Quiz 8

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School

California State University, Long Beach *

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Course

300

Subject

Mechanical Engineering

Date

Feb 20, 2024

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docx

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3

Uploaded by JusticeDugong1998

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1. What is the length of a segment with coordinate end points of (3,3) and (9,5)? AB 2 = (x1 - x2) 2 + (y1 - y2) 2 AB 2 = (9 - 3) 2 + (5 - 3) 2 √ AB 2 = √ (9 - 3) 2 + (5 - 3) 2 AB = 6.3 2. If the hip move through 75deg over a 0.2s time period, what was its average angular velocity? velocity final = 75 o , t = .2s ω = ∆ θ / ∆t ω = ( 75 - 0) / (.2-0) ω = 75 / 0.2 ω = 375deg / s 3. If segment A is 2m and segment B is 1.3m, what is the relative angle between the two segments if the “C” length is 2.5m? Segment A = 2m, Segment B= 1.3, Segment C = 2.5m C 2 = A 2 + B 2 − 2ABcosØ 2.5 2 = 2 2 + 1.3 2 - 2(2)(1.3)cosØ 6.25 = 4 + 1.69 - 5.2cosØ 6.25 - 5.69 = -5.2cosØ .56 / -5.2 = cosØ -.1077 = cosØ Cos -1 = -.1077 Deg = 96.2 4. If the elbow starts at a 90deg flexed position (the relative angle between the humerus and ulna) and ends with a 175 deg position, how much range of motion did it got through? Deg Inital = 90, Deg final = 175 ROM = Deg final - Deg Inital ROM = 175 - 90 ROM = 85 deg extension 5. One radian is equal to: 57.3 deg 6. What is the angular velocity of a joint which moves through an angular rotation of 2.3 rad over a 1.2s time period?
ω = ∆ θ / ∆t ω = 2.3 rad / 1.2s ω = (2.3 * 57.3) / 1.2s ω = 131.79 / 1.2 ω = 1089.8 deg/s 7. If the absolute angle of segment 1 is 100deg and the absolute angle of the adjoining segment 2 is 145deg, what is the relative angle between the two segments? angle 1 = 100, Angle 2 = 145 α = θ 2 - θ 1 180 - 45 = 135 α = 145 - 100 α = 45 8.If a segment has distal coordinates of (3,2) and proximal coordinates of (8,8), what is the absolute angle of the segment. tanØ = (y1 - y2) / (x1 - x2) tan -1 = (2 - 8) / (3 - 8) 50.2deg 9. 2.3rad is equal to how many degrees? 2.3rad * 57.3deg 131.8deg 10. If the knee starts in a static position (180deg) and move to a 90deg position over a 0.2s time period, what is the average angular acceleration of the knee? Deginitial= 180deg, Degfinal 90, t = 0.2s Angular Velocity Agular Acceleration ω = ∆ θ / ∆t a = ∆ ω / ∆t ω = (90 - 180) / 0.2s a = 450 / 0.2s
ω = 90 / 0.2 a = 2250deg/s/s ω = 450 deg/s
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