A charged box (m=445 g, ????=+2.50 μC) is placed on a frictionless incline plane. Another charged box (????=+75.0 μC) is fixed in place at the bottom of the incline. If the inclined plane makes an angle theta of 35.0∘ with the horizontal, what is the magnitude of the acceleration of the box when it is 59.0 cm from the bottom of the incline?

Respuesta :

The concept required to perform this exercise is given by the coulomb law.

The force expressed according to this law is given by

[tex]F= \frac{kqQ}{r^2}[/tex]

Where,

[tex]k = 8.99 * 10^9 N m^2 / C^2.[/tex]

q = charges of the objects

r= distance/radius

Our values are previously given, so

[tex]q= 2.5*10^{-6}C\\Q= 75*10^{-6}C\\r=0.59[/tex]

Replacing,

[tex]F=\frac{kqQ}{r^2}[/tex]

[tex]F= \frac{(8.99 x 10^9)(2.5*10^{-6})(75*10^{-6})}{0.59^2}[/tex]

[tex]F= 4.8423N[/tex]

The force acting on the block are given by,

[tex]F-mgsin\theta = ma[/tex]

[tex]a = \frac{F-mgsin\theta}{m}[/tex]

[tex]a = \frac{4.8423-(0.445)(9.8)sin(35)}{0.445}[/tex][tex]a = 10.31m/s^2[/tex]

Therefore the box is accelerated upward.