1. A ball of mass m falls from height h, to height he near the h, it has a speed
ID: 1784475 • Letter: 1
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1. A ball of mass m falls from height h, to height he near the h, it has a speed vr Ignore air resistance a. u=0 surface of the Earth, as shown at right. When the ball passes h Consider system S, consisting of the ball and the Earth. i. As the ball falls from h, to h, does the total energy of system S increase, decrease, or stay the same? Earth Earth Explain by considering the net work by external forces on system S ii. Consider the following discussion: Student 1: The changes to system S are all internal, so its gravitational potential energy doesn't change. Since the kinetic energy of the ball increases, the total energy of system S increases. Student 2: "I think that the change in potential energy of the system is zero because the distance the ball moves is small compared to the size of the earth. The change in total energy of system S is equal to the change in kinetic energy of the ball." With which student, if either, do you agree? Explain. ii. Write an expression for each of the following quantities in terms of the given variables and any physical constants. If any of these are zero, state so explicitly. the change in kinetic energy of system S the change in potential energy of system S the net work by external forces on system S iv. Write an equation that relates the expressions above. v. Solve your equation from part iv for the final speed of the ball. Is your result consistent with what you would obtain using kinematics and your knowledge of the acceleration due to gravity near the Earth's surface? If not, resolve the inconsistency ©Pearson Tutorials in Introductory Physics McDermott, Shaffer, and the P.E.G., U. Wash. Custom 2 nd Ed., for U.CO, BoulderExplanation / Answer
i. as the ball falls , total mechanical energy of the earth ball system remains the same. it is due to , when ball falls, its potential energy decrease and same amount of energy appears in the kinetic energy, which eventally increases the speed of the ball.talking about external forces, there is no such external force. gravitational force is internal force.
ii. i do not agree with any of the students statements. both are incorrrect. even though radius of the earth is very large, potentail enery changes which increse or decrese the kinetic energy.
iii. (KE+PE)i= (KE+PE)f
1/2 mv^2-GMm/r=1/2mV^2-GMm/R
V=(v^2+2Gmm(1/R-1/r))^0.5
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