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
1
m v 2  U  x   const 
2
v12  v02 
2
U  x0   U  x1  
m
2
8.0 J / m2  1.0 m 2   2.0 J / m4  1.0 m 4 
v   5.0 m / s  

 0.20 kg  
2
1
2
 125  m / s 
2
v1  11. 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.
coefficient of kinetic friction is 0.25.
The
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
 = 0.25
2.2 kg
25
E  W f    mg cos  L
   0.25  2.2 kg  9.8 m / s 2   cos 25  2.0 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.
v
m / 2k
2.
v
m/k
3.
(1/4) m v2
4.
m v2 / 4k
5.
v
4
m/k
1
1
1

m v2  K  k x2  2  k x2 
2
2
2

xv
m
2k
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
U  mgh   700 N 10m  2m   8400 J
10 m
2m
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
2
1
1
3
2
2
2

6  10 kg  v  10.0 N / m   5.00  10 m   1.00  10 m  



2
2
v  2.00 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.
mg/2
2.
mg
3.
2mg
4.
3mg
5.
mgr
v2
T  mg  m
r
1 2
mv  m g r
2

T  3mg
T
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.
2R
5.
zero
mg y 
1 2
mv
2
mv 2
 mg  n  mg
R

1
mg y  mgR
2

y
1
R
2
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.
2gL
2.
3gL
3.
4gL
4.
5gL
5.
7gL
At top,
T=0:
v2
g
L
E Conservation :


v 2  gL
1
1 2
2
m V  mv  2mg L
2
2
V 2  v 2  4 g L  5gL
V  5g L
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
1.
2.
its mechanical energy is a minimum
the forces on it are balanced
3.
it is not accelerating
4.
its speed is a minimum
5.
it experiences a net upward force
mv 2
F
yˆ
r
E  const
F
a
m
1 2
mv  E  mg ymax
2