A bowling ball encounters a 0.760 m vertical rise on the way back to the ball ra

Question

A bowling ball encounters a 0.760 m vertical rise on the way back to the ball rack, as the drawing Illustrates. Ignore frictional losses and assume that the mass of the ball Is distributed uniformly. The translational speed of the ball is 4.00 m/s at the bottom of the rise. Find the translational speed at the top. (A) 5.23 m/s (B) 5.00 m/s (C) 4.64 m/s (D) 2.32 m/s (E) 0.00 m/s A helicopter has two blades, each of which can be approximated as a thin rod of length 6.2 m and mass 240 kg. The blades are rotating at an angular speed of 42 rad/s. What is the total moment of inertia of the two blades about the axis of rotation? (A) I = 5230 kg m^2 (B) I = 4050 kg m^2 (C) I = 6150 kg m^2 (D) I = 520 kg m^2 (E) I = 50 kg m^2 In a performance test two cars take the same time to accelerate from rest up to the same velocity. Car A has a mass of 1500 kg, and car B has a mass of 2000 kg. During the test, which car has the greater change in momentum? (A) The change in momentum is the same for both cars. (B) The change in momentum is greater for car A. (C) The change in momentum is greater for car B. For the two cars in Problem 19, which one experiences the greater impulse? (A) Car A experiences the greater impulse. (B) Car B experiences the greater impulse. (C) Both cars experience the same impulse.

Explanation / Answer

17)from conservation of energy

0.5mv^2 +0.5Iw^2 = mgh +0.5mv2^2 + 0.5Iw2^2

moment of inertia of ball = 2mr^2/5

v = rw = 4m/s, h = 0.76 m

0.5v^2 +(0.5)(2/5)v^2 = gh +0.5v2^2 +(0.5*0.4)v2^2

0.5*4^2 +(0.5)(0.4)*4^2 = 9.8*0.76+ 0.5v2^2 +0.5*(0.4)v2^2

v2 = 2.32 m/s

correct option is (D)

18) L = 6.2 m , m = 240 kg , w = 42 rad/s

I = (mL^2/3) +(mL^2/3)

I = 2*240*6.2^2/3 = 6150 kg.m^2

correct option is (C)

19) correct option is (A)

20) correct option is (C)

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