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60
1. What is the mass M in the system as given in the
Figure if m=8.0 kg ?
mg  2T sin 60 C
T  Mg
 M  4.6 Kg
 
M
m
2. If M = 1.1 kg, what is the tension in string 1?
Mg  T1 sin 40  T2 cos 40
(1)
cos 40
T2 cos 50  T1 cos 40  T2  T1
cos 50
From (1)


cos 2 40

 T1[

sin
40
]  Mg  T1  40 N
cos 50
T2
50
40
T1
3. At an instant when a 4.2 kg object has an acceleration equal to (5i + 3j)
m/s2, one of the two forces acting on the object is known to be (12i + 22j)
N. Determine the magnitude of the other force acting on the object.
 




m(5i  3 j )  12i  22 j  F2 x i  F2 y j Newton’s second law)




 9i  9.4 j  F2 x i  F2 y j  F2  92  (9.4) 2  13.0 N
4. A 5.0-kg mass is suspended by a string from the ceiling of an
elevator that is moving upward with a speed which is decreasing at a
constant rate of 2.0 m/s in each second. What is the tension in the
string supporting the mass?
T
v
a
t
 2.0m / s 2
ma  T  mg

a
 T  m(a  g )  39 N
mg
5.The apparent weight of a fish in an elevator is greatest when the elevator
a.
b.
c.
d.
e.
moves downward at constant velocity.
moves upward at constant velocity.
accelerates downward.
accelerates upward.
is not moving.
ma  T  mg  T  m(a  g )
(d)
Like the picture
Above in 4.
6. If P = 6.0 N, what is the magnitude of the force exerted on block 1 by
block 2?
p
2kg
T1
T1
3kg
T2
2a  p  T1  T1  p  2a
(5  3  2)a  p  a  0.6m / s 2
 T1  6  2  0.6  4.8 N
5kg
T2
7.
Two identical springs with spring constant 50 N/m support
a 5.0 N weight as in the picture below. What is the change in
length of each spring when the weight is hung on the springs.?
5 N  2kL cos 30
8.
 L  5.8cm
All three bodies have the same mass
m and k  0.20 . Find the acceleration.
3ma  mg  2 k mg
m
 a  2.0m / s 2
m
k
9. As a particle moves along the x axis it is acted upon by a single
conservative force given by Fx = (20 – 4.0 x) N where x is in m. The
potential energy associated with this force has the value +30 J at the
origin (x = 0). What is the value of the potential energy at x = 4.0 m?
W  u  [u f  ui ]  u f  ui
4
W   (20  4 x)dx  u f  ui  u f  18.0 J
0
m
10. A 2.0-kg particle has an initial velocity of (5i – 4j) m/s. Some
time later, its velocity is (7i + 3j) m/s. How much work was done by
the resultant force during this time interval, assuming no energy is
lost in the process?
1
1
2
2
mv f  mvi
2
2
49  9
vi  25  16
W  KE 
vf 
 W  17 J
11. The force an ideal spring exerts on an object is given by Fx = –kx,
where x measures the displacement of the object from its equilibrium
(x = 0) position. If k = 60 N/m, how much work is done by this force as
the object moves from
0
  kxdx  1.2 J
0.2
12. The horizontal surface on which the block slides is frictionless.
The speed of the block before it touches the spring is 6.0 m/s. How
fast is the block moving at the instant the spring has been
compressed 15 cm? ( k = 2.000 N/m, M=2.0 kg))
1
1
1
2
2
mvi  kx2  mv f  v f
2
2
2
13. A 0.60-kg object is suspended from the ceiling at the end of a
2.0-m string. When pulled to the side and released, it has a speed
of 4.0 m/s at the lowest point of its path. What maximum angle
does the string make with the vertical as the object swings up?
mgL(1  cos  ) 

1
mv 2
2

14. A 20-kg mass is fastened to a light spring (k
= 380 N/m) that passes over a pulley as shown.
The pulley is frictionless, and the mass is
released from rest when the spring is
unstretched. After the mass has dropped 0.40 m,
what is its speed?
00 
1 2 1 2
kd  mv  mgd  v
2
2
15. A 1.2-kg mass is projected up a rough circular track (radius =
0.80 m) as shown. The speed of the mass at point A is 8.4 m/s, and at
point B, it is 5.6 m/s. How much work is done on the mass between
A and B by the force of friction?
1
1
2
2
W f  mvA  mvB  mg 2 R  W f  4.7 J
2
2
16. The gravitational potential energy U of an object of mass
m=10.2 kg near the Earth’s surface is shown in the Figure, where
y=0 corresponds to the ground. Assume that the mechanical energy is
200 J and neglect friction.
What is the force acting on the object at the location where the
kinetic energy is equal to the potential energy
F 
dU 
 100 J

dx  y  2 m
since U(x) is a straight line
17. A blimp is filled with 200 m3 of helium. How much mass can the
balloon lift? The density of helium is 1/7 that of air, and the density of air
is 1.25 kg/m3.
B   airVHe g   He VHe g  Mg  M  214kg
18. A waiter in a restaurant fills a pitcher full of water and ice so that water
would spill out if any more were added. As the ice starts to melt
a.
the water level in the pitcher falls.
b.
the water level in the pitcher remains the same.
c.
water starts to flow out the spout of the pitcher.
d.
the pressure on the bottom of the pitcher decreases
Answer: b) : level remains the same, since the ice displays its volume after
melting and the water level is retained.,
19. A container filled with water to
a depth H=2.5 m. The container is
tightly sailed and above the water
the pressure is P1=1.34x105 N/m2.
A small hole is punched at a height
h=1.0 above the bottom of the
container. What is the velocity of
the water through the hole?
p1  W g ( H  h) 
P1
H
Water
1
W v2 2  p0  v2  1.74m / s
2
20. Water (density 1000 kg/m3) flowing in a horizontal pipe discharges at
The rate of 4x10-3 m3/s. At a point in the pipe where the cross-section area
is 1.0 x10-3 m2 the pressure is 1.60x105 N/m2 . What is the cross-section
area of a concentration in the pipe if the pressure there is reduced to
1.6x105 N/m2 ?. Give your answer in cm2.
m3
Av1  4  10
 v1  4m / s
s
1
1
2
2
p1  v1  p2  v2  v2  9.79m / s
2
2
A1v1  A2 v2  A2  4.1cm 2
3
h