The box of negligible size is sliding down along a curved path defined by the pa

Question

The box of negligible size is sliding down along a curved path defined by the parabola y=0.4x2. When it is a A(xA = 2 m, yA = 1.6 m), the speed is v = 6 m/s and the increase in speed is dv/dt = 3 m/s2 . (Figure 1)

Part A

Determine the magnitude of the acceleration of the box at this instant.

Express your answer to three significant figures and include the appropriate units.

Figure 1 of 1

The box of negligible size is sliding down along a curved path defined by the parabola y=0.4x2. When it is a A(xA = 2 m, yA = 1.6 m), the speed is v = 6 m/s and the increase in speed is dv/dt = 3 m/s2 . (Figure 1)

Part A

Determine the magnitude of the acceleration of the box at this instant.

Express your answer to three significant figures and include the appropriate units.

Figure 1 of 1

Explanation / Answer

Given Y(x) = 0.4*x^2

dY/dx = 0.8*x

d2Y/dx2 = 0.8

acceleration = a = sqrt(at^2+an^2)

at =dV/dt = 3

an = v^2/Rho

Rho = [1+(dY/dx)^2]^3/2 / [ d2Y/dx2 ]

Rho = 8.4 m

an = v^2/Rho = 6^2/8.4 = 4.28 m/s^2

acceleration = sqrt ( 3^2+4.28^2)

acceleration = 5.23 m/s2

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