Answer to Question #266042 in Classical Mechanics for Jason

Question

An ice glider, that has a mass of 1640 kg, is initially moving at 20 m/s NW. A wind accelerates the glider at 2.5 m/s? 20° E of N for eight second. Then the wind shifts to 48°E of N accelerating the glider at 1.8 m/s for 11 seconds. 1) What is the glider's initial kinetic energy? 2) What is the glider's velocity at t= 8 s? 3) How much energy did the wind transfer to the glider during the 8 s? 4) What was the glider's velocity after the 11s the second wind gust was active? 5) How much energy did the wind transfer to the glider during the 19s? 6) What was the glider's average speed from t = 0 s to t = 19 s? 7) What was the glider's displacement from t = 0 s to t = 19 s? 8) What was the glider's average velocity from t = 8stot=198? 9) What was the glider's final kinetic energy? 10) A student contends that the glider will have the largest force at t = 19 s since it has the most kinetic energy at that time. Is this contention reasonable? Explain.

Answer 1

1)

$E_0=\frac{mv_0^2}2=328~kJ.$

2)

$v_1=v_0+a_1t_1\cos65°=28.5~\frac ms.$

3)

$\Delta E_1=E_1-E_0=\frac m2(v_1^2-v_0^2)=338~kJ.$

4)

$v_2=v_1+a_2t_2\cos 93°=27.5~\frac ms.$

5)

$\Delta E_2=|E_2|+|E_1|=\frac m2(v_1^2-v_2^2+v_1^2-v_0^2)=384~kJ.$

6)

$v_{av}=\frac{(v_0+v_1)t_1+(v_1+v_2)t_2}{2(t_1+t_2)}=26.4~\frac ms.$

7)

$s=v_0t_1+\frac{a_1t_1^2}2\cos 65°+v_1t_2+\frac{a_2t_2^2}2\cos 93°=501.6~m.$

8)

$v_{av}'=\frac{v_1+v_2}2=28~\frac ms.$

9)

$E_2=E_0+\Delta E_2=712~kJ.$

10)

$F_{max}\to t_1=8~s.$