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A $1-$ lb stone is dropped down the "bottomless pit" at Carlsbad Caverns and strikes the ground with a speed of $95 \mathrm{ft} / \mathrm{s}$. Neglecting air resistance, $(a)$ determine the kinetic energy of the stone as it strikes the ground and the height $h$ from which it was dropped. $(b)$ Solve part $a$ assuming that the same stone is dropped down a hole on the moon. (Acceleration of gravity on the moon $=5.31 \mathrm{ft} / \mathrm{s}^{2}$.)

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a. $=140.1 \mathrm{ft}$b. $h=849.8114 \approx 850 \mathrm{ft}$

Physics 101 Mechanics

Chapter 13

Kinetics of Particles: Energy and Momentum Methods

Work

Moment, Impulse, and Collisions

Energy Conservation

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04:30

In classical mechanics, impulse is the integral of a force, F, over the time interval, t, for which it acts. In the case of a constant force, the resulting change in momentum is equal to the force itself, and the impulse is the change in momentum divided by the time during which the force acts. Impulse applied to an object produces an equivalent force to that of the object's mass multiplied by its velocity. In an inertial reference frame, an object that has no net force on it will continue at a constant velocity forever. In classical mechanics, the change in an object's motion, due to a force applied, is called its acceleration. The SI unit of measure for impulse is the newton second.

04:05

In physics, a conservative force is a force that is path-independent, meaning that the total work done along any path in the field is the same. In other words, the work is independent of the path taken. The only force considered in classical physics to be conservative is gravitation.

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high in the given problem. Mask off the stone is £1 the speed with which it it strikes. The ground has given us 95 fit for second, and acceleration due to gravity in FPs system is having a value 32.17 fit per second squared. So in the first part of the problem, first of all, we have to find the kinetic energy off this stone when it strikes the ground. So using the usual expression for kinetic energy Uh huh. And these were this clinic. Energy comes out Toby half into £1 multiplied by 95 fit our second to the whole square, which, if you find if you calculate, this value comes out. Toby 4000 512 0.5 found fit. This is one off the answer for first part off the problem. The answer for kinetic energy? No. In the same part of the problem in the first part, we have to find the height from which the stone is dropped. So for that purpose, we will use the energy conservation. So using the concept that kinetic energy at the ground level is equal to potential energy at the point from which the stone waas dropped. So for kind of technology, this is half and we square for potential energy thesis M g h canceling this m The expression for H comes out Toby. We square by two g so plugging in the known values this is 95 to the whole square, divided by two in 2 32.17 So this edge from which the stone was dropped comes out Toby 740.6 hit. This is the second answer for the first part off the problem. No. In the second part of the problem, they are saying if the stone is dropped on the surface off moon So what will be these two answers hands we can see on the surface off moon. The answer for Connecticut energy will remain same. That is given us half and the Squire so no change off acceleration due to gravity due to exploration to gravity. So the kind of technology remains same. 4512.5 found fit. But answer for this second part means height from which the stone was dropped. It will be changed because it includes the acceleration due to gravity so each dash will be equals Toe We square by two g dash for we This is 95 having whole square to into the value off acceleration due to gravity on the surface of wool has been given us 5.31 So this edge dash here comes out Toby 849.8 fit or we can say this is 850 ft. So this is the answer for the second part off the problem. Thank you.

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