A 57.8 kg person is walking. assume his leg acts like a rigid pendulum that rota
ID: 1769215 • Letter: A
Question
A 57.8 kg person is walking. assume his leg acts like a rigid pendulum that rotates about the ground (he does not bend his knee). Assume that his walking velocity is equal to the tangenital velocity of the hip. as his COM rotates in an arc, the force necessary to continually alter the direction of motion is equal to the body mass multiplied by the tangenital velocity squared divided by the radius of the arc. If the weight of the person does not provide a force at least this large the person will leave the ground.
a) If his leg length (r) is 0.75m, what is the maximum velocity that he could walk on earth (g=-9.81 m/s/s) without leaving the ground?
b) How fast could he walk if he were 67.8 kg?
c) How fast could he walk on the moon using the same walking technique (g= -1.6 m/s/s)?
d) What happens if he tries to walk faster?
---1) He'll have to take shorter steps at the faster speed in order to stay on the moon
---2) He will leave the ground because gravity is insufficient
---3) He will leave the ground because centripetal acceleration would decrease
e) How fast could he walk on earth if his leg length was 0.8m?
f) What is the centripetal acceleration about the ankle if he walks at 1.5m/s and leg length is 0.81m?
I realize this is a long and (probably) difficult question, but I will definitely rate your answers once they come in! Sorry the image is right there in the question... After I typed out everything. Thanks in advance for your help!
A 57.8 kg person is walking. assume his leg acts like a rigid pendulum that rotates about the ground (he does not bend his knee). Assume that his walking velocity is equal to the tangential velocity of the hip. as his COM rotates in an arc, the force necessary to continually alter the direction of motion is equal to the body mass multiplied by the tangential velocity squared divided by the radius of the arc. If the weight of the person does not provide a force at least this large the person will leave the ground. a) If his leg length (r) is 0.75m, what is the maximum velocity that he could walk on earth (g=-9.81 m/s/s) without leaving the ground? b) How fast could he walk if he were 67.8 kg? c) How fast could he walk on the moon using the same walking technique (g= -1.6 m/s/s)? d) What happens if he tries to walk faster? ---1) He'll have to take shorter steps at the faster speed in order to stay on the moon ---2) He will leave the ground because gravity is insufficient ---3) He will leave the ground because centripetal acceleration would decrease ---4) More than one answer is correct e) How fast could he walk on earth if his leg length was 0.8m? f) What is the centripetal acceleration about the ankle if he walks at 1.5m/s and leg length is 0.81m? I realize this is a long and (probably) difficult question, but I will definitely rate your answers once they come in! Sorry the image is right there in the question... After I typed out everything. Thanks in advance for your help!Explanation / Answer
a) mg = mv^2/r
v^2 = gr
v = sqrt(9.81*0.75)= 2.71 m/s
b) didnt dependon mass, so 2.71 m/s
c) v = sqrt(1.6*0.75)= 1.10 m/s
d) he will leavetheground because gravity is insufficient
d) in worksheet
v = sqrt(9.81*0.8)= 2.80 m/s
e) a = v^2/r = 1.5^2/0.81= 2.78 m/s^2
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