ProblemSet1_Fa23-KEY (2)

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University of Massachusetts, Amherst *

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430

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Health Science

Date

Dec 6, 2023

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pdf

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KIN 430 – Problem Set 1 Name: _______________ KIN 430 – Biomechanics Fall Semester 2023 Problem Set #1 (25 points) – Due on by Wednesday Sept 27 th 5pm. To receive full credit, you should complete the problem set by the due date In completing this problem set, do all of your calculations in the space provided. Staple all the sheets of paper for this problem set together before you turn it in. You must show your calculations to receive full credit, even if you have the correct answers . You must hand your problem set to a person. If you hand it in to Dr. Boyer’s mailbox please get a stamp from the front office first. 1. (2 pts.) Dr Boyer throws a ball for her dog. If the ball leaves her hand with a velocity of 6m/s at an angle of 30 degrees to the ground, what are the horizontal and vertical components of ball velocity. Horizontal _________________________ Vertical __________________________ 2. (2 pts.) During the upward flight phase of a jump, is the acceleration of the center of mass positive or negative? Explain the reasoning for your answer. Answer key 5 196m11 3 mls Acceleration is negative The person is moving in a positive direction the velocities positive to start argon to zero at the top v14
KIN 430 – Problem Set 1 3. (5 pts.) The table below contains velocity-time data for the center of mass of the human body in free-fall. Use numerical differentiation to calculate the missing acceleration data, and use numerical integration to calculate the missing position data for all time frames. Be sure to use the appropriate equations for the first and last data points when determining the accelerations (you must calculate the accelerations, don’t just write in -9.81). For this assignment, you must do all calculations by hand, show all of your work (attach a separate sheet of paper if needed), and report final answers in the table provided with at least 2 decimal places to receive full credit. time (s) position (m) velocity (m/s) acceleration (m/s 2 ) 0.150 1.7 -0.085 0.200 -0.576 0.250 -1.066 0.300 -1.557 0.350 -2.047 Iii 1.683 I 1,642 1.577 Iff I 1 487 450.05 I Sissuittitvilat a a VÉÉ as I a IE S 1.7 46 0.57650 08510.017 S 1.683 s 1,68s off 0664 576 1.05 a s ftp 085 4.81 n 5 1.642 s 1.642 141.557 1.066 1.05 q 576 9.01 53 1.576 as 2 1 0 9.81 Sys 1.577 142.047 1.5577 05 ay É 9.80
KIN 430 – Problem Set 1 4. (4 pts.) While on a recent geocaching treasure hunt (en.wikipedia.org/wiki/Geocaching), Matthew Stafford was trekking through farmland in Northern Michigan. From his car, he first headed East at 2.00 m/s for 7 minutes, then North at 4.25 m/s for 2 minutes, and finally West at 1.50 m/s for 1 minute. What is his total distance covered and the resultant displacement in meters? For displacement, give a magnitude and direction. (Direction should be expressed as an angle relative to the horizontal.) Distance: ___________________ Displacement: ___________________ 5. (4 pts.) Dr. Boyer asked Erica and Ross to track, using motion capture with measurement unit mm and recorded at 25 Hz , a box’s position while being lifted from the floor to a shelf. For simplicity, they decided to divide the trajectory (horizontal, vertical) of the box into 3 stage (floor, mid lift, & placement). After processing the data, they found the positions of the 3 stages to be (0, 0), (-100, 1200), & (400, 1100), respectively. If you assume the box followed a straight line between stages and each stage was 25 frames of data to complete: what is the total distance covered, the resultant displacement, speed, and velocity of the box from the start of the lift to placement? Note: Answers should be expressed in SI units. For displacement and velocity, provide a magnitude and direction. (Direction should be expressed as an angle relative to the horizontal.) Distance: _____________ Displacement: ___________________ Speed: _____________ Velocity: ___________________ 1440m 1.5 16090 in 4.25 2.60 510m 407m at pnasqotgyoabio Monjjjf5 dnelnasF.s'T 906.97m y anole tant 34.2160 0.857m s 0.58mg at 700 M gg yg Displace G ti 1 1 70.02 Tig M 7 primasmontsoos 1 1.714m velocity É 00.585 1 speed.tt 85
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