Question
Asked Nov 10, 2019
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8
A0.5 kg cart connected to a light spring for which the force constant is 20.0 N/m oscillates on a
frictionless, horizontal air track. The cart is released from x 3.00 cm with an initial velocity of
V 0.1 m/s. Find:
(A) the amplitude of this motion
(B) The maximum speed of the cart?
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8 A0.5 kg cart connected to a light spring for which the force constant is 20.0 N/m oscillates on a frictionless, horizontal air track. The cart is released from x 3.00 cm with an initial velocity of V 0.1 m/s. Find: (A) the amplitude of this motion (B) The maximum speed of the cart?

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Expert Answer

Step 1

Given information:

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т 3D 0.5 kg т k 20 N/m х%3D3 сm v -0.1 m/s

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Step 2

Here, m is the mass of the cart, k is the spring constant, x is the displacement from the mean position and v is the velocity at that position.

(a)

Apply the energy conservation and plug the required values to obtain the amplitude A.

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1 kA 2 2 2 2 1 1 kx 2 A = mv2 x+ k A = (0.5 kg)(-0.1 m/s) (20 N/m) A (0.03 m) A 3.39x10 m

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Step 3

(b)

Write the formula for the angular frequency(ω) ...

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k m (20 N/m) (0.5 kg) =6.32 rad/s

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