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.
in simple steps
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).
To determine the acceleration of the proton, we can use the following equation:
a = (F_net) / m
Where:
a = acceleration
F_net = net force acting on the object
m = mass of the object
In this case, the net force acting on the proton is due to the electric field, E. The force experienced by a charged particle in an electric field is given by:
F = q * E
Where:
F = force
q = charge of the particle
E = electric field
Since the proton has a positive charge, the force and the acceleration will also be in the positive x-direction.
The mass of a proton is approximately 1.67 x 10^-27 kg.
Now, let's calculate the force:
F = q * E
F = (1.6 x 10^-19 C) * (-6 x 10^5 N/C)
F = -9.6 x 10^-14 N
Since the net force is acting in the positive x-direction, we don't need to consider the negative sign. Therefore, the net force is 9.6 x 10^-14 N.
Now, we can determine the acceleration:
a = F_net / m
a = (9.6 x 10^-14 N) / (1.67 x 10^-27 kg)
a ≈ 5.75 x 10^12 m/s^2
Hence, the acceleration of the proton is approximately 5.75 x 10^12 m/s^2.
To determine the acceleration of the proton, we can use the equation of motion:
vf^2 = vi^2 + 2ad
Where:
- vf is the final velocity of the proton (which will be zero, as it comes to rest)
- vi is the initial velocity of the proton
- a is the acceleration of the proton
- d is the distance traveled by the proton
In this case, we are given that the initial velocity (vi) is zero, and the distance traveled (d) is 7.00 cm.
So the equation becomes:
0^2 = 0 + 2a(7.00 cm)
Simplifying it further:
0 = 14.00 a cm
To solve for acceleration (a), we need to convert the distance from centimeters (cm) to meters (m) since the SI unit of acceleration is m/s^2.
1 cm = 0.01 m
So, 7.00 cm = 0.07 m
Now we can rewrite the equation:
0 = 14.00 a (0.07 m)
Next, divide both sides of the equation by 14.00 (0.07 m):
0 / (14.00 x 0.07 m) = a
Simplifying it further:
0 = a
Therefore, the acceleration of the proton is 0 m/s^2.