A person bending forward to lift a load "with his back" rather than "with his knees" can be injured by large forces exerted on the muscles and vertebrae. The spine pivots mainly at the fifth lumbar vertebra, with the principal supporting force provided by the erector spinalis muscle in the back. To see the magnitude of the forces involved, and to understand why back problems are common among humans, consider the model shown in the figure for a person bending forward to lift a 200-N object. The spine and upper body are represented as a uniform horizontal rod of weight $350 \mathrm{~N}$, pivoted at the base of the spine. The erector spinalis muscle, attached at a point two thirds of the way up the spine, maintains the position of the back. The angle between the spine and this muscle is $12.0^{\circ}$. Find the tension in the back muscle and the compressional force in the spine.

When a person stands on tiptoe (a strenuous position), The total gravitational force on the body $\overrightarrow{\mathbf{F}}_g$ is supported by the force $\overrightarrow{\mathbf{n}}$ exerted by the floor on the toes of one foot, where $\overrightarrow{\mathbf{T}}$ is the force exerted by the Achilles tendon on the foot and $\overrightarrow{\mathbf{R}}$ is the force exerted by the tibia on the foot. Find the values of $T, R$, and $\theta$ when $F_g=700 \mathrm{~N}$.

The arm weighs $41.5 \mathrm{~N}$. The gravitational force on the arm acts through point $A$. Determine the magnitudes of the tension force $\overrightarrow{\mathbf{F}}_t$ in the deltoid muscle and the force $\overrightarrow{\mathbf{F}}_s$ exerted by the shoulder on the humerus (upper-arm bone) to hold the arm in the position shown.

A painter climbs a ladder leaning against a smooth wall. At a certain height, the ladder is on the verge of slipping. If the ladder of length L leans at an angle $\theta$ with the horizontal, what is the lever arm for this horizontal force with the axis of rotation taken at the base of the ladder?

Figure shows a claw hammer as it is being used to pull a nail out of a horizontal board. If a force of $150 \mathrm{~N}$ is exerted horizontally as shown, find (a) the force exerted by the hammer claws on the nail and (b) the force exerted by the surface on the point of contact with the hammer head. Assume that the force the hammer exerts on the nail is parallel to the nail.

A 10.0-kg cylinder rolls without slipping on a rough surface. At an instant when its center of gravity has a speed of 10.0 m/s, determine its total kinetic energy.

For its size, the common flea is one of the most accomplished jumpers in the animal world. A 2.0-mm-long, 0.50-mg critter can reach a height of 20 cm in a single leap.

Neglecting air drag, what is the takeoff speed of such a flea?

A 10.0-kg cylinder rolls without slipping on a rough surface. At an instant when its center of gravity has a speed of 10.0 m/s, determine the translational kinetic energy of its center of gravity.

Two bowling balls each have a mass of 6.8 kg. They are located next to each other with their centers 21.8 cm apart. What gravitational force do they exert on each other?

A 10.0-kg cylinder rolls without slipping on a rough surface. At an instant when its center of gravity has a speed of 10.0 m/s, determine the rotational kinetic energy about its center of gravity.

A bicycle wheel has a diameter of 64.0 cm and a mass of 1.80 kg. Assume that the wheel is a hoop with all the mass concentrated on the outside radius. The bicycle is placed on a stationary stand, and a resistive force of 120 N is applied tangent to the rim of the tire. What force is required if you shift to a 5.60-cm-diameter sprocket?

A large grinding wheel in the shape of a solid cylinder of radius 0.330 m is free to rotate on a frictionless, vertical axle. A constant tangential force of 250 N applied to its edge causes the wheel to have an angular acceleration of 0.940 rad/s$^2$. What is the moment of inertia of the wheel?

A large grinding wheel in the shape of a solid cylinder of radius 0.330 m is free to rotate on a frictionless, vertical axle. A constant tangential force of 250 N applied to its edge causes the wheel to have an angular acceleration of 0.940 rad/s$^2$. What is the mass of the wheel?

A hungry bear weighing 700 N walks out on a beam in an attempt to retrieve a basket of goodies hanging at the end of the beam. The beam is uniform, weighs 200 N and is 6.00 m long, and it is supported by a wire at an angle of $\theta=60.0^{\circ}$. The basket weighs 80.0 N. (a) Draw a force diagram for the beam. (b) When the bear is at x = 1.00 m, find the tension in the wire supporting the beam and the components of the force exerted by the wall on the left end of the beam. (c) If the wire can withstand a maximum tension of 900 N, what is the maximum distance the bear can walk before the wire breaks?