance of 0.75 m?
V^2=Vo^2+2ax
3.5x10^7=2a(0.75)
3.5x10^7=1.50a
divide by 1.50 on both sides to get "a" by itself
a = 2.3x10^7 m/s^2
next use Newton's 2nd law F=ma
F=(9.1x10^-31)(2.3x10^7) *9.1x10^-31 is the mass of the electron)
your answer is F = -1.3x10^3 Newtons
Done.
you need to Square 3.5x 10^7 so that its (3.5x 10^7)^2 / 1.50 = a
Step 1: Look up the mass of the electron and call it m.
The mass of an electron is approximately 9.10938356 × 10^-31 kilograms.
Step 2: Compute the required acceleration a, using the equation V = sqrt(2 a X).
Given:
V = 3.5 × 10^7 m/s (final speed)
X = 0.75 m (distance)
Rearrange the equation to solve for acceleration a:
V = sqrt(2 a X)
(3.5 × 10^7) = sqrt(2 a × 0.75)
Square both sides:
(3.5 × 10^7)^2 = 2 a × 0.75
Simplify:
a = [(3.5 × 10^7)^2] / [2 × 0.75]
Step 3: Calculate the required force, using the equation F = m a.
F = m a
F = (9.10938356 × 10^-31) × a
Substitute the value of a calculated in step 2 and then solve for F.
To calculate the force required to move an electron from rest to a speed of 3.5 x 10^7 m/s in a distance of 0.75 m, we need to follow these steps:
1. Look up the mass of an electron. The mass of an electron is approximately 9.10938356 x 10^-31 kg. Let's call this value "m."
2. Compute the required acceleration "a" using the equation:
V = sqrt(2 a X)
Rearranging the equation, we can solve for "a":
a = V^2 / (2 X)
Plug in the given values:
a = (3.5 x 10^7 m/s)^2 / (2 * 0.75 m)
3. Calculate the acceleration "a":
a = 1.225 x 10^15 m^2/s^2
4. Finally, calculate the force "F" using the equation:
F = m a
Plug in the mass of an electron and the calculated acceleration:
F = (9.10938356 x 10^-31 kg) * (1.225 x 10^15 m^2/s^2)
The resulting force required on the electron is:
F ≈ 1.113 x 10^-15 N (Newton)