A cubic crate of side s= 2.0 m is top-heavy: its CG is 18 cm above its true center. How steep an incline can the crate rest on without tipping over? [Hint: The normal force would act at the lowest corner.]

(11) A tapered log 3.0 m long weighs 210 N and has its center of gravity 1.0 m from the thick end. It is being used as a bridge across a ditch and is supported at its ends by the edges of the ditch. A 600 N man stands on the log 1.0 m from the thin end. How much support is required at each end of the log? 3m FN=mant eug+ 1.om

The taho vendor carries a 1.5 m long light plank over his shoulder. At the ends of the plank are two buckets weighing 40 N and 60 N respectively. (a) Find the value of force F exerted by his shoulder. Neglect the weight of the plank. ( b) Where should he support the plank for it to be balanced horizontally

The bones of the forearm (radius and ulna) are hinged to the humerus at the elbow. The biceps muscle connects to the bones of the forearm about 2.15 cm beyond the joint. ,Biceps muscle Assume the forearm has a mass of 2.35 kg and a length of 0.445 m. When the humerus and the biceps are nearly vertical and the forearm is horizontal, if a person wishes to Humerus- hold an object of mass 5.75 kg so that her forearm remains motionless, what is the force exerted by the biceps muscle? Radius M Elbow- Ulna force: N Hand

A parking garage is designed for two levels of cars. To make more money, the owner decides to double the size of the gar- age in each dimension (length, width, and number of levels). For the support columns to hold up four floors instead of two, how should he change the columns’ diameter? (a) Double the area of the columns by increasing their diameter by a factor of 2. (b) Double the area of the columns by increasing their diameter by a factor of V2. (c) Quadruple the area of the columns by increasing their diameter by a factor of 2. (d) Increase the area of the columns by a factor of 8 by increasing their diameter by a factor of 2V2. (e) He doesn't need to increase the diameter of the columns.

Two men are carrying a ladder of length 1 by supporting it at its ends. At what distance x from one end must a can of paint, of mass 1/4 of that of the ladder, be suspended so that the men carry equal loads?

A solid consist of a cylinder and a hemisphere of equal radius fixed base to base. Find the ratio of the radius to the height of the cylinder. So that the solid has its centre of gravity at the common face. Hint. For stable equilibrium, the centre of the body should be below the common face or maximum lie on it. So take the centre of gravity of the body at a distance (a) from the bottom of the hemisphere Final Answer should be √2 : 1

The length of wire increases by 9 mm when weight of 2.5 kg is hung from the free end of wire. If all conditions are kept the same and the radius of wire is made thrice the original radius, find the increase in length.

3) A uniform board 7.5 m long with a mass of 73 kg is attached to a wall with a pivot. A rope with a tension of 850 N that makes an angle of 45° with the horizontal is attached 0.3 m from the left end of the beam and connects the beam to the same wall as the pivot to keep the system balanced. You place an 83 kg wooden crate on the board. How far from the left end can a wooden crate be placed without breaking the rope? (see figure below) 47 Ⓒ = 45°