Question

Please include all equations, thank you

9. A girl is dragging a suitcase along a rough surface by pulling horizontally on a rope that is attached to it. Draw'a free body diagram for the suitcase. If the coefficient of kinetic friction is 0.54 and the mass of the suitcase is 20 kg, and the girl is pulling with a force of 200 N, find the horizontal acceleration of the suitcase.

Answer 1

Free body diagram for the suitcase:

Forces acting on the suitcase are,

i) Weight of the suitcase $mg$ vertically downward

ii) Normal force $N$ vertically upwards

iii) Frictional force $F_k$ horizontally to left

iv) Force $F$ from the rope, horizontally to right

Net force on the suitcase in the vertical direction is zero, $N=mg$

Frictional force $F_k=\mu_k N=\mu _k mg$

Net force on the suitcase in the horizontal direction is $F-F_k=ma$

$F-\mu_kmg=ma$

$a=\frac{F-\mu_kmg}{m}$

$a=\frac{200-0.54*20*9.81}{20}=4.703\,m/s^2$

Horizontal acceleration of the suitcase is $a=4.703\,m/s^2$