A lunch tray is being held in one hand, as the figure illustrates. The mass of the tray itself is 0.237 kg. and its center of gravity is located at its geometrical center. On the tray is a 1.19-kg plate of food and a 0.241-kg cup of coffee. Obtain (a) the force 7 exerted by the thumb and (b) the force exerted by the four fingers. Both forces act perpendicular to the tray, which is being held parallel to the ground.

A crane of mass m1 = 3 000 kg supports a load of mass m2 = 10 000 kg as shown in Figure P10.36. The crane is pivoted with a frictionless pin at A and rests against a smooth support at B. Find the reaction forces at (a) point A and (b) point B. Figure P10.36

A man stands on a merry-go-round that is rotating at 2.5 rad/s. If the coefficient of static friction between the man’s shoes and the merry-go-round is s=0.5 , how far from the axis of rotation can he stand without sliding?

When tightening a bolt, you push perpendicularly on a wrench with a force of 165 N at a distance of 0.140 m from the center of the bolt. How much torque are you exerting in newton-meters (relative to the center of the bolt)?

Part of riding a bicycle involves leaning at the correct angle when making a turn, as seen below. To be stable, the force exerted by the ground must be on a line going through the center of gravity. The force on the bicycle wheel can be resolved into two perpendicular components—friction parallel to the road (this must supply the centripetal force) and the vertical normal force (which must equal the system’s weight). (a) Show that (as defined as shown) is related to the speed vand radius of curvature rof the turn in the same way as for an ideally banked roadway—that is, =tan1(v2/rg) . (b) Calculate for a 12.0-m/s turn of radius 30.0 m (as in a race).

Suppose just two external forces act on a stationary, rigid object and the two forces are equal in magnitude and opposite in direction. Under what condition does the object start to rotate?

Jamal and Dayo are lifting a large chest, weighing 207 lb, by using the two rope handles attached to either side. As they lift and hold it up so that it is motionless, each handle makes a different angle with respect to the vertical side of the chest (Fig. P5.76). If the angle between Jamals handle and the vertical side is 25.0 and the angle between Dayos handle and the vertical side of the chest is 30.0, what are the tensions in each handle? FIGURE P5.76

BIO The arm in Figure P10.35 weighs 41.5 N. The gravitational force on the arm acts through point A. Determine the magnitudes of the tension force F1 in the deltoid muscle and the force Fs exerted by the shoulder on the humerus (upper-arm bone) to hold the arm in the position shown. Figure P10.35

BIO When a gymnast performing on the rings executes the iron cross, he maintains the position at rest shown in Figure P10.85a. In this maneuver, the gymnasts feet (not shown) are off the floor. The primary muscles involved in supporting this position are the latissimus dorsi (lats) and the pectoralis major (pecs). One of the rings exerts an upward fore Fh on a hand as shown in Figure P10.85b. The force Fs is exerted by the shoulder joint on the arm. The latissimus dorsi and pectoralis major muscles exert a total force Fm on the arm. (a) Using the information in the figure, find the magnitude of the force Fm. (b) Suppose an athlete in training cannot perform the iron cross but can hold a position similar to the figure in which the arms make a 45 angle with the horizontal rather than being horizontal. Why is this position easier for the athlete? Figure P10.85

Two children push on opposite sides of a door during play. Both push horizontally and perpendicular to the door. One child pushes with a force of 17.5 N at a distance of 0.600 m from the hinges, and the second child pushes at a distance of 0.450 m. What force must the second child exert to keep the door from moving? Assume friction is negligible.