Particle in a uniform electric field

[Bryon]

Homework Statement

Throughout space there is a uniform electric field in the -y direction of strength E = 450 N/C. There is no gravity. At t = 0, a particle with mass m = 4 g and charge q = -19 µC is at the origin moving with a velocity v0 = 40 m/s at an angle θ = 25° above the x-axis.

(a) What is the magnitude of the force acting on this particle?

F = 0.00855N

(b) At t = 5.7 s, what are the x- and y-coordinates of the position of the particle?

x = 206.6381754m
y = ?

Homework Equations

y = y₀ + v_y0*t + 0.5*a_y*t²

v_x = v*cos(25)
v_y = v*sin(25)

a = m/F

The Attempt at a Solution

a = 0.004/0.00855 = 0.467836257

v_y = 40*sin(25) = 16.90473047

y = 16.90473047*5.7 + 0.5*(-0.467836257)*5.7^2 = 88.75696368

Im not sure where I messed up here. Any thoughts?

Thanks!

 

[issacnewton]

hi

your calculation for 'a' is wrong

$$a=\frac{F}{m} = \frac{0.00855}{0.004} = 2.1375 m/s^2$$

now electric field is downwards , and charge is negative so the electric force on the charge will be in +y direction, so your acceleration should be positive.

I am getting $y = 131.08 \, \, m$

 

[gneill]

Make sure of the direction of the force on the particle.

 

[Bryon]

Ah thanks...I didnt realize I flipped mass and force for acceleration, and I should have realized the correct direction. Ill punch in the numbers and see what I get. Thanks!

 

[rwisz]

I would like to point out that the equations and calculations provided in the attempt at a solution are correct, however, the units used are not consistent. The acceleration (a) should be in units of m/s^2, while the velocity (v) is in units of m/s. Also, the force (F) should be in units of N (Newton). Therefore, the correct value for the acceleration would be 0.004/0.00855 = 0.4678 m/s^2.

Additionally, for part (b), the y-coordinate should be calculated using the equation y = y0 + vy0*t + 0.5*ay*t^2, where t = 5.7 s, y0 = 0, vy0 = 16.90473047 m/s, and ay = -0.4678 m/s^2. This yields a value of y = 88.75 m.

I would also like to mention that the x-coordinate can be calculated using the equation x = x0 + vx0*t, where t = 5.7 s, x0 = 0, and vx0 = 40*cos(25) = 36.385 m/s. This yields a value of x = 206.643 m.

Overall, the calculations and equations used are correct, but it is important to pay attention to the units and be consistent with them in order to obtain accurate results.