Answer the questions? answer # 8=1 A particle rotates counterclockwise in a circ

Question

Answer the questions? answer # 8=1

A particle rotates counterclockwise in a circle of radius 8.5 m with a constant angular speed of 5.6 rad/s. At t = 0, the particle has an x coordinate of 3.4 m Determine the x coordinate of the particle at t = 1.17 s. Answer in units of m Find the x component of the particle's velocity at t = Find the x component of the particle's accel-eration at t = 1.17 s. Answer in units of m/s2 The motion of a piston in an auto engine is simple harmonic. The piston travels back and forth between the extreme points 7.8 cm apart. What is the maximum speed of the pis¬ton when the engine is running at 8973 rpm (revolution per minute)? Answer in units of m/s Consider a car engine running at constant speed. That is, the crankshaft of the engine rotates at constant angular velocity while each piston moves back-and-forth in its cylinder according to the rules of simple harmonic motion. Suppose the two extremal positions xmax and xmin of a piston are 4.58 cm from each other When the crankshaft of the engine rotates at 3570 rpm (revolutions per minute), what is the maximal speed |t>|max of the piston? Consider the simplified single-piston engine in the figure. The piston rod oscillates in simple harmonic motion. The wheel of radius 0.96 m rotates at a constant angular speed of 8.5 rad/s.

Explanation / Answer

I believe you only require #8..

If you want others too, please LET ME KNOW :)

x = A cos(wt + phi)

v = dx/dt = -A w sin(wt + phi)

at t=0, x= 0

cos( phi) = 0

hence

phi = pi /2 or 3 pi/2

Now, at t=0, v is +ve,

- A w sin(phi) > 0

since A and w are positive,

sin(phi) < 0

hence

phi = 3 pi /2

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