Problem 14.84 A bolt of mass 2.10×10 2 kg moves with SHM that has an amplitude o

Question

Problem 14.84

A bolt of mass 2.10×102 kg moves with SHM that has an amplitude of 0.235 m and a period of 1.515 s . The displacement of the bolt is + 0.235 m when t=0.

Part A

Find the displacement of the bolt at time t = 0.490 s .

-0.105

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Part B

Find the magnitude of the force acting on the bolt at time 0.490 s .

Part C

Find the direction of the force acting on the bolt at time t = 0.490 s .

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Part D

What is the minimum time required for the bolt to move from its initial position to the point x = -0.175 m ?

Please help me with parts B and D

Thank you

Problem 14.84

A bolt of mass 2.10×102 kg moves with SHM that has an amplitude of 0.235 m and a period of 1.515 s . The displacement of the bolt is + 0.235 m when t=0.

Part A

Find the displacement of the bolt at time t = 0.490 s .

x =

-0.105

m

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Answer Requested

Part B

Find the magnitude of the force acting on the bolt at time 0.490 s .

Part C

Find the direction of the force acting on the bolt at time t = 0.490 s .

+x-direction -x-direction

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Correct

Part D

What is the minimum time required for the bolt to move from its initial position to the point x = -0.175 m ?

Please help me with parts B and D

Thank you

t = s

Explanation / Answer

m = 2.1*10^-2 kg
A = 0.235 m
T = 1.515 s = 2*pi*sqroot(m/k), so k = 0.36
and w = sqroot(k/m) = 4.14

x = Acos(wt + phi)
x = 0.235cos(4.14t + phi)
at t = 0
0.235 = 0.235cos(phi), phi = 0
x = 0.235cos(4.14t)

at t= 0.490
x = -0.10408 m

F = -kx = 0.037469 N

Direction, positive x axis

at x = -0.175m
t = 0.582 s

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