The distributed loading w = wo sin 0, measured per unit length, acts on the curved rod shown in (Figure 1). Figure 1 of 1 w = wo sin 0

Find the cross product for (a) and (b) and (c) and and (d) and

Perform the following calculations and express your answer using the correct number of significant digits. (a) A man has two bags weighing 13.5 lb and one bag with a weight of 10.2 lb. What is the total weight of the bags? (b) The force Fon an object is equal to its mass mmultiplied by its acceleration a . If a wagon with mass 55 kg accelerates at a rate of 0.0255m/s2 , what is the force on the wagon? (The unit of force is called the newton and it is expressed with the symbol N.)

The first atomic bomb was detonated on July 16, 1945, at the Trinity test site about 200 mi south of Los Alamos. In 1947, the U.S. government declassified a film reel of the explosion. From this film reel, British physicist G.I. Taylor was able to determine the rate at which the radius of the fireball from the blast grew. Using dimensional analysis, he was then able to deduce the amount of energy released in the explosion, which was a closely guarded secret at the time. Because of this, Taylor did not publish his results until 1950. This problem challenges you to recreate this famous calculation. (a) Using keen physical insight developed from years of experience, Taylor decided the radius rof the fireball should depend only on time since the explosion, t, the density of the air, , and the energy of the initial explosion, E. Thus, he made the educated guess that r=kEabtcfor some dimensionless constant kand some unknown exponents a,b, and c. Given that [E]=ML2T-2 , determine the values of the exponents necessary to make this equation dimensionally consistent. (Hint: Notice the equation implies that k=rEabtcand that [k]=1 ). (b) By analyzing data from high-energy conventional explosives, Taylor found the formula he derived seemed to be valid as long as the constant khad the value 1.03. From the film reel, he was able to determine many values of rand the corresponding values of t. For example, he found that after 25.0 ms, the fireball had a radius of 130.0 m. Use these values, along with an average air density of 1.25kg/m3 , to calculate the initial energy release of the Trinity detonation in joules (J). (Hint: To get energy in joules, you need to make sure all the numbers you substitute in are expressed in terms of SI base units.) (c) The energy released in large explosions is often cited in units of “tons of TNT” (abbreviated “t TNT”), where 1 t TNT is about 4.2 GJ. Convert yow answer to (b) into kilotons of TNT (that is, kt TNT). Compare your answer with the quick-and-duty estimate of 10 kt TNT made by physicist Enrico Fermi shortly after witnessing the explosion from what was thought to be a safe distance. (Reportedly, Fermi made his estimate by dropping some shredded bits of paper right before the remnants of the shock wave hit him and looked to see how far they were carried by it.)

A certain hydraulic system is designed to exert a force 100 times as large as the put into it. (a) What must be the ratio of the area of the cylinder that is being controlled to area of the master cylinder? (b) What must be the ratio of their diameters? (c) By what factor is the distance through which the output force moves reduced relative to the distance through which input force moves? Assume no losses due to friction.

Find the angles that vector makes with the and axes.

Show that (BC)A is the volume of the parallelepiped, with edges formed by the three vectors in the following figure.

Check Your Understanding Suppose we want the formula for the volume of a sphere. The two expressions commonly mentioned in elementary discussions of spheres are 4r2 and 4r3/3 . One is the volume of a sphere of radius r and the other is its surface area. Which one is the volume?

For the three-dimensional vectors in the following figure, find (a) GH , (b) GH , and (c) GH .

A fluid ounce is about 30mL. What is the voIume of a 12 fl-oz can of soda pop in cubic meters?