Answer to Question #220042 in Mechanics | Relativity for Alex

Question

a -A box of mass 10 kg is pulled by a mass-less rope with a force of 40 N. The rope

makes an angle of 30deg with the horizontal. Draw the free-body diagram showing

all forces on the box. Determine the acceleration of the box if the coefficient of

kinetic friction between the floor and the box is 0.2. Take g =10 ms-2 .

b-A ball of mass 100 g strikes a wall with the speed 2.0 ms^-1 and bounces off the

wall in the opposite direction with the same speed. Calculate the impulse of the

ball.

Answer 1

a.

$\textsf{Given}:\\ m=10 kg\\ F=40N\\ \mu=0.2\\ \theta=30\degree\\ \hspace{0.01cm}\\ N-W = ma_y\\ N-W=0 (a_y=0)\\ N=W\\ N=mg\\ N=10kg \times 9.81ms^{-2}\\ N=98.1N\\ \hspace{0.1cm}\\ F_R=\mu\times N\\ F_R=0.2\times98.1N\\ F_R=19.62N\\ \hspace{0.1cm}\\ Fcos\theta-F_R=ma_x\\ 40N\times cos(30\degree)-19.62N=10kg\times a\\ a=1.5ms^{-1}$

b.

$\textsf{Given:}\\ m=100g=0.1kg\\ u=2.0ms^{-1}\\ v=-2.0ms^{-1} \\ \hspace{0.1cm} \\ I=\Delta P\\ I=m(v-u)\\ I=0.1(-2.0-(2.0)\\ I=0.1\times-4.0\\ I=-0.4Ns\\ \textsf{The negative value of the impulse indicates that it's}\\ \textsf{direction is opposite to the initial direction of the ball}\\ \textsf{before impact.}$