100 J of kinetic energy but no gravitational potential energy if GPE of the ground is assumed to be zero.
<h3>Explanation</h3>
Kinetic Energy
The ball carries kinetic energy for being in motion. The size of that energy is given as:
where
- is the mass of the object, and
- is its speed.
SI units:
- : joules.
- : kilograms.
- : meters per second.
For this ball:
.
Gravitational Potential Energy
Whether the ball carries gravitational potential energy depends on the point of zero potential energy. The ball would carry GPE if the point of zero potential energy is chosen underground. However, the question emphasizes that the ball is "on the ground," which <em>implies</em> that the ground is the reference with a GPE of zero.
The gravitational field near the Earth's surface is constant. As a result, GPE is proportional to height relative to the ground (or the point of zero GPE). The ball is on the ground. Its height is zero. As a result, its GPE is also zero.
P=E/t
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Part A.
To get the acceleration of the system we consider the two blocks as a single mass. For this situation we have, from Newton's second law, that:
where T is the tension in the upper sting and W is the weight of the system. Solving the equation for a we have:
Therefore the acceleration of the system is 2.42 meters per second per second.
Part B.
Now, that we have the acceleration of the system we analyze the lower block individually; for this block the equation of motion is:
where T' is the tension in the lower rope, W' is the weight of the lower block and m2 is its mass. Solving for the tension we have that:
Therefore the tension in the lower rope is 2.93 N
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