A conservative force which can be derived from the potential energy function U = r²y², acts on an object moving in 2 dimensions. The object moves from the initial position in = (x = 2, y = 3), to the final position Fin = (x = 1, y = 1). The initial kinetic energy of the object at Fin = (x = 2, y = 3), is 100 Joules. Find the final kinetic energy of the object.
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![Problem 2
A conservative force which can be derived from the potential energy function
U = r²y², acts on an object moving in 2 dimensions. The object moves from the
initial position in = (x = 2, y = 3), to the final position in = (x = 1, y = 1). The
initial kinetic energy of the object at Fin =(r= 2, y = 3), is 100 Joules. Find the final
kinetic energy of the object.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2a374032-eb6a-452e-b499-5bf877eae559%2F70c9bfca-1cc4-46be-8d0b-35851476ae1c%2Fyy90mzl_processed.jpeg&w=3840&q=75)
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- Consider an object of mass m = 4 kg on a frictionless table. The object experiences a repulsive force F = a/x2 + b/x, where F is in newtons and x is the position of the object relative to the origin. Write an expression for the work done by the repulsive force on the object as it moves from an initial position of x1 to a final position of x2. If the object starts at a position of x1 = 8.5 m apart, how much work, in joules, is required by an external force to bring it to a position of x2 = 2.5 m apart when a = 19 and b = 11? If the object starts at rest at a position x3 = 1.3 m and is released, at what speed v, in meters per second, will the object be moving when it is at position x4 = 12.5 m?A horizontal force of magnitude 41.3 N pushes a block of mass 3.92 kg across a floor where the coefficient of kinetic friction is 0.576. (a) How much work is done by that applied force on the block-floor system when the block slides through a displacement of 4.79 m across the floor? (b) During that displacement, the thermal energy of the block increases by 40.5 J. What is the increase in thermal energy of the floor? (c) What is the increase in the kinetic energy of the block? (a) Number i Units (b) Number i Units (c) Number i UnitsA child of mass m = 27 kg slides down a slide of height h = 2.1 m without friction. Let gravitational potential energy be zero at ground level. Write an expression for the child's total mechanical energy, E, at the top of the slide, in terms of the variables in the problem and the acceleration due to gravity g. Calculate the change in the child's potential energy, ΔU in joules, from the top to the bottom of the slide at ground level (i.e. ΔU = Uground- Utop). What is the child's final speed, vf in m/s?
- A horizontal force of magnitude 40.1 N pushes a block of mass 3.85 kg across a floor where the coefficient of kinetic friction is 0.553. (a) How much work is done by that applied force on the block-floor system when the block slides through a displacement of 4.78 m across the floor? (b) During that displacement, the thermal energy of the block increases by 38.0 J. What is the increase in thermal energy of the floor? (c) What is the increase in the kinetic energy of the block?A horizontal force of magnitude 44.1 N pushes a block of mass 4.47 kg across a floor where the coefficient of kinetic friction is 0.576. (a) How much work is done by that applied force on the block-floor system when the block slides through a displacement of 3.31 m across the floor? (b) During that displacement, the thermal energy of the block increases by 38.0 J. What is the increase in thermal energy of the floor? (c) What is the increase in the kinetic energy of the block? (a) Number i Units (b) Number Units (c) Number i UnitsA horizontal force of magnitude 37.4 N pushes a block of mass 3.83 kg across a floor where the coefficient of kinetic friction is 0.639. (a) How much work is done by that applied force on the block-floor system when the block slides through a displacement of 3.86 m across the floor? (b) During that displacement, the thermal energy of the block increases by 39.5 J. What is the increase in thermal energy of the floor? (c) What is the increase in the kinetic energy of the block? (a) Number Units (b) Number i Units (c) Number Units >
- A 12.0 kg box is given an initial push that starts it sliding across the floor. It eventually comes to a stop. If the box has an initial velocity of 3.5 m/s, how much work is done by friction to cause it to come to a stop? (Yes, you are correct, you do not know the coefficient of friction.)A horizontal force of magnitude 35.9 N pushes a block of mass 4.07 kg across a floor where the coefficient of kinetic friction is 0.552. (a) How much work is done by that applied force on the block-floor system when the block slides through a displacement of 3.46 m across the floor? (b) During that displacement, the thermal energy of the block increases by 40.2 J. What is the increase in thermal energy of the floor? (c) What is the increase in the kinetic energy of the block? (a) Number i (b) Number i (c) Number i ! Units J ! Units Units5m μ 7. A mass m = 2 kg is released from the top of an incline plane 5 m long and at an angle of 37° to the horizontal. The mass slips to the bottom of the incline, strikes a spring which compresses and projects the mass back up. The coefficient of friction between the mass and the incline is μ = 0.2. Using energy principles, find how far back up the incline the mass m moves before it comes to rest. 700002 k 37° E m