12. [2pt] You are calculating the maximum speed at which a car can drive through

Question

12. [2pt] You are calculating the maximum speed at which a car can drive through a level turn with radius r. Starting from the basic equations you derive Here, g is free fall acceleration and Mus the coefficient for static friction. Let v1 be the speed for a turn with radius r1. What is the maximum speed for a turn of twice that radius?? 13. [2pt] You are calculating the acceleration for a car that rolls down frictionless an inclined ramp. Starting from a freebody diagram and Newton?s Law Here, g is free fall acceleration and theta the angle of the incline with respect to horizontal. Let a1 be the acceleration for a car of mass m1. What is the acceleration for a car of twice that mass? 14. [2ptj You are calculating the speed at which a dropped rock will hit the bottom of a deep well. Employing conservation of mechanical energy, you derive Here, d is the depth of the well and g is free fall acceleration. Let v1 be the speed for a well with a depth of d1. For a well that is half as deep the Speed would be 15. [2pt] A roller coaster cart approaches a sequence of two hills, the second twice as high as the first. At the top of the first hill, the cart has slowed down to 75% of its initial speed. Which statement is correct? (Ignore friction.) A) The cart will stop in the valley between the two hills. B) The cart will not make it up to the second hill. C) The cart will come to rest at the top of the second hill. D) The cart will pass over the second hill.

Explanation / Answer

12) so at double the radius

v = sqrt( mu g 2 r) = sqrt( 2) sqrt( mu g r) = sqrt(2) v1

so E)

13) does depend on mass so the same so D)

14)

so v = sqrt( 2 g d/2) = sqrt(2 g d)/sqrt(2) = v1/sqrt(2)

so C)

15)

so Ei = Ef

1/2 mv^2 = 1/2 m (0.75 v)^2 + m g h

1/2 v^2 - 1/2 (0.75 v^2) = g h

0.5*v^2 *(1-0.75^2) = g h

gh = 0.5 v^2 * 0.4375

so if we double h

m g 2h = 0.5 m v^2 * 2*0.4375 = 0.875 * 0.5 m v^2

so it will have enough energy to get over hill since this is less than 1/2 mv^2

D)

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