A force F = bx^3 acts in the x direction, where the value of b is 3.7 N/m^3. How

Question

A force F = bx^3 acts in the x direction, where the value of b is 3.7 N/m^3. How much work is done by this force in moving an object from x = 0.00 m to x = 24 m? 11 J 31 J 37 J 42 J An electron moves with a constant horizontal velocity of 3.0 times 10 m/s and no initial vertical velocity as it enters a deflector inside a TV tube. The electron strikes the screen after traveling 40 cm horizontally and 50 cm vertically upward with no horizontal acceleration. What is the constant vertical acceleration provided by the defector? (The effects of gravity can be ignored.) 5.6 times 10^13 m/s^2 1.9 times 10^2 m/s^2 2.8 times 10^13 m/s^2 7.5 times 10^3 m/s^2 A particle experiences a force given by F(x) = alpha - beta x^3. Find the potential field U(x) the particle is in. (Assume that the zero of potential energy is located at x = 0.) U(x) = 3 beta x^2 U(x) = -ax + beta/4 x^4 U(x) = -3 beta x^2 U(x) = ax - beta/4 x^4 A lava flow is threatening to engulf a small town. A 350-m-wide, 40-cm thick tongue of 1200 C lava is advancing at the rate of 1.0 m per minute. The mayor devises a plan to stop the lava in its tracks by flying in large quantities of 20 degree C water and dousing it. The lava has density 2500 kg/m^3 specific heat 1100 J/kg middot K, melting temperature 800 degree C and heat of fusion 4.0 times 10^5 J/kg How many liters of water per minute, at a minimum, will be needed to save the town? Express your answer with the appropriate units.

Explanation / Answer

part 1 )

W = integral F.dx from 0 to 2.4 m

F =bx^3

b = 3.7 N/m^3

W = bx^/4 from 0 to 2.4

W = 30.69 = 31 J

part 3 )

U = -dF/dx

F = alpha - beta*x^3

dF/dx = 3*betax^3

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