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AleksandrR [38]
3 years ago
7

One end of a spring with a force constant of k = 10.0 N/m is attached to the end of a long horizontal frictionless track and the

other end is attached to a mass m = 2.20 kg which glides along the track. After you establish the equilibrium position of the mass-spring system, you move the mass in the negative direction (to the left), compressing the spring 2.48 m. You then release the mass from rest and start your stopwatch, that is x(t = 0) = −A, and the mass executes simple harmonic motion about the equilibrium position. Determine the following.(a) displacement of the mass (magnitude and direction) 1.0s after it is released
(b) velocity of the mass (magnitude and direction) 1.0s after it is released
(c) acceleration of the mass (magnitude and direction) 1.0s after it is released
(d) force the spring exerts on the mass (magnitude and direction) 1.0s after it is released
(e) How many times does the object oscillate in 12.0s?
Physics
1 answer:
koban [17]3 years ago
3 0

Answer:

-2.478

0.379

11.14

24.78

Explanation:

Angular frequency of spring in harmonic motion is given by?

ω = √(k/m)

ω = √(10/2.2)

ω = √4.54

ω = 2.13 s^-1

If at t=0 the mass is in negative amplitude (x = -A = -2.48 m) then we describe the position with negative cosine

x(t) = -A * cos(ωt)

x(t) = -2.48 * cos(2.13 * 1)

x(t) = -2.48 * 0.9993

x(t) = -2.478

Velocity and acceleration are 1st and 2nd derivative of position

b)

v(t) = Aω * sin(ωt)

v(t) = 2.48 * 2.13 * sin(2.13 * 1)

v(t) = 5.282 * sin2.13

v(t) = 5.282 * 0.03717

v(t) = 0.379 m/s

c)

a(t) = Aω^2 * cos(ωt)

a(t) = 2.48 * 2.12² * cos(2.13 * 1)

a(t) = 2.48 * 4.494 * cos2.13

a(t) = 11.15 * 0.9993

a(t) = 11.14 m/s²

d)

F = -k * x(t)

F = -10 * -2.478

F = 24.78 N

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where bold indicates vectors.

In the case, the work of the friction force on a circular surface is requested.

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the path traveled half the length of the circle

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for the complete calculation it is necessary to know the friction coefficient, if we assume that μ = 0.1

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      m = 0,±1, ±2, ...

As they tell us that they measure the dark stripes, we are in a case of destructive interference, let's use trigonometry to find the sins tea

      tan θ = y / x

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In the interference experiments the measured angle is very small so we can approximate the tangent

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We substitute in the destructive interference equation

     d (y / x) = (m + ½) λ

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The first dark strip occurs for m = 0 and the third dark strip for m = 2. Let's find the distance for these and subtract it

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The separation between these strips is Δy

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