Question

6) While Alice is doing a push-up, at one moment her body is in a horizontal position, supported only by two upwards-directed normal forces, one on the feet (Nf ) and one of the hands (Nh). The hands are placed right in front of the head, which is 1.7 m (Alice’s height) away from the feet. Alice’s center of mass is 0.95 m from her feet and 0.75 m from her head, and her total mass is 75 kg. a) Make a free body diagram for Alice indicating where each of the three forces (the weight and the two normals) is acting, and write two equilibrium equations: one balancing the forces, and one balancing the torques. (Make explicit where you choose to place the pivot point for the torque equation; for example, whether it is the feet or the head). b) Use the equations you wrote to find the value of each of the two normal forces.

Answer 1

Solution Given: Alice's height = 1.7m Alice's mass = 75kg. (a) FBD ANK NE k 0.95m x 0.75m 750 g= it is gravitational to constant weight of Alic = 75.79.8 N 1 g = 9.8m/52 - = 735 N' equilibrium eqin 1) Nf+Nh=735 Dequ | 2) Alf (p.4s) - Nh(75)=0 - rh. we need to choose an axis of rotation. Any Axis will work because the system is at rest, in equilibrium Suppose we choose the central of mass. The torque I from the hand cause positive rotation and forque from the feet cause negative rotation that .. Nfco.gr) -th(0.75 0 (6) from ear hd, we get Nh - Nf (1.267) put value of Nh in reon lot , we get Nft Nf (1.267)=735 Nf = 324.217 N) Nh= 410.78 N Teacher's Signature