CALC A proton with mass m moves in one dimension. The potential-energy function is U ( x ) = ( α/x 2 ) − ( β/x ), where α and β are positive constants. The proton is released from rest at x 0 = α/β. (a) Show that U ( x ) can be written as U ( x ) = α x 0 2 [ ( x 0 x ) 2 − x 0 x ] Graph U ( x ). Calculate U ( x 0 ) and thereby locate the point x 0 on the graph. (b) Calculate v ( x ), the speed of the proton as a function of position. Graph v ( x ) and give a qualitative description of the motion. (c) For what value of x is the speed of the proton a maximum? What is the value of that maximum speed? (d) What is the force on the proton at the point in part (c)? (e) Let the proton be released instead at x 1 = 3 α / β . Locate the point on the graph of U ( x ). Calculate v ( x ) and give a qualitative description of the motion. (f) For each release point ( x = x 0 and x = x 1 ), what are the maximum and minimum values of x reached during the motion?
CALC A proton with mass m moves in one dimension. The potential-energy function is U ( x ) = ( α/x 2 ) − ( β/x ), where α and β are positive constants. The proton is released from rest at x 0 = α/β. (a) Show that U ( x ) can be written as U ( x ) = α x 0 2 [ ( x 0 x ) 2 − x 0 x ] Graph U ( x ). Calculate U ( x 0 ) and thereby locate the point x 0 on the graph. (b) Calculate v ( x ), the speed of the proton as a function of position. Graph v ( x ) and give a qualitative description of the motion. (c) For what value of x is the speed of the proton a maximum? What is the value of that maximum speed? (d) What is the force on the proton at the point in part (c)? (e) Let the proton be released instead at x 1 = 3 α / β . Locate the point on the graph of U ( x ). Calculate v ( x ) and give a qualitative description of the motion. (f) For each release point ( x = x 0 and x = x 1 ), what are the maximum and minimum values of x reached during the motion?
CALC A proton with mass m moves in one dimension. The potential-energy function is U(x) = (α/x2) − (β/x), where α and β are positive constants. The proton is released from rest at x0 = α/β. (a) Show that U(x) can be written as
U
(
x
)
=
α
x
0
2
[
(
x
0
x
)
2
−
x
0
x
]
Graph U(x). Calculate U(x0) and thereby locate the point x0 on the graph. (b) Calculate v(x), the speed of the proton as a function of position. Graph v(x) and give a qualitative description of the motion. (c) For what value of x is the speed of the proton a maximum? What is the value of that maximum speed? (d) What is the force on the proton at the point in part (c)? (e) Let the proton be released instead at x1 = 3α/β. Locate the point on the graph of U(x). Calculate v(x) and give a qualitative description of the motion. (f) For each release point (x = x0 and x = x1), what are the maximum and minimum values of x reached during the motion?
Problem
A moving electron has a Kinetic Energy K1. After a net amount of work is done on it, the electron is moving one-quarter as fast in the opposite direction. What is the work done
W in terms of Kq?
Solution
To solve for the work done, first we must determine what is the final kinetic energy of the electron.
By concept, we know that
K1=(1/2)mv²,
K2=(1/2)mv2
But it was mentioned that:
so, Kz in terms of v is
K2=(
)mv²1
Substituting the expression for K1 results to
K2=(
Since work done is
W=AK=K
-K
Evaluating results to
W=(
)K1
Question 11: The force associated with the following potential energy
U (x, y, z) = –kxy² z3
is the only force acting on a particle of mass m. Here, k is a constant. The
particle is initially at rest and at the origin. Assuming that the particle is
passing through position (x = 1 meter, y = 1 meter, z = 2 meter), find the
speed of the particle at that position.
Select one:
O V2k/m
O 2/2k/m
O Vk/m
O 4/k/m
2/k/m
II. A) What are the gravitational potential energies for Peter (mass is 80.0 kg), David (mass is 60.0 kg),
and Mark (mass is 75.0 kg) from the graph. Choose the ground as the zero potential energy level, take g
10.0 m/s. B) How much work the gravitational force has to do to bring Mark and David to the ground
(think about positive and negative work)?
Daviel
4.00m
Peter
Ground
help!
3 Mark
5.00m
Chapter 7 Solutions
University Physics with Modern Physics (14th Edition)
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