All Solutions
Page 130: Section Review
Known:
$$
begin{align*}
m&=25 mathrm{kg} \
mu &=0.15 \
end{align*}
$$
Unknown:
$$
begin{align*}
F_f&=? \
\
F_N&=F_g \
&=mcdot g \
&=25 mathrm{kg}cdot 9.8 mathrm{m/s^2} \
&=24.5 mathrm{N} \
\
F_f&=mucdot F_N \
&=0.15cdot 245 mathrm{N} \
&=boxed{36.75 mathrm{N}}
end{align*}
$$
F_f=36.75 mathrm{N}
$$
Known:
$$
begin{align*}
m&=2.3 mathrm{g} \
s&=0.35 mathrm{m} \
mu&=0.24 \
end{align*}
$$
Unknown:
$$
begin{align*}
v_i&=? \
\
F&=F_f \
mcdot a&=mucdot F_g \
mcdot a&=mu cdot mcdot g \
a&=0.24cdot cdot 9.8 mathrm{m/s^2} \
&=2.352 mathrm{m/s^2} \
\
v_i^2&=2cdot acdot s \
v_i&=sqrt{2cdot 2.352 mathrm{m/s^2}cdot 0.35 mathrm{m}} \
&=boxed{1.283 mathrm{m/s}}
end{align*}
$$
v_i=1.283 mathrm{m/s}
$$
Known:
$$
begin{align*}
m&=40 mathrm{kg} \
mu&=0.43 \
end{align*}
$$
Unknown:
$$
begin{align*}
F_{max}&=? \
\
F_{max}&=F_f \
&=mucdot cdot mcdot g \
&=0.43cdot 40 mathrm{kg}cdot 9.8 mathrm{m/s^2} \
&=boxed{168.6 mathrm{N}}
end{align*}
$$
F_{max}=168.6 mathrm{N}
$$
Known:
$$
begin{align*}
m&=13 mathrm{kg} \
F_1&=20 mathrm{N} \
F_2&=25 mathrm{N} \
a_1&=0 mathrm{m/s^2} \
a_2&=0.26 mathrm{m/s^2} \
end{align*}
$$
Unknown:
$$
begin{align*}
mu_s&=? \
mu_k&=? \
\
a_1&=0 mathrm{m/s^2} Rightarrow F_{fs}>F_1 \
F_{fs}&>F_1 \
mu_scdot mcdot g&> 20 mathrm{N} \
mu_s&>dfrac{20 mathrm{N}}{mcdot g} \
mu_s&>dfrac{20 mathrm{N}}{13 mathrm{kg}cdot 9.8 mathrm{m/s^2}} \
mu_s&>boxed{0.157} \
\
F_2&=F+F_{fk} \
F_2&=mcdot a+mu_kcdot mcdot g \
mu_k&=dfrac{F_2-mcdot a}{mcdot g} \
&=dfrac{25 mathrm{N}-13 mathrm{kg}cdot 0.26 mathrm{m/s^2}}{13 mathrm{kg}cdot 9.8 mathrm{m/s^2}} \
&=boxed{0.1697}
end{align*}
$$
begin{align*}
mu_s&>0.157 \
mu_k&=0.1697
end{align*}
$$
