Question

Consider a woman lifting a 60N. Find the tension in her back muscle and compression in her spine muscle when her back is horizontal. Approximate the situation as shown in (b) and assume this upper part of her body to weigh 250N with the centre of gravity as indicated.

Answer 1

Assume the distance between the line if force of block and force of 250 N is x:

and the 'pivot point' is in the woman's waist s meters from the force of 250 N, so we have

$$0=M_{back}-250s-60(s+x),$$

$$M_{back}=250s+60(s+x),$$

this is the moment of force exerted by the back muscles required not to fall down. Assume the distance from waist to the point of maximum tension in the back muscles is d and the spring constant of muscles is k. Hence the tension and the compression will be

$$T=M_{back}/d=[250s+60(s+x)]/d,$$

$$c=T/k=[250s+60(s+x)]/(kd).$$