Physics- Torques Question?

The question is: There is a patient in neck traction and has skull calipers, as can be seen on the diagram below. I have to find the maximum value of the suspended mass that will cause no tension or other force in the neck, knowing that the mass of the head is 4.2 kg and the coefficient of friction between the bed and the head is 0.2

The head is 4.2 kg, weighing (4.2 * 9.8 ) = 41.16 N

The most force you can put on the head without moving it is:

(mu) * (w_head) = 0.2 * 41.16 N = 8.232 N

You said correctly that F_f = T.
I’m not sure what your second equation is saying, because your diagram isn’t labelled with the terms you’ve used.

The tension in the line would be (mg), the mass of the block times the gravitational constant:

T = mg

Substituting:

F_f = T = mg

You also know that:

cos(15) * F_f = 8.232 N

because that’s the most force you can put on the head without moving it, and cos(15) gives the horizontal component of the tension in the line.

Substituting again, then,

F_f = (8.232 N) / cos(15) = mg

m = (8.232 N) / (cos(15) * g)

m = 8.232 / (cos(15) * 9.81) = 0.869 kg

cervical neck traction

Cervical Neck Traction $7.09 This Neck traction was designed and developed for the prevention and treatment of cervical vertebral disease, Based on the air -Traction , Neck Traction allows for deep neck muscle relaxation. Relief of tension, muscles spasms, stress and pressure in the neck , shoulders, head and cervical vertebral area. You can feel the results in just a few short minutes. Neck Traction can effectively aid the t…

North American Healthcare JB4866 Arched Back Stretcher $16.95 Gently Relieves Pressure Helps Relieve Aches And Pains Increases Flexibility Improves Posture Provide Firm Yet Comfortable Support. Great For Aching Muscles Stress & More Gently Relieves Pressure Helps Relieve Aches & Pains Increases Flexibility Improves Posture Provides Firm Yet Comfortable Support Only 2.2 lbs. so you can take it anywhere10 inches W x 15 inches L….

Real-Ease Neck and Shoulder Relaxer $24.99 Doctor Riter’s real-ease neck support helps release neck and shoulder tension in just 10 15 minutes a day.unique, cervical shaped support perfectly cradles your neck at the base of your skull to help release muscle tension in the neck, shoulders and jaw….

LapWorks Riser iPad Stand For iPad 1, 2 & 3 Adjustable Incline For Easy Typing And 360 Degree Rotation Use as an iPad Digital Picture Frame With Grippy Rubber Pads For Traction $29.95 The Riser is compatible with the iPad 2 and iPad 3. The Riser iPad Stand can elevate the iPad 4″ closer to eye level and has an incline range of 90 degrees that goes from completely lay-flat to absolutely vertical. And the Riser can rotate your iPad 360 degrees switching easily from landscape to portrait and back again. Can also be used as a Digital Picture Frame. All of the Riser’s surfaces tha…

Traction Cuff Women’s Knit Longsleeve V-neck Top The TractionCuffTM is a patent-pending long-sleeve Modal® cotton shirt that helps to absorb perspiration during your workout. This innovative new design incorporates non-slip ‘cuffs’ and a ‘thumb-hole’ at the end of the sleeves that allow the wearer to pull the end of the sleeve over their thumb, which allows the cuff to transform into a ‘half-glove’. The non-slip silicone material on the lower h…

Apple iPod Classic (80GB) Silicone Skin Case (Smoke) $4.99 Durable and protects your Apple iPod Classic from scratches and bumps Protects without compromising your Apple iPod Classic’s functions: allows you to protect, view and navigate your screen without removing it from its case. Anti-slip material gives the device added traction and holding comfort, preventing the device from falling off smooth surface. Lightweight, stretchable and extremely durabl…