homework 08 – – Due: Mar 22 2007, 4:00 am
1
Question 1, chap 7, sect 2.
part 1 of 2
5 points
The force required to stretch a Hooke’s-law
spring varies from 0 N to 22 N as we stretch
the spring by moving one end 6
.
58 cm from
its unstressed position.
Find the force constant of the spring.
Correct answer: 334
.
347 N
/
m (tolerance
±
1
%).
Explanation:
At the extended position, we can write
Hooke’s law, (
F
=
k x
) solved for
k
.
k
=
F
x
=
22 N
0
.
0658 m
= 334
.
347 N
/
m
Question 2, chap 7, sect 2.
part 2 of 2
5 points
Find the work done in stretching the spring.
Correct answer: 0
.
7238 J (tolerance
±
1 %).
Explanation:
Having determined
k
, we can determine the
work done in stretching the spring. This is
just the energy stored in the spring,
W
=
1
2
k x
2
=
1
2
(334
.
347 N
/
m) (0
.
0658 m)
2
= 0
.
7238 J
Question 3, chap 8, sect 1.
part 1 of 1
8 points
A toy gun is powered by a spring with
k
= 359 N
/
m; in the ”charged” position, the
spring is compressed by 2 cm. The gun is
loaded with a 15 g ball, the spring is compre-
seed, the gun is aimed vertically up, and then
ihe spring is released and the ball shoots out.
How high with the ball rise above the point
where the spring becomes un-compressed?
Take
g
= 9
.
8 m
/
s
2
and neglect the air resis-
tance and other frictional forces.
Correct answer: 0
.
468435 m (tolerance
±
1
%).
Explanation:
Let :
m
= 15 g = 0
.
015 kg
,
x
= 2 cm = 0
.
02 m
,
k
= 359 N
/
m
,
and
g
= 9
.
8 m
/
s
2
.
Applying conservation of energy for the mo-
tion,
U
0
+
K
s
=
U
f
−
mg x
+
1
2
k x
2
=
mg h
Thus
h
=
k x
2
2
mg
−
x
=
(359 N
/
m) (0
.
02 m)
2
2 (0
.
015 kg) (9
.
8 m
/
s
2
)
−
0
.
02 m
=
0
.
468435 m
.
Question 4, chap 8, sect 1.
part 1 of 2
10 points
The two blocks are connected by a light
string that passes over a frictionless pulley
with a negligible mass. The block of mass
m
1
lies on a rough horizontal surface with a
constant coe±cient of kinetic friction
μ
. This
block is connected to a spring with spring
constant
k
. The second block has a mass
m
2
.
The system is released from rest when the
spring is unstretched, and
m
2
falls a distance
h
before it reaches the lowest point.
Note:
When
m
2
is at the lowest point, its
velocity is zero.
m
1
m
2
k
m
1
m
2
h
h
μ
Consider the moment when
m
2
has de-
scended by a distance
s
, where
s
is less than
h
.