Answer to Question #150387 in Classical Mechanics for Dion Gray

Question

A child starts sledding from rest, going down a 40-m-long 7.5° incline, then coasting across a horizontal stretch. The mass of sled + child is 35 kg, and the coefficient of kinetic friction is 0.060.
Determine how much energy that is transferred to thermal energy.

Answer 1

$E = E_p+E_k+Q$

$\text{where:}$

$E \text { energy, }E_p \text { potential energy,}$

$E_k \text { kinetic energy, }Q \text{ internal energy}$

$\text{at the top of the slope:}$

$E_1 = E_{p1}+ E_{k1}+Q_1= E_{p1}+Q_1$

$E_{k1}= 0 \text{ as }V= 0\text{ (body speed)}$

$\text{the sled has finished moving:}$

$E_2 = E_{p2}+ E_{k2}+Q_2= E_{p2}+Q_2$

$E_{k2}= 0 \text{ as }V= 0\text{ (body speed)}$

$\text{No action of outside forces according to the law of conservation of energy:}$

$E_1=E_2;Q_2-Q_1=E_{p1}-E_{p2}= mg\Delta{}h$

$\Delta{h}= l *sin\alpha=40*\sin{7.5^0}= 5.22\text{ slope height}$

$mg\Delta{}h=35*9.8*5,22=1 790.46 J$

Answer: 1 790.46 J energy that is transferred to thermal energy