Q07.Conservation of Energy
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Transcript of Q07.Conservation of Energy
Q07. Conservation of Energy
1. A 0.20-kg particle moves along the x-axis under the influence of a stationary object. The potential energy is given by :
U(x) = (8.0 J/m2) x2 + (2.0 J/m4) x4
where x is in coordinate of the particle. If the particle has a speed of 5.0 m/s when it is at x = 1.0 m, its speed when it is at the origin is:
1. 0
2. 2.5 m/s
3. 5.7 m/s
4. 7.9 m/s
5. 11 m/s
21
2mv U x const 2 2
1 0 0 1
2v v U x U x
m
2 2 42 2 41
25.0 / 8.0 / 1.0 2.0 / 1.0
0.20v m s J m m J m m
kg
2125 /m s
1 11. /v m s
2. A 2.2-kg block starts from rest on a rough inclined plane
that makes an angle of 25° with the horizontal. The
coefficient of kinetic friction is 0.25. As the block
goes 2.0 m down the plane, the mechanical energy of the
Earth-block system changes by:
1. 0
2. –9.8 J
3. 9.8 J
4. –4.6 J
5. 4.6 J
cosfE W mg L
25
2.2 kg = 0.25
20.25 2.2 9.8 / cos25 2.0kg m s m
9.8 J
3. A block of mass m is initially moving to the right on a
horizontal frictionless surface at a speed v. It then
compresses a spring of spring constant k. At the
instant when the kinetic energy of the block is equal to
the potential energy of the spring, the spring is
compressed a distance of:
1.
2.
3. (1/4) m v2
4. m v2 / 4k
5.
/ 2v m k
/4
vm k
/v m k
2 2 21 1 12
2 2 2mv K k x k x
2
mx v
k
4. A 700-N man jumps out of a window into a fire net 10 m
below. The net stretches 2 m before bringing the man
to rest and tossing him back into the air. The
maximum potential energy of the net, compared to it's
unstretched potential energy, is:
1. 300 J
2. 710 J
3. 850 J
4. 7000 J
5. 8400 J
700 10 2 8400U mgh N m m J
10 m
2 m
5. A toy cork gun contains a spring whose spring constant
is 10.0 N/m. The spring is compressed 5.00 cm and then
used to propel a 6.00-g cork. The cork, however, sticks
to the spring for 1.00 cm beyond its unstretched length
before separation occurs. The muzzle velocity of this
cork is:
1. 6.32 m/s
2. 1.63 m/s
3. 2.00 m/s
4. 2.08 m/s
5. 2.45 m/s
2 23 2 2 21 16 10 10.0 / 5.00 10 1.00 10
2 2kg v N m m m
2.00 /v m s
5cm 1cm
6. A small object of mass m, on the end of a light cord, is held
horizontally at a distance r from a fixed support as shown.
The object is then released. What is the tension in the cord
when the object is at the lowest point of its swing?
1. m g / 2
2. m g
3. 2 m g
4. 3 m g
5. m g r
2vT mg m
r
mg
T
21
2mv m g r
3T mg
6. A small object of mass m starts at rest at the position shown
and slides along the frictionless loop-the-loop track of radius
R. What is the smallest value of y such that the object will
slide without losing contact with the track ?
1. R /4
2. R /2
3. R
4. 2 R
5. zero
21
2mg y mv
2mvmg n mg
R
1
2mg y mgR
1
2y R
7. A ball of mass m, at one end of a string of length L,
rotates in a vertical circle just fast enough to prevent the
string from going slack at the top of the circle. The speed
of the ball at the bottom of the circle is:
1.
2.
3.
4.
5.
3gL
2gL
7gL
5gL
4gL
2vg
L 2v gL
2 21 12
2 2m V mv mgL
2 2 4V v gL 5gL
5V gL
At top, T = 0 :
E Conservation :
8. A rectangular block is moving along a frictionless path
when it encounters the circular loop as shown. The block
passes points 1,2,3,4,1 before returning to the horizontal
track. At point 3:
1. its mechanical energy is a minimum
2. the forces on it are balanced
3. it is not accelerating
4. its speed is a minimum
5. it experiences a net upward force
E const1. its mechanical energy is a minimum
2. the forces on it are balanced
3. it is not accelerating
4. its speed is a minimum
5. it experiences a net upward force
2
ˆmv
rF y
mF
a
2max
1
2mv E mg y