Question

a box of books weighing 235N moves at a constant velocity across the floor when the box it pushed with a force of 405N exerted downward at an angle of 35.2 degrees. how much momentum does the box posses?

Answer 1

Question 19061

Let $F_{1} = 405N, \varphi = 35.2$ degrees.

While accelerating from zero velocity to given velocity, $m\frac{v^2}{2} = F_1\cos \varphi a\frac{t^2}{2} = F_1\cos \varphi \frac{vt}{2}$ . Also, from the $2^{\mathrm{nd}}$ Newtons law: $p = m\nu = t \cdot F_1\cos \varphi \Rightarrow t = \frac{F_1\cos\varphi}{p}$ . Plugging this into first equation gives: $\frac{mv^2}{2} = F_1^2\frac{\cos^2\varphi}{2m} \Rightarrow p = m\nu = F_1\cos \varphi = 330m / s$ .