A 20 kg 0object is acted on by a conservative force given by , with F in newton 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=2.0 m? (b) If the object has a velocity of 4.0 m/s in the negative direction of the x-axis when it is at x=5.00 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 -8.0 J when the object is at x=0?
a) The P.E. of the system associated with the force when the object is at x=2.0 m is 19.4 J
b) The speed of the object when it passes through the origin is 6.37 m/s
c) Answer for part a) will be 11.4 J and that for part b) will be 6.37 m/s when P.E. of the system when the object is at x=0 is-8.0 J.
The mass of an object is m=20 kg
The force applied to an object is
The potential energy of the object at x=0 is,
The velocity of an object is v=4.0 m/s in the negative direction of the x-axis when it is at x=0
Using the formula for work done on a system by an external force, we can find the stopping distance of an automobile.
The potential energy or work done by the system, (1)
The total energy of the system, (2)
From the law of conservation of energy,
We are given that the force applied to an object is
Then P.E associated with it is using equation (1) is given as:
Therefore, the P.E. of the system associated with the force when the object is at x=2.0 m is equal to 19.4J
But, it has the speed of
From equation (3), we can get the initial speed of the object as follows:
Therefore, the speed of an object when it passes through the origin is 6.37 m/s
From part a), we can write that,
If then, the new potential energy is given as:
will be the same as before because on both sides of the equation part (b) cancels out.
So it is independent of .
Therefore, the answer for part a) will be 11.4 J and that for part b) will be 6.37 m/s.
A collie drags its bed box across a floor by applying a horizontal force of 8.0 N . The kinetic frictional force acting on the box has magnitude 5.0 N . As the box is dragged through 0.70 m along the way, what are (a) the work done by the collie’s applied force and (b) the increase in thermal energy of the bed and floor?
Approximately of water falls 50 m over Niagara Falls each second. (a) What is the decrease in the gravitational potential energy of the water–Earth system each second? (b) If all this energy could be converted to electrical energy (it cannot be), at what rate would electrical energy be supplied? (The mass of 1 m3 of water is 1000 kg .) (c) If the electrical energy were sold at 1cent/KW.h , what would be the yearly income?
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