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physics - 1 The potential energy of an object constrained...

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1. The potential energy of an object constrained to the x axis is given by U ( x ) = 6 x 2 8 x 3 , where U is in joules and x is in meters. (a) Determine the force F x associated with this potential-energy function. F x = (b) Assuming no other forces act on the object, at what positions is this object in equilibrium? (Enter your answers from smallest to largest.) x 1 = x 2 = (c) Which of these equilibrium positions are stable and which are unstable? point x 1 is in point x 2 is in 2. A simple Atwood's machine uses two masses, m 1 and m 2 . Starting from rest, the speed of the two masses is 6.0 m/s at the end of 3.0 s. At that instant, the kinetic energy of the system is 50 J and each mass has moved a distance of 9.0 m. Determine the values of m 1 and m 2 . m 1 = kg m 2 = kg 3. The 5.0 kg object below is released from rest at a height of 5.0 m on a curved frictionless ramp. At the foot of the ramp is a spring of force constant k = 400 N/m. The object slides down the ramp and into the spring, compressing it a distance x
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