Answer to Question #178907 in Physics for Andu

Question

The box is pulled by the force Fx, which causes it to accelerate a = 2 m / s². Find a) the work performed by the force Fx, when the box is moved by 5 m; b) work performed by friction force, if the coefficient of friction is 0.4.

Answer 1

I assume $F_x$ is the net force acted on the body. Then the mass of the box can be found from the second Newton's law:

$$m = \dfrac{F_x}{a}$$

where $a = 2m/s^2$ is the acceleration of the box.

a) By definition, the work of the constant force applied along the body's path is given as follows:

$$A _x= F_xs$$

where $s = 5m$. Thus, obtain:

$$A_x = 5F_x\space\space (J)$$

b) By definition, the friction force on the horizontal surface is given as follows:

$$F_f = \mu mg$$

where $\mu = 0.4$ is the coefficient of friction, and $g = 9.8m/s$ is the garaviational acceleration. Thus, the work of the friction force is:

$$A_f = \mu mgs = \mu\dfrac{F_x}{a}g\\ A_f = 0.4\cdot \dfrac{F_x}{2}\cdot 9.8 = 1.96F_x \space \space (J)$$

Answer. a) 5Fx, b) 1.96Fx.