A 170 g block attached to a spring with spring constant 2.1 N horizontally on a

Question

A 170 g block attached to a spring with spring constant 2.1 N horizontally on a frictionless table. Its velocity is 23 cm/s when xU= -4.6 cm. What is the amplitude of oscillation? Express your answer to two significant figures and include the appropriate units. A =0.64 cm What is the block's maximum acceleration? Express your answer to two significant figures and include the appropriate units. a_max = What is the block's position when the acceleration is maximum? Express your answer to two significant figures and include the appropriate units. x = What is the speed of the block when x1 = 3.5 cm? Express your answer to two significant figures and include the appropriate units. v1 =

Explanation / Answer

As we know that

x(t) = A*cos(w*t + Phi_0)

PE in spring = kx^2/2
KE of mass = mv^2/2
Total energy E = constant, so
kx^2 + mv^2 = 2E

Plug in the numbers in consistent units:

2.1x0.046^2 + 0.17x0.23^2 = 2E
2E = 0.0134366

1) The max amplitude occurs when v = 0
2.1 x^2 = 0.0134366
x = 0.079989m = 7.9989cm

3) Position when the acceleration is the maximum is at the max amplitude

2) Force on ball at max amplitude = kx = 2.1 x 0.079989 = 0.167978 N
Acceleration = force / mass = 0.167978 / 0.17 = 0.9881102 m/s^2 = 98.81102 cm/s^2

4) kx^2 + mv^2 = 2E
2.1x0.035^2 + 0.17 v^2 = 0.0134366
v = 0.252797 m/s = 25.2797 cm/s

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