A block is attached to a non–linear spring and moves in 2D. The energy function of the block is given by
U(x, y) = 6.00yx − 4.50xy^3
(a) What are the units of the constants?
(b) Assuming the mass of the block is 0.500 kg, what is the acceleration of the block at (x, y) = (0.250, 0.500)?
Physics help?
2016-02-25 4:35 pm
回答 (1)
2016-02-25 6:07 pm
✔ 最佳答案
(a) U is in Joules, so6.00 must have units of J/m² (since it is multiplied by two distance values)
4.50 must have units of J/m⁴ (since it is multiplied by four distance values)
(b) Fx = ∂U/∂x = 6.00y - 4.50y³
and so when y = 0.500, Fx = 2.44 N
Fy = ∂U/∂y = 6.00x - 13.5xy²
and so when x = 0.250 and y = 0.500, Fy = 0.656 N
Then |F| = √(Fx² + Fy²) = 2.52 N
and acceleration
|a| = |F| / m = 2.52N / 0.500kg = 5.05 m/s² ◄
Hope this helps!
收錄日期: 2021-04-21 17:06:32
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