Transcript Q05. Using Newtons Laws
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
/
m
2 )
x
2 + (2.0
J
/
m
4 )
x
4 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.
2.
3.
4.
5.
0 2.5 5.7 7.9 11
m m m m
/ / / /
s s s s
1 2
m v
2
v
1 2 5.0
125 2
const
v
1 2
v
0 2 2
m
2 0.20
kg
8.0
/ 2 1.0
m
2 2.0
/ 4 1.0
m
4
v
1 11.
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.
2.
3.
4.
5.
0 –9.8 J 9.8 J –4.6 J 4.6 J
W f
mg
cos
L
9.8
J
kg
9.8
2 cos 25 2.0
m
2.2 kg 25 = 0.25
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
/ 2
k
2.
3.
4.
5.
v
(1/4)
m v
2
m v
2 / 4
k v
4
1 2
m v
2
K
1 2
k x
2 1 2
k x
2
x
v m
2
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.
2.
3.
4.
5.
300
J
710
J
850
J
7000
J
8400
J
U
mgh
700
N
10
m
2
m
8400
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.
2.
3.
4.
5.
6.32 1.63 2.00 2.08 2.45
m m m m m
/ / / / /
s s s s s
1 2 3 2 1 2 10.0
v
2.00
2
m
2
m
2 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.
3.
4.
5.
m g
2
m g
3
m g m g r
T
mg
m v
2
r
1 2
mv
2
m g r T
3
mg 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.
2.
3.
4.
5.
R R R
2
R
/4 /2 zero
m g y
1 2
mv
2
mv
2
mg R mg m g y
1 2
mgR
y
1 2
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.
2
g L
3
g L
4
g L
5
g L
7
g L
At top,
T
= 0 :
v
2
g L
v
2
gL E
Conservation : 1 2
m V
2 1 2
mv
2 2
mg L
V
2
v
2 4
g L
5
g L V
5
g 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.
2.
3.
4.
5.
its mechanical energy is a minimum the forces on it are balanced it is not accelerating its speed is a minimum it experiences a net upward force
1.
2.
3.
4.
5.
its mechanical energy is a minimum the forces on it are balanced
F
mv
2
r
it is not accelerating its speed is a minimum it experiences a net upward force 1 2
mv
2
E
const
a
F
m mg y
max