## MasteringPhysics Assignment Print View

[Return to Standard Assignment View ] What Velocity vs. Time Graphs Can Tell You A common graphical representation of motion along a straight line is the v vs. t graph, that is, the graph of (instantaneous) velocity as a function of time. Fuel better learning: Mastering creates truly personalized online learning experiences that help students make real progress in their courses and in their lives. Having . MasteringPhysics: Assignment Print View 30 of 37 9/16/07 AM Introduction to MC Problem Format Learning Goal: To introduce you to the format of a problem with hints and subparts. This question will introduce you to the format of a problem in MasteringChemistry. Problems consist of several fundamental parts%(5).

Multiple choice questions are penalized as described in the online help. You are allowed 7 attempts per answer. Ups and Downs Description: Several qualitative and conceptual questions involving objects launched upward in the gravitational field of Earth in the absence of non-conservative forces. Learning Goal: To apply the law of conservation of energy to an object launched upward in the gravitational field of the earth. In the absence of nonconservative forces such as friction and air resistance, the total mechanical energy in a closed system is conserved.

This is one masteringphysics assignment print view case of the law of conservation of energy. In this problem, you will apply the law of conservation of energy to different objects launched from the earth. The energy transformations that take place involve the object's kinetic energy and its gravitational potential energy.

The law of conservation of energy for such cases implies that masteringphysics assignment print view sum of the object's kinetic energy and potential energy does not change with time. This idea can be expressed by the equationwhere "i" denotes the "initial" moment and "f" denotes the "final" moment. Since any two moments will work, the choice of the moments to consider is, technically, up to you.

That choice, though, is usually suggested by the question posed in the problem. First, let us consider an object launched vertically upward with an initial speed. Neglect air resistance, masteringphysics assignment print view. Part A As the projectile goes upward, what energy changes take place?

ANSWER: j k l m n is negative j k l m n is positive j is zero k l m n i depends on the choice of the "zero level" of potential energy j k l m n Usually, the zero level is chosen so as to make the relevant calculations simpler. In this case, it makes good sense to assume that at the ground level--but this is not, by any means, the only choice! Part D Using conservation of energy, find the maximum height to which the object will rise. Express your answer in terms of and the magnitude of the acceleration of gravity, masteringphysics assignment print view.

It is comforting to know that our new approach yields the same answer. Part E At what height above the ground does the projectile have a speed of?

Hint F. You know that at the initial heightthe speed is. All of the energy is kinetic energy, masteringphysics assignment print view, and so, the total energy is. At the maximum height, all of the energy is potential energy, masteringphysics assignment print view. Since the gravitational potential energy is proportional tohalf of the initial kinetic energy must have been converted to potential energy when the projectile is at.

Thus, the kinetic energy must be half of its original value i. You need to determine the speed, as a multiple ofthat corresponds to such a kinetic energy. Express your answer in terms of and. Use three significant figures in the numeric coefficient.

For such situations, using conservation of energy leads to a quicker solution than can be produced by kinematics. Part G A ball is launched as a projectile with initial speed at masteringphysics assignment print view angle above the horizontal. Using conservation of energy, find the maximum height of the ball's flight.

Part G. Here, the best choice of "final" moment is the point at which the ball reaches its maximum height, since this is the point we are interested in. The slope makes an angle with the horizontal, masteringphysics assignment print view. Using conservation of energy, find the maximum vertical height to which the ball will climb. Express your answer in terms of, and. You may masteringphysics assignment print view may not use all of these quantities. The difference between this situation and the projectile case is that the ball moving up a slope has no kinetic energy at masteringphysics assignment print view top of its trajectory whereas the projectile launched at an angle does.

Part I A ball is launched with initial speed from the ground level up a frictionless hill, masteringphysics assignment print view. The hill becomes steeper as the ball slides up; however, the ball remains in contact with the hill at all times. Description: Several questions that require the students to predict the characteristics of the particle's motion direction of force, acceleration, equilibrium positions, etc, masteringphysics assignment print view. Learning Goal: To be able to interpret potential energy diagrams and predict the corresponding motion of a particle.

Potential energy diagrams for a particle are useful in predicting the motion of that particle, masteringphysics assignment print view. These diagrams allow one to determine the direction of the force acting on the particle at any point, the points of stable and unstable equilibrium, the particle's kinetic energy, etc. Consider the potential energy diagram shown.

The curve represents the value of potential energy as a function of the particle's coordinate. The horizontal line above the curve represents the constant value of the total energy of the particle. The total energy is the sum of kinetic and potential energies of the particle. The key idea in interpreting the graph can be expressed in the equation where is the x component of the net force as function of the particle's coordinate.

Note the negative sign: It means that the x component of the net force is negative when the derivative is positive and vice versa. For instance, if the masteringphysics assignment print view is moving to the right, and its potential energy is increasing, the net force would be pulling the particle to the left.

If you are still having trouble visualizing this, consider the following: If a massive particle is increasing its gravitational potential energy that is, moving upwardthe force of gravity is pulling in the opposite direction that is, downward.

If the x component of the net force is zero, the particle is said to be in equilibrium. There are two kinds of equilibrium: Stable equilibrium means that small deviations from the equilibrium point create a net force that accelerates the particle back toward the equilibrium point think of a ball rolling between two hills.

Unstable equilibrium means that small deviations from the equilibrium point create a net force that accelerates the particle further away from the equilibrium point think of a ball on top of a hill. In answering the following masteringphysics assignment print view, we will assume that there is a single varying force acting on the particle along the x axis.

Therefore, we will use the term force instead of the cumbersome x component of the net force. Hint A. ANSWER: j k l m n directed to the right i j k l m masteringphysics assignment print view directed to the left j equal to zero k masteringphysics assignment print view m n Consider the graph in the region of point A, masteringphysics assignment print view. If the particle is moving to the right, it would be "climbing the hill," and the force would "pull it down," that is, pull the particle back to the left.

Another, more abstract way of thinking about this is to say that the slope of the graph at point A is positive; therefore, the direction of is negative. Hint B. Hint C. ANSWER: j k l m n directed to the right j k l m n directed to the left i equal to zero j k l m n The slope of the graph is zero; therefore, the derivativeand.

Hint D. ANSWER: j k l m n directed to the right j k l m n directed to the left i equal to zero j k l m n If the net force is zero, so is the acceleration. The particle is said to be in a state of equilibrium. Hint E. This implies that the x component of the force on a particle at this location is negative, or that the force is directed to the left, just like at A. What can you say now about the acceleration? This implies that the x component of the force on a particle at this location is positive, or that the force is directed to the right, masteringphysics assignment print view, just like at C.

What can you now say about the acceleration? ANSWER: i j k l m n directed to the right j k l m n directed to the left j equal to zero k l m n As you can see, small deviations from equilibrium at point B cause a force that accelerates the particle further away; hence the particle is in unstable equilibrium. Part G Name all labeled points on the graph corresponding to unstable equilibrium. Hint G. List your choices alphabetically, with no commas or spaces; for instance, if you choose points B, D, and E, type your answer as BDE.

Hint H. Think of a ball rolling between two hills, masteringphysics assignment print view. Hint I. Part J Name all labeled points such that when a particle is released from rest there, it would accelerate to the left.

Part J. If the acceleration is to the left, masteringphysics assignment print view, so is the force. If the x component of the force at a point is negative, then the derivative of at that point is positive. Of these three points, which one corresponds to the greatest magnitude of acceleration of the particle? Hint K. ANSWER: i j k l m n A j k l m n E jG k l m n If the total energy of the particle is known, masteringphysics assignment print view, one can also use the graph of to draw conclusions about the kinetic energy of the particle since.

As a reminder, on this graph, the total energy is shown by the horizontal line. Part L What point on the graph corresponds to the maximum kinetic energy of the moving particle? Hint L. For example, think of a pendulum which has only one force equilibrium point--at the very bottom. Part M At what point on the graph does the particle have the lowest speed? 