Question 7.8: The impact of carrying a heavy backpack Assume that you are ......
The impact of carrying a heavy backpack
Assume that you are carrying a backpack with several books in it for a combined mass of 10 kg (Earth exerts about a 100-N gravitational force on it). This means that each of the two straps pulling on the trapezius muscle exerts a force of about 50 N on the muscle. This causes the muscle to deflect about 6° from the horizontal on each side of the strap. Estimate the force that the trapezius muscle exerts on its connecting points on the neck and shoulder (similar to the connections of the rope to the tree and the car in the previous example).
Sketch and translate Our sketch of the situation is shown below. Choose the section of muscle under the strap as the system of interest.
Simplify and diagram The force diagram shows the pull of the muscle tissue at an angle of 6° above the horizontal and the 50-N downward force exerted by the strap on that section of muscle.
Represent mathematically We can apply the same equation we used to get the car out of the rut:
T_{\text {Bone on Muscle }}=\frac{F_{\text {Strap on Muscle }}}{2 \sin \theta}
Solve and evaluate Substituting the known information in the above equation, we get
T_{\text {Bone on Muscle }}=\frac{50 \mathrm{~N}}{2 \sin 6^{\circ}}=240 \mathrm{~N}(\text { or } 54 \text{ }\mathrm{lb})
This force is almost 2.5 times larger than the force exerted by Earth on the backpack.
Try it yourself: A 70-kg tightrope walker stands in the middle of a tightrope that deflects upward 5.0° on each side of where he stands. Determine the force that each half of the rope exerts on a short section of rope beneath the walker’s feet.
Answer: 3900 N.