A patient is sitting on a treatment table, hooked up to a cervical (neck) tracti

Question

A patient is sitting on a treatment table, hooked up to a cervical (neck) traction device. The traction device is pulling his head with 120N in a direction 32° above horizontal. The mass of the head is 4kg.

a) Calculate the gravitational force acting on the head (head weight). Make sure to consider the direction of force (up (+) or down (-)).

b) Calculate the vertical component (Fy) of the neck traction force.

c) Calculate the horizontal component (Fx) of the neck traction force.

d) What is the magnitude of the sum of the forces from the traction device and the head weight? (Hint: horizontal component of the head weight = 0).

e) What is the direction of the sum of the forces from the traction device and the head weight relative to horizontal?

Explanation / Answer

here ,

a)

gravitaional force = 4 * 9.8

gravitaional force = 39.2 N

the gravitaional force is 39.2 N

b)

Now , for the traction force

Fy = F * sin(theta)

Fy = 120 * sin(32)

Fy = 63.6 N

the vertical component of the neck is 63.6 N

c)

Fx = F * cos(theta)

Fx = 120 * cos(32)

Fx = 101.8 N

the magnitude of the neck is 101.8 N

d)

net force ,

Fnet = 101.8 i + j *(63.6- 39.2)

Fnet = 101.8 i + 24.4 j

magnitude of net force = sqrt(101.8^2 + 24.4^2)

magnitude of net force = 104.7 N

the magnitude of net force is 104.7 N

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