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A 20 kg object is acted on by a conservative force given by F = −3.0x...

A 20 kg object is acted on by a conservative force given by F = −3.0x − 5.0x2, with F in newtons and x in meters. Take the potential energy associated with the force to be zero when the object is at x = 0. (a) What is the potential energy of the system associated with the force when the object is at x = 5.0 m? (b) If the object has a velocity of 2.0 m/s in the negative direction of the x axis when it is at x = 7.0 m, what is its speed when it passes through the origin? (c) What are the answers to (a) and (b) if the potential energy of the system is taken to be −6.0 J when the object is at x = 0?

Please provide a step by step solution. Thank you so much for your help!

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Answer #1

The conservative force is given as F- 3x-5x The potential energy of the system is, dU--Fd Integrating the above equation. 3x2 5x AtU(0) Therefore,

mne 285.833 J 2(285.833 J) 1n 2(285.833 J) 20 kg -5.346 m/s 3x2 5x Now, (0) с Therefore,

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