A net force of 1.6×10−15 N acts on an electron over a displacement of 7.1 cm, in the same direction as the net force. (a) What is the change in kinetic energy of the electron (joules)?
ΔKE=Work=Fs=
=1.6x10^-15 x 0.071=
=1.136x10^-16 J
To find the change in kinetic energy of the electron, we can use the work-energy theorem. According to this theorem, the work done on an object is equal to the change in its kinetic energy.
The formula for work is given by:
Work = Force × Displacement × cosθ
Where:
- Force is the magnitude of the net force acting on the object.
- Displacement is the magnitude of the displacement of the object.
- θ is the angle between the net force and the displacement vector. In this case, since the net force and the displacement are in the same direction, cosθ = 1.
Let's use this formula to calculate the work done on the electron:
Work = (1.6×10^(-15) N) × (7.1 cm) × (1)
First, we should convert the displacement from centimeters to meters:
Displacement = 7.1 cm = 7.1 × 10^(-2) m
Now, let's substitute the values into the equation:
Work = (1.6 × 10^(-15) N) × (7.1 × 10^(-2) m) × (1)
To simplify the calculation, we can express the net force and displacement in scientific notation:
Work = (1.6 × 7.1 × 10^(-15) × 10^(-2)) N·m
= 1.136 × 10^(-16) N·m
Since work is equal to the change in kinetic energy, we can conclude that the change in kinetic energy of the electron is 1.136 × 10^(-16) Joules.