Question

Consider a $65kg$ ice skater is being pushed by two other with forces $F_1=26.4N$ and $F_2=18.6N$ as shown in the figure. If the coefficient of static friction is $0.04$ and coefficient of kinetic friction is $0.02$, which of the following option(s) is/are correct?
(Take $g=10m/s^2$)

• A. Net force acting on the skater is $32.3N$.
• B. Acceleration of the skater is $0.23m/s^2$.
• C. Kinetic friction experienced by skater is $26N$.
• D. Kinetic friction experienced by skater is $13N$.

Answer 1

Answer: (A), (B), (D)

The correct options are
A Net force acting on the skater is $32.3N$.
B Acceleration of the skater is $0.23m/s^2$.
D Kinetic friction experienced by skater is $13N$.

Net force acting on the skater,
$F_{net}=\sqrt{F_1^2+F_2^2}=\sqrt{(26.4{)}^2+(18.6{)}^2}=32.3N$
Reaction on skater, $N=mg=65\times 10=650N$
Static friction, $f_s={\mu }_{s}N=0.04\times 650=23N$
Since $F_{net}>f_s$, Therefore skater slides along the direction of resultant.
Kinetic friction, $f_k={\mu }_{k}N=0.02\times 650=13N$
Acceleration of the skater, $a=\frac{F_{net}-f_k}{m}=\frac{32.3-13}{62}=0.23m/s^2$