A particle (q-4.0 mC.m-50 g) has a velocity of 25 m/s in the positive x direction when it first enters a region where the electric field is uniform (60 N/C in the positive y direction). What is the speed of the particle 5.0 s after it enters this region?
is simple steps
To find the speed of the particle 5.0 s after it enters the region with the electric field, we can use the following steps:
1. First, calculate the force experienced by the particle due to the electric field.
Force (F) = charge (q) * electric field (E)
Given q = -4.0 mC and E = 60 N/C
F = (-4.0 x 10^-3 C) * (60 N/C)
F = -240 x 10^-3 N
2. Next, calculate the acceleration experienced by the particle using Newton's second law.
Force (F) = mass (m) * acceleration (a)
Given m = 50 g = 0.05 kg
a = F / m
a = (-240 x 10^-3 N) / (0.05 kg)
a = -4800 m/s^2
3. Now, we can find the final velocity of the particle after 5.0 s using the formula for uniformly accelerated motion.
v = u + at
Given u = 25 m/s (initial velocity), a = -4800 m/s^2 (acceleration), and t = 5.0 s
v = 25 m/s + (-4800 m/s^2) * (5.0 s)
v = 25 m/s - 24000 m/s
v = -23975 m/s
4. Finally, find the speed of the particle, which is the magnitude of the velocity (since speed is a scalar quantity).
speed = |v|
speed = |-23975 m/s|
speed = 23975 m/s
Therefore, the speed of the particle 5.0 s after entering the region with the electric field is 23975 m/s.
To find the speed of the particle 5.0 s after it enters the region, you can follow these steps:
Step 1: Determine the magnitude and direction of the electric force acting on the particle.
To find the electric force, you can use the equation:
F = q * E
where F is the electric force, q is the charge of the particle, and E is the electric field.
Given that the charge of the particle is q = -4.0 mC and the electric field is E = 60 N/C in the positive y direction, you can substitute these values into the equation:
F = (-4.0 mC) * (60 N/C) = -240 mN in the negative z direction.
Step 2: Use the electric force to find the acceleration of the particle.
The electric force is related to the mass (m) and acceleration (a) of the particle by the equation:
F = m * a
Rearranging the equation to solve for acceleration:
a = F / m
Since the given mass is m = -50 g, you need to convert it to kilograms:
m = -50 g = -0.050 kg
Substituting the values into the equation:
a = (-240 mN) / (-0.050 kg) = 4,800 m/s² in the negative z direction.
Step 3: Calculate the change in velocity using the acceleration and time.
The change in velocity (Δv) can be found using the equation:
Δv = a * t
Substituting the values into the equation:
Δv = (4,800 m/s²) * (5.0 s) = 24,000 m/s in the negative z direction.
Step 4: Determine the final velocity of the particle.
The final velocity is the initial velocity (v₀) plus the change in velocity (Δv):
v = v₀ + Δv
Given that the initial velocity is v₀ = 25 m/s in the positive x direction, you can substitute the values:
v = 25 m/s (positive x) - 24,000 m/s (negative z) = -23,975 m/s
Step 5: Calculate the speed of the particle.
The speed is the magnitude of the velocity vector, so take the absolute value of the final velocity to get the speed:
Speed = |-23,975 m/s| = 23,975 m/s
Therefore, the speed of the particle 5.0 s after it enters the region is 23,975 m/s.
To find the speed of the particle 5.0 seconds after it enters the region with the electric field, we can use the equations of motion and the equation for the force experienced by a charged particle in an electric field.
Here are the simple steps to find the speed of the particle:
Step 1: Calculate the force experienced by the charged particle due to the electric field.
- The electric force (F) can be calculated using the equation F = q * E, where q is the charge of the particle (given as -4.0 mC) and E is the electric field strength (given as 60 N/C).
- Substitute the values into the equation to find the force.
Step 2: Calculate the acceleration of the particle.
- The force experienced by the particle is in the y direction, so we need to find the acceleration in the y direction (ay).
- We know that force (F) = mass (m) * acceleration (a), so rearrange the equation to find acceleration: a = F / m.
- Substitute the values of the force (from Step 1) and the mass of the particle (given as 50 g) into the equation to find the acceleration.
Step 3: Calculate the change in velocity of the particle in the y direction.
- Since the acceleration is constant, we can use the equation for uniformly accelerated motion in y-direction with initial velocity (uy), final velocity (v), and time (t): Δv = a * t.
- Substitute the value of the acceleration (from Step 2) and the time (given as 5.0 s) into the equation to find the change in velocity in the y direction.
Step 4: Calculate the y-component of the final velocity of the particle.
- Since the particle's initial velocity is in the positive x direction and there is no acceleration in the x direction, the final velocity in the x direction will be the same as the initial velocity.
- Therefore, the y-component of the final velocity (v_y) is simply the change in velocity in the y direction (from Step 3).
Step 5: Calculate the magnitude of the final velocity.
- To find the speed (magnitude of velocity) of the particle, we can use the Pythagorean theorem.
- The magnitude of the final velocity (v) can be found using the equation: v = √(v_x^2 + v_y^2).
- Substitute the value of the initial velocity (given as 25 m/s in the positive x direction) and the y-component of the final velocity (from Step 4) into the equation to calculate the magnitude of the final velocity.
Step 6: Round the final answer to the appropriate number of significant figures or decimal places, if required.
Following these steps will allow you to find the speed of the particle 5.0 seconds after it enters the region with the electric field.