ProblemSet3-Fa23-key

Name: __________________________ KIN 430 – Biomechanics Fall Semester 2023 Problem Set #3 (25 points) – Due on by Wednesday, Nov 15 th 2023 by 5pm. Answer the following questions by placing your answers in the spaces provided. Staple the separate sheets of paper before you turn it in. You must show your calculations to receive full credit, even if you have the correct answers . Don’t forget to include proper SI units ! 1. (5 pts.) a. An 70 kg student in the UMass body shop brags to his friend of equal mass that he can press 200kg on a leg press (see image or Google “leg press” if you are unfamiliar with the machine). The leg press is angled at 55 degrees above horizontal, starts from rest, and the leg press slider has a 0.25 static coefficient of friction. Draw the FBD for the forces acting on the foot plate of the leg press. What is the extension force he needs to apply to move the leg press foot plate? Draw the FBD for the leg press. Leg Presser’s Leg extension force applied (N): ____________ Answer key 1888.52N t.FI am Fp she Fact Fit Feud 2281.34 1607.18 Fpub 21888.52N

b. The student’s friend (also 70kg) counters that he can squat 125kgs. Assume the head, arms, and trunk (HAT) typically make up 68% of the total body weight, the squatter moves upward from rest, and ignore stability requirements and lower body mass (e.g. so you will only consider the student’s HAT mass while squatting and not for the leg press). How much is he actually lifting? Draw the FBD for the squat. Draw the FBDs for squat: Squatter’s Leg Strength (N): ____________ 2. ( 3 pts. ) While pushing off against a diving board, a diver generates an upward vertical force that increases linearly from 0 N to 1700 N over the first 0.20 s, remains constant for the next 0.1 s, and then decreases steadily back to 0 N over the next 0.20 s (see the graph below showing force versus time). If her mass is 70 kg and her initial upward velocity was 0 m/s, what will her vertical velocity be at the instant she leaves the diving board (when the force goes to 0 N at 0.5 s). Keep in mind that the entire time, the downward gravitational force will also be applying an impulse to the diver’s body. (Hint: it is easiest to solve this problem using impulse-momentum.) Upward linear velocity upon leaving the diving board _______________ Fyi 1ft 1693.21 N Fiat 70 0.68 481 466.96 n Float 125 9.81 1226.25N F push Fiat Food 1693.21N 70.9.81 686.7 tbh th f tbh Imp w 686.765 I 343.35 2 38 mls Imp I 0 2711700 0.17117007 40.2711700 510 Inga s 510 343.35 166.65Ns aus 1645 2 38m Is

4. ( 5 pts. ) A power lifter with a body mass of 125 kg performs a “dead lift,” raising a barbell with a mass of 400 kg to a height of 0.38 m in a time of 1.7 s. An Olympic weightlifter with a body mass of 82 kg performs a “power clean,” lifting a barbell with a mass of 94 kg to a height of 0.89 m in a time of 0.85 s. Determine the mechanical work and power for both of these athletes on the weights they lifted (do not attempt to include body mass in your work calculation). Also divide each lifters’ power output by their body mass to evaluate which lifter is more powerful in an absolute sense (W) and which lifter is more powerful in a relative sense (W/kg)? Power Lifter Olympic Lifter Mechanical work: __________ __________ Mechanical power: __________ __________ Mechanical power relative to body mass: __________ __________ Which lifter is more powerful in an absolute sense? ____________ Which lifter is more powerful in a relative sense? ____________ 5. (2 pts.) Bob is jumping on a trampoline. Each time he impacts the trampoline, his vertical momentum is altered by a resistive impulse that slows his velocity to zero (in other words, his motion stops for an instant when the trampoline material is maximally stretched). If immediately prior to impacting the trampoline his 68 kg body is moving downward at 7.1 m/s, what is the impulse that is applied by the trampoline to slow his velocity to zero? If the time required to slow Bob’s velocity to zero was 0.35 s, what is the force applied by the trampoline? Resistive impulse that stops Bob’s motion ______________ Resistive force that stops Bob’s motion ______________ Ws Fd 1491.12N 820.7mn p Y 877.13W 965.53W 7.0174k 11.774kg Olympic Olympic POTw 400 9.81.0.38 Of w 94.9.81 0.89 820.7mn w 1491.12mn p 84 965.53W p 14,941187713W p 9681 11.774k Pre stg 7.0174kg 482.8ns 1379.4N Ft Mav Fts MOV Ft 482.8 Imp 68 F g 357 482.8 Imps 482.8 F 1379.4N

6. (4pts) Olympic cross-country ski champion, Henrik Henrikson, is using a new ski wax, Gripola, that is supposed to stop his ski from slipping backwards when he pushes off against the snow (it gives him a coefficient of static friction between the ski and the snow of 0.35). While skiing, he applies a 1000 N force, directed downwards and backwards, at an angle of 75deg to the horizontal (see figure). Based on this information, what is: a) the magnitude of the normal reaction force (FR) between the ski and the snow, b) the magnitude of the force trying to cause sliding (FSLIDE) between the ski and the snow, and c) what is the magnitude of the limiting value of friction (FLIM) d) will the ski slip? Magnitude of F R ____________ Magnitude of F SLIDE ____________ Magnitude of F LIM ____________ Will ski slip? ___________________ 965.93N 258.82N n gg 338.08N 1000.575 no 965.93N off Flims 035 965.93 Flin 338.08N