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Chapter 7: Q15Q (page 317)

Question: Figure 7.48 is a portion of a graph of energy terms vs, time for a mass on a spring, subject to air resistance. Identify and label the three curves as to what kind of energy each represents. Explain briefly how you determined which curve represented which kind of energy.

Short Answer

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Answer

Curve Ahas potential energy U=Ug+Us, curve Bhas kinetic energy Kand the curve Chas total energyE=K+U .

Step by step solution

01

Definition of Energy

The energy is the capacity to perform work in physics. The potential energy, kinetic energy, thermal energy, electrical energy, chemical energy, nuclear energy, and other kinds of energy are all examples of potential energy. There is also heat and work (energy transmitted from one body to another).

02

Analysing all the labels of the curve 

Let the mass is initially motionless.

The potential energy can only exist in the initial condition when both gravitational and elastic exists.

From the given graph, the curve A has the system's potential energy.

As the system is initially motionless so, the total energy of the system in curve Ais equals to the potential energy at this time that is U=Ug+Us.

The mass acquires kinetic energy when potential energy falls due to the stretching (or compressing) of the spring.

From the given figure, the curve Bis designated as the system's kinetic energy.

The equilibrium position is reached when U is at its lowest and K is at its highest.

From the given figure, the curve C has been determined as the system's total energy.

Therefore, it is concluded that, Curve Ahas potential energyU=Ug+Us , curve Bhas kinetic energy Kand the curve Chas total energy E=K+U.

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Most popular questions from this chapter

8.0脳1020kgA package of mass 9kgsits on an airless asteroid of massand radius 8.7脳105m. We want to launch the package in such a way that it will never come back, and when it is very far from the asteroid it will be traveling with speed 226 m/s. We have a large and powerful spring whose stiffness is 2.8脳105N/m. How much must we compress the spring?

When a falling object reaches terminal speed, its kinetic energy reaches a constant value. However, the gravitational energy of the system consisting of object plus Earth continues to decrease. Does this violate the principle of conservation of energy? Explain why or why not.

Write an equation for the total energy of a system consisting of a mass suspended vertically from a spring, and include the Earth in the system. Place the origin for gravitational energy at the equilibrium position of the mass and show that the changes in energy of a vertical spring-mass system are the same as the changes in energy of a horizontal spring-mass system.

Niagara Falls is about 50m high. What is the temperature rise in kelvins of the water from just before to just after it hits the rocks at the bottom of the falls, assuming negligible air resistance during the fall and that the water doesn't rebound but just splats onto the rock? It is helpful (but not essential) to consider a 1g drop of water.

180鈥塯 of boiling water (temperature 100鈥�0C, heat capacity 4.2鈥塉/K/g) are poured into an aluminum pan whose mass is 1050 g and initial temperature 26鈥�0C(the heat capacity of aluminum is 0.9鈥塉/K/g).

(a) After a short time, what is the temperature of the water?

(b) What simplifying assumptions did you have to make? (1) The thermal energy of the water doesn't change. (2) Thermal energy of the aluminum doesn't change. (3) Energy transfer between the system (water plus pan) and the surroundings was negligible during this time. (4) The heat capacities for both water and aluminum hardly change with temperature in this temperature range.

(c) Next you place the pan on a hot electric stove. While the stove is heating the pan, you use a beater to stir the water, doing 29541 J of work and the temperature of the water and pan increases to 86.9鈥�0C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?
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