At1=0, a proton is projected in the positive x-direction into a region of a uniform electric field of E=-6x1051. The proton travels 7.00 cm as it comes to rest. Determine The acceleration of the proton.

Question

in simple steps

Answer 1

To determine the acceleration of the proton, we can apply Newton's second law of motion, which states that the force acting on an object is equal to the product of its mass and acceleration (F = ma). In this case, the force is due to the electric field, given by the equation F = qE, where q is the charge of the proton and E is the electric field strength.

Step 1: Identify the given variables.
- Charge of the proton (q) = +1.6 x 10^-19 C (Coulombs)
- Electric field strength (E) = -6 x 10^5 N/C (Newtons per Coulomb)

Step 2: Calculate the force acting on the proton.
Since F = qE, we can substitute the given values:
F = (1.6 x 10^-19 C) * (-6 x 10^5 N/C)
F = -9.6 x 10^-14 N

Step 3: Apply Newton's second law of motion.
We know that F = ma, so we can rearrange the equation to solve for acceleration:
a = F/m

Step 4: Determine the mass of the proton.
The mass of a proton is approximately 1.67 x 10^-27 kg. Therefore,
m = 1.67 x 10^-27 kg

Step 5: Substitute the values into the equation for acceleration.
a = (-9.6 x 10^-14 N) / (1.67 x 10^-27 kg)
a ≈ -5.75 x 10^12 m/s^2

Step 6: The acceleration of the proton is approximately -5.75 x 10^12 m/s^2 in the positive x-direction. The negative sign indicates that the acceleration is opposite to the direction of the positive x-axis (opposite to the proton's initial velocity).