Question #266713

An ice glider is traveling 35 degrees W of S at 6 m/s when the wind exerts a force of 860 N 18 degrees N of W for three seconds. The mass of the glider is 215 kg. Complete the chart below and then answer the questions that follow.


t(s): 0, 1, 2, 3

East v (m/s): --3.44, t = 1, t = 2, t = 3

North v (m/s): --4.92, t = 1, t = 2, t = 3


What is the glider's initial kinetic energy?

What is the glider's kinetic energy at t = 2?

How much energy does the wind put into the glider in the 3 s interval?

What is the glider's average speed for the three second interval?

What is the glider's average velocity for the three second interval?


1
Expert's answer
2021-11-16T09:54:05-0500

v0=6msv_0 = 6\frac{m}{s}

We introduce a coordinate system with the basis: E,N\text{We introduce a coordinate system with the basis: }\vec E,\vec N

v0E=sin35°v0=3.44v_{0E}= -\sin35\degree *v_0=-3.44

v0N=cos35°v0=4.92v_{0N}= -\cos35\degree *v_0=-4.92

F=maF= ma

a=Fm=860215=4a = \frac{F}{m}=\frac{860}{215}= 4

aE=sin18°a=1.24a_{E}= -\sin18\degree *a=-1.24

aN=cos18°a=3.80a_{N}= -\cos18\degree *a=-3.80

v=v0+atv= v_0+at

vE=v0Е+aЕt=3.441.24tv_E= v_{0Е}+a_Еt=-3.44-1.24t

vN=v0N+aNt=4.923.80tv_N= v_{0N}+a_Nt=-4.92-3.80t


t(s)0123vE3.444.685.927.16vN4.928.7212.5216.32\begin{matrix} t(s) & 0 &1&2&3\\ v_E& -3.44&-4.68&-5.92&-7.16\\ v_N& -4.92&-8.72&-12.52&-16.32\\ \end{matrix}


EK0=mv022=215622=3870JEK_0 =\frac{mv_0^2}{2}= \frac{215*6^2}{2}= 3870J

v2=v2E2+v2N2=5.922+12.522=13.85msv_2 = \sqrt{v_{2E}^2+v_{2N}^2}= \sqrt{5.92^2+12.52^2}=13.85\frac{m}{s}

EK2=mv222=21513.8522=20621JEK_2 =\frac{mv_2^2}{2}= \frac{215*13.85^2}{2}= 20621J

v3=v3E2+v3N2=7.162+16.322=17.82msv_3 = \sqrt{v_{3E}^2+v_{3N}^2}= \sqrt{7.16^2+16.32^2}=17.82\frac{m}{s}

EK3=mv322=21517.8222=34123JEK_3 =\frac{mv_3^2}{2}= \frac{215*17.82^2}{2}= 34123J

ΔEK=EK3EK0=30253J\Delta EK = EK_3-EK_0= 30253J

vavg=v0+v33=7.94msv_{avg}= \frac{v_0+v_3}{3}= 7.94\frac{m}{s}


Answer:\text{Answer:}

EK0=3870JEK_0 = 3870J

EK2=20621JEK_2 =20621J

ΔEK=30253J\Delta EK = 30253J

vavg=7.94msv_{avg}= 7.94\frac{m}{s}



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