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ME 261 Spring 2007 Test 2 solution

# ME 261 Spring 2007 Test 2 solution - 29 s m 17 27 45 sin 30...

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ME 261 - Spring 2007 – Solution to Test 2 Problem 1 The number of teeth for each gear is: A: 9; B: 78; C=13; D: 90. The size of the teeth is the same. The radius of each gear will be proportional to the number of teeth so ... , C . n r , C . n r B B A A = = . At the point of contact between two gears, the linear velocity is the same so D D C C B B A A r r and r r ϖ = ϖ ϖ = ϖ In terms of the number of teeth, D D C C B B A A n n and n n ϖ = ϖ ϖ = ϖ So, rpm 60 1 90 13 26 3 n n and rpm 26 3 78 9 1 n n D c c D B A A B = = ϖ = ϖ = = ϖ = ϖ 60 1 A D = ϖ ϖ A B C D R / V 2 C D r / V 2

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Problem 2 Normal and tangential components of the velocity before impact: 45 cos 30 and 45 sin 30 Normal and tangential components of the velocity after impact: ( 29 45 cos 30 and 45 sin 30 8 . 0 Velocity after impact:

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Unformatted text preview: ( 29 [ ] [ ] s / m 17 . 27 45 cos 30 45 sin 30 8 . 2 2 = + Angle with the plane ( 29 o 66 . 38 45 cos 30 45 sin 30 8 . tan = β ⇒ = β Angle with the vertical: 45-38.66= 6.34 o 45 o 30 m/s 45 o 30 m/s 45 o 30 m/s β Problem 3 Q A B Q’ A B B’ Q’’ Q’’’ Q P Q’ A B Q’’ Q P Problem 2 A B C D Side view Top view Problem 3 A tennis ball with a coefficient of restitution of 0.8 is moving horizontally until it hits a smooth inclined concrete surface as shown. Find the velocity of the ball after impact. 45 o 30 m/s...
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ME 261 Spring 2007 Test 2 solution - 29 s m 17 27 45 sin 30...

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