How Do Forces Balance When Standing on Tiptoe?

[wowdusk]

Homework Statement

When a person stands on tiptoe (a strenuous position), the position of the foot is as shown in Figure P8.16a. The total gravitational force on the body, Fg, is supported by the force n exerted by the floor on the toes of one foot. A mechanical model of the situation is shown in Figure P8.16b, where T is the force exerted by the achilles tendon on the foot and R is the force exerted by the tibia on the foot. Find the values of T, R, and theta when Fg = 700 N.

for the picture go here http://qaboard.cramster.com/physics-topic-5-1064-cpi0.aspx

Figure P8.16

Homework Equations

The Attempt at a Solution

i'm really confused...

 

[tiny-tim]

The total gravitational force on the body, Fg, is supported by the force n exerted by the floor on the toes of one foot. A mechanical model of the situation is shown in Figure P8.16b, where T is the force exerted by the achilles tendon on the foot and R is the force exerted by the tibia on the foot. Find the values of T, R, and theta when Fg = 700 N.

Hi wowdusk!

n = F_g = 755N (or is it 700N? I'm confused ).

The foot is in equilibrium, so everything should add to zero.

Take components of force vertically and horizontally, and also take moments of force about some point (I suggest the end of the R force).

What equations do you get?

 

[nlightner]

I can provide a response to this content by breaking it down and applying scientific principles and equations.

Firstly, the concept of objects in equilibrium means that the forces acting on an object are balanced, resulting in a net force of zero and thus no acceleration. In this case, the person standing on tiptoe is in equilibrium because the forces acting on their foot are balanced.

The total gravitational force, Fg, is equal to the weight of the person, which in this case is 700 N. This force is supported by the normal force, n, exerted by the floor on the toes of one foot. This normal force is perpendicular to the surface of the floor and is equal in magnitude to Fg.

In the mechanical model shown in Figure P8.16b, there are two additional forces acting on the foot - the force exerted by the achilles tendon, T, and the force exerted by the tibia, R. These forces are both acting at an angle, theta, with respect to the horizontal.

To find the values of T, R, and theta, we can use the principle of equilibrium, which states that the sum of all forces acting on an object must be equal to zero. In this case, the forces acting on the foot are Fg, n, T, and R. Therefore, we can set up the following equation:

Fg + n + T + R = 0

Substituting in the values for Fg and n, we get:

700 N + 700 N + T + R = 0

Solving for T and R, we get:

T = -1400 N
R = -700 N

This means that T and R are both directed downwards, and their magnitudes are 1400 N and 700 N, respectively. The negative sign indicates that these forces are acting in the opposite direction to the positive direction we have defined.

To find theta, we can use the equation:

tan(theta) = R/T

Substituting in the values for R and T, we get:

tan(theta) = (-700 N)/(-1400 N)

Solving for theta, we get:

theta = 30 degrees

Therefore, when Fg = 700 N, the values of T, R, and theta are -1400 N, -700 N, and 30 degrees, respectively. This means that the person standing on tiptoe