Question #177165

The final answer should be in the format of "tolerance of ± in the third significant digit."


A car is traveling around a circular track of a 730-ft radius. If the magnitude of its total acceleration is 11 ft/sec2 at the instant when its speed is 50 mi/hr, determine the rate at which the car is changing its speed.

at = ± _________ ft/sec2


Write the vector expression for the acceleration a of the mass center G of the simple pendulum in both n-t and x-y coordinates for the instant when θ = 33° if θ˙ = 2.41 rad/sec and θ¨ = 4.445 rad/sec2.

a = (_____ en + _____ et) ft/sec2

a = (_____ i + ______ j) ft/sec2





1
Expert's answer
2021-04-01T18:41:38-0400

1)

at=av2r=10.997 fts2,a_t=a-\frac{v^2}{r}=10.997~\frac{ft}{s^2},

2)

an=v2r=rθ2=vθ,a_n=\frac{v^2}{r}=r\theta'^2=v\theta',

at=v=rθ,a_t=v'=r\theta'',

an=1.4672.41=3.535en,a_n=1.467\cdot 2.41=3.535e_n,

at=7304.445=3244.850et,a_t=730\cdot 4.445=3244.850e_t,

i=atsinθancosθ=1770.237,i=-a_tsin\theta-a_ncos\theta=-1770.237,

j=atcosθansinθ=2719.435.j=a_t cos\theta-a_n sin \theta=2719.435.



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