Midterm Review Winter/Spring 2018.
Free Fall Acceleration (1).
How long is the ball in the air?
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restart; g:=9.81*m/s^2: vi:=27.0*m/s: t:=2*vi/g; |
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(1) |
Greatest height reached:
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th:=t/2: hmax:=th*(vi/2); |
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(2) |
First time when the ball has half its initial velocity:
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(3) |
Inexperienced Pilot TLH-ATL (2):
Average speed vaver, speed in still air v0, correct angle.
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restart; assume(km>0); DY:=361.0*km: DX:=130.0*km: DT:=(94.0/60.0)*h: |
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vaver:=sqrt(DY^2+DX^2)/DT; v0:=DY/DT; vw:=83.0*km/h: theta:=arcsin(vw/v0)*rad; |
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pi:=evalf(Pi): rad:=(180.0/pi)*deg: thdeg:=theta; |
Off the cliff (3): H=g*t^2/2
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restart; pi:=evalf(Pi): t:=sqrt(2*H/g): x:=v0*t; |
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(5) |
Motion and Forces (4):
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M:=3.76*kg: F:=14.8*kg*m/s^2: theta:=17.0*pi/180: t:=5.10*s: ax:=F*cos(theta)/M: vx:=ax*t; |
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(6) |
Spring Accelerometer (5):
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(7) |
Inclined Plane Acceleration (6): a=g*sin(theta).
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g:=9.81*m/s^2: v1:=1.48*m/s: t:=1.20*s: v2:=4.84*m/s: a:=(v2-v1)/t; |
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theta:=arcsin(a/g)*rad; rad:=180*deg/pi: thdeg:=theta; |
Moving and Ice Block (7):
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restart; Fmin=mus*m*g/(cos(theta)+mus*sin(theta)); zero:=-sin(theta)+mus*cos(theta); |
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(9) |
Work-Kinetic Energy (Car) (8):
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M:=1270.0*kg: hr:=3600*s: km:=1000*m: v:=84.0*km/hr; Ki:=M*v**2/2: |
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Work:=-Ki*J*s^2/kg/m^2; DelK:=-Ki; |
Block Sliding into Spring (9): k*x^2/2=E.
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assume(m>0); g:=9.81*m/s^2: M:=1.9*kg: H:=0.69*m: k:=465.0*kg/s^2: |
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E:=M*g*H; x:=sqrt(2*E/k); |
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(11) |
Block and Loop-the-Loop (10):
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restart; W:=m*vA^2/2-m*g*(h-2*R); |
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(12) |
Gravitational acceleration (11):
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Rearth:=6.37*10**6*m: g:=9.81*m/s^2: a:=4.6*m/s^2: H:=Rearth*sqrt(g/a)-Rearth; |
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(13) |
Blocks and compressed Spring (12):
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m1:=2.4*kg: m2:=4.6*kg: x:=0.78*m: v1:=2.6*m/s: v2:=m1*v1/m2; |
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(14) |
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k:=(m1*v1**2+m2*v2**2)/x^2; |
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(15) |
Mass Mass-Spring Collision (13):
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m2:=2.7*kg: m1:=2.45*kg: v1:= 1.40*m/s: M:=m1+m2: v:=m1*v1/M; K:=M*v**2/2: |
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dK=K-m1*v1**2/2; assume(m>0); k:=189.0*kg/s^2: xmax:=sqrt(2*K/k); |
