help solving all SHOW YOUR WORK For problems 11-14, you need to show your work a

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SHOW YOUR WORK For problems 11-14, you need to show your work and may get partial credit if your work demonstrates your understanding of the concepts (5 pts each) 11) An object is launched with a speed of 50 m/s at an angle of 30 above the horizontal. Write out the vector velocity for this object in the standard i.j format. 12) What is the centripetal acceleration required to keep a 2 kg toy plane rotating in a circle of radius 0.5 m at a speed of 6 m/s? 0.5 13)What is the mass of an object which weighs 27.5 N? 27.5 14) Consider a simple pendulum on earth which is 0.4 m long What is the period of this pendulum?

Explanation / Answer

11)

Given

speed is v = 50 m/s , the angle theta 30 degrees

the

velocity vector is V = vx m/s i + Vy m/s j

where Vx = V cos theta and Vy = v sin theta

so V = 50 cos30 m/s i + 50 sin 30 m/s j

the velocity vector is

V = 43.30 m/s i + 25 m/s j

12)

mass m = 2 kg , speed v = 6 m/s, radius is r = 0.5 m

we know that the centripetal force is  

F = mv^2/r = ma

a_cen = v^2/r

a_cen = 6^2/0.5 = 72 m/s^2

13)

weight W = 27.5 N  

we know that weight W = mg

m = W/g

m = 27.5/9.8 kg

m = 2.806 kg

14) simple pendulum with length l = 0.4 m

we knwo that the time period of a simple pendulum is T = 2pi sqrT(l/g)

T = 2pi sqrt(0.4/9.8) s

T = 1.2694 s

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