In the figure, a block weighing 12.3 N, which can slide without friction on an i

Question

In the figure, a block weighing 12.3 N, which can slide without friction on an incline at angle 6 = 50.0degree, is connected to the top of the incline by a massless spring of unstretched length 0.540 m and spring constant 140 N/m. The block is initially at its equilibrium position, (a) How far from the top of the incline is the block's equilibrium point? (b) If the block is pulled slightly down the incline and released, what is the period of the resulting oscillations? The suspension system of a 2100 kg automobile "sags" 9.6 cm when the chassis is placed on it. Also, the oscillation amplitude decreases by 36% each cycle. Estimate the values of (a) the spring constant k and (b) the damping constant b for the spring and shock absorber system of one wheel, assuming each wheel supports 525 kg.

Explanation / Answer

a)

here

parallel to incline

F * sin(theta) = Fs

m * g * sin(theta) = k * x

x = m*g* sin(theta) / k

x = 12.3 * sin50 / 140

x = 0.0673 m

this is the length the spring will be stretched when the mass is added.

the unextended length was 0.54 m so the position from the top will be

x = 0.54 + 0.0673 = 0.6073 m

b)

by using the formula

T = 2 * pie * sqrt( m / k )

T = 2 * 3.14 * sqrt( (12.3 / 9.8 ) / 140)

T = 0.594 sec

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