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Show that for two scalar fields f and g:
∇.[∇f ×( f ∇g)]= 0.
To find the optimum shape for a cross-section of a beam against bending, beam sections of a square, circle and equilateral triangle with the same cross-sectional area (A) are considered. If the beams have the same length (L), Young’s Modulus (E) and support condition, determine which shape of the beam is the best against bending?
In the system shown in the figure below, a horizontal force F with arrowx acts on an object of mass m2 = 7.40 kg. The horizontal surface is frictionless. Consider the acceleration of the sliding object as a function of Fx.

(a) For what values of Fx does the object of mass m1 = 1.80 kg accelerate upward? (Indicate the direction of the force with the sign of your answer. Let the positive x direction be to the right.)
Fx >

(b) For what values of Fx is the tension in the cord zero? (Indicate the direction of the force with the sign of your answer. Let the positive x direction be to the right.)
Fx ≤
The gravitational force on a baseball is -Fgĵ. A pitcher throws the baseball with velocity vî by uniformly accelerating it straight forward horizontally for a time interval Δt = t − 0 = t. If the ball starts from rest, determine the following: (Use any variable or symbol stated above along with the following as necessary: g for the acceleration due to gravity.

(a) Through what distance does it accelerate before its release?
d =

(b) What force does the pitcher exert on the ball?
vector FP =
A man 2 meters tall stands 3 meters from a pin hole camera. how is the image affected when he moves 1 meter closer to the camera?
A UNIFORM METER RULE IS PIVOTED AT P IN 70cm mark on the meter rule force 0.1 And 0.4N Are Applied At M The 60Cm Mark And Q The 85Cm Mark. If The Rule Is In Equilibrium .Find The Mass Of The Rule.Take g=10ms-2
A 5.29 kg ball is attached to the top of a vertical pole with a 2.31 m length of massless string. The ball is struck, causing it to revolve around the pole at a speed of 4.41 m/s in a horizontal circle with the string remaining taut. Calculate the angle, between 0° and 90°, that the string makes with the pole.
A 1290-kg car pulls a 270-kg trailer. The car exerts a horizontal force of 3.6 × 103 N against the ground in order to accelerate.
What force does the car exert on the trailer? Assume an effective friction coefficient of 0.16 for the trailer.
The pulley is suspended by a cord C. Suppose that m1 = 1.3 kg and m2 = 4.0 kg .
Determine the tension in the cord that supports the pulley C after the masses are released and before one hits the ground. Ignore the mass of the pulley and cords.
A basketball leaves a player's hands at a height of 2.20 m above the floor. The basket is 3.05 m above the floor. The player likes to shoot the ball at a 40.0 ∘ angle.
If the shot is made from a horizontal distance of 6.60 m and must be accurate to ±0.23m (horizontally), what is the range of initial speeds allowed to make the basket?
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