Question

**Learning Goal:**

To understand how to apply the law of conservation of energy to situations with and without nonconservative forces acting.

The law of conservation of energy states the following:

In an isolated system the total energy remains constant.

If the objects within the system interact through gravitational
and elastic forces only, then the total *mechanical* energy
is conserved.

The mechanical energy of a system is defined as the sum of
*kinetic energy* *K* and *potential energy*
*U*. For such systems in which no forces other than the
gravitational and elastic forces do work, the law of conservation
of energy can be written as

*K*i+*U*i=*K*f+*U*f,

where the quantities with subscript "i" refer to the "initial" moment and those with subscript "f" refer to the final moment. A wise choice of initial and final moments, which is not always obvious, may significantly simplify the solution.

The kinetic energy of an object that has mass *m* and
velocity *v* is given by

*K*=12*m**v*2.

Potential energy, in contrast, has many forms. Two forms that
you will be dealing with often are *gravitational* and
*elastic* potential energy. Gravitational potential energy
is the energy possessed by elevated objects. For small heights, it
can be found as

*U*g=*m**g**h*,

where *m* is the mass of the object, *g* is the
acceleration due to gravity, and *h* is the elevation of the
object above the *zero level*. The zero level is the
elevation at which the gravitational potential energy is assumed to
be zero. The choice of the zero level is dictated by convenience;
typically (but not necessarily), it is selected to coincide with
the lowest position of the object during the motion explored in the
problem.

Elastic potential energy is associated with stretched or
compressed elastic objects such as springs. For a spring with a
force constant *k*, stretched or compressed a distance
*x*, the associated elastic potential energy is

*U*e=12*k**x*2.

When all three types of energy change, the law of conservation
of energy for an object of mass *m* can be written as

12*m**v*2i+*m**g**h*i+12*k**x*2i=12*m**v*2f+*m**g**h*f+12*k**x*2f.

The gravitational force and the elastic force are two examples of conservative forces. What if nonconservative forces, such as friction, also act within the system? In that case, the total mechanical energy will change. The law of conservation of energy is then written as

12*m**v*2i+*m**g**h*i+12*k**x*2i+*W*nc=12*m**v*2f+*m**g**h*f+12*k**x*2f,

where *W*nc represents the work done by the
nonconservative forces acting on the object between the initial and
the final moments. The work *W*nc is usually
*negative*; that is, the nonconservative forces tend to
decrease, or*dissipate*, the mechanical energy of the
system.

In this problem, we will consider the following situation as
depicted in the diagram: (Figure 1) A block of mass *m*
slides at a speed *v* along a horizontal smooth table. It
next slides down a smooth ramp, descending a height *h*, and
then slides along a horizontal rough floor, stopping eventually.
Assume that the block slides slowly enough so that it does not lose
contact with the supporting surfaces (table, ramp, or floor).

You will analyze the motion of the block at different moments using the law of conservation of energy.

**Using conservation of energy, find the speed vb
of the block at the bottom of the ramp.**

**Express your answer in terms of some or all the
variables m, v, and h and any
appropriate constants.**

Answer #1

Set the ground level as zero gravitational potential energy. Use
conservation of energy to solve for the final velocity of the
sliding block on the frictionless surface (it will be a function of
the incline height, ℎ). Note: the block starts from rest. Show your
work below or on your own separate page.
3 5. Using conservation of energy, solve for the final
translational velocity of the center of mass, ?, of a rolling
object with moment of inertia, ?,...

Revisiting the ballistic pendulum. In lab we used both
conservation of momentum and conservation of energy to relate the
launch speed of a projectile to the maximum height of the swing of
a pendulum. Here we will study the parts of this problem in a bit
more detail.
(a) Briefly explain why momentum is conserved during the
collision of the projectile and the pendulum, but mechanical energy
is not conserved.
(b) Briefly explain why mechanical energy (kinetic plus
potential energy)...

As you know, a common example of a harmonic oscillator is a mass
attached to a spring. In this problem, we will consider a
horizontally moving block attached to a spring. Note that,
since the gravitational potential energy is not changing in this
case, it can be excluded from the calculations.
For such a system, the potential energy is stored in the spring
and is given by
U=12kx2,
where k is the force constant of the spring and
x is...

Question 1 (1 point)
Which is not necessary in order to do work on an object (use the
scientific definition of work)?
Question 1 options:
There must be a change in momentum.
A net force must be applied to the object.
The object must undergo a displacement.
A component of the force must be in the direction of motion.
Question 2 (1 point)
The change in gravitational potential energy for a 1.9 kg box
lifted 2.2 m is:
Question 2...

1.The momentum of an object is not dependent on which one of
the following quantities?
a) acceleration b) inertia
c) mass
d) velocity
2.Which one of the following statements concerning the
momentum of a system when the net force acting on the system has a
positive value is true?
a) The momentum of the system is increasing.
b) The momentum of the system is decreasing.
c) The momentum of the system is equal to zero kg m/s. d)
The...

Questions (use complete sentences)
1) What is a conservation law? What is the basic approach taken
when using a conservation law?
2) Could the linear momentum of a turtle be greater than the
linear momentum of a horse? Explain.
3) Carts A and B stick together whenever they collide. The mass
of A is twice that of B. How could you roll the carts so that they
would be stopped after a collision?
4) How can a satellite’s speed decrease...

1)
a) A block of mass m slides down an inclined plane starting
from
rest. If the surface is inclined an angle theta above the
horizontal,
and the block reaches a speed V after covering a distance D along
the
incline, what is the coefficient of kinetic friction?
b) at a distance D1 (still on the incline), the block
comes to an
instantaneous standstill against a spring with spring constant k.
How
far back up does the block? Why do...

Q1.Energy is defined as
the ability to do work.
the conservation of displacement.
the distance traveled divided by time.
the time rate of doing work.
Q2.While rearranging a dorm room, a student does 300 J
of work in moving a desk 2.0 m. What was the magnitude of the
applied horizontal force?
150 N
600 N
0 N
2940 N
Q3.Power
is force divided by time.
is work divided by time.
is work times time.
has the same units as...

Two boxes are stacked, with box B placed on top of box A. If box
A is pushed such that both boxes move with a decreasing speed, is
there any friction on either box?
(a) Kinetic friction on box A and no friction on box B (b)
Kinetic friction on box A and static friction on box B
(c) Kinetic friction on box A and kinetic friction on box B (d)
Static friction on box A and kinetic friction on...

ch 6
1:
It is generally a good idea to gain an understanding of the
"size" of units. Consider the objects and calculate the kinetic
energy of each one.
A ladybug weighing 37.3 mg
flies by your head at 3.83 km/h
.
×10
J
A 7.15 kg
bowling ball slides (not rolls) down an alley at 17.5 km/h
.
J
A car weighing 1260 kg
moves at a speed of 49.5 km/h.
5:
The graph shows the ?-directed force
??...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 25 minutes ago

asked 32 minutes ago

asked 44 minutes ago

asked 48 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago