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A car is traveling around a horizontal circular track with radius r = 290 m at a

ID: 1408010 • Letter: A

Question

A car is traveling around a horizontal circular track with radius r = 290 m at a constant speed v = 20 m/s as shown. The angle ?A = 30° above the x axis, and the angle ?B = 54° below the x axis.

A) What is the magnitude of the car’s acceleration?

B) What is the x component of the car’s acceleration when it is at point A

C) What is the y component of the car’s acceleration when it is at point A

D) What is the x component of the car’s acceleration when it is at point B

E) What is the y component of the car’s acceleration when it is at point B

F) As the car passes point B, the y component of its acceleration is:

-increasing

-decreasing

-constant

Explanation / Answer

Here ,

A) magnitude of acceleration , a = v^2/r

magnitude of acceleration , a =20^2/(290)

magnitude of acceleration , a =1.38 m/s^2

the magnitude of acceleration is 1.38 m/s^2

B)

at A

x - component of acceleration = - a * cos(30)

x - component of acceleration = -1.38 * cos(30)

x - component of acceleration = -1.195 m/s^2

the x - component of acceleration is -1.195 m/s^2

C)

y - component of acceleration = a * sin(30)

y - component of acceleration = 1.38 * sin(30)

y - component of acceleration = 0.69 m/s^2

the y - component of acceleration is 0.69 m/s^2

D)

at point B

x - component of acceleration = a * cos(54)

x - component of acceleration = 1.38 * cos(54)

x - component of acceleration = 0.811 m/s^2

the x - component of acceleration is 0.811 m/s^2

E)

y - component of acceleration = a * sin54)

y - component of acceleration = 1.38 * sin(54)

y - component of acceleration = 1.12 m/s^2

the y - component of acceleration is 1.12 m/s^2

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