3. A 2.0-kg projectile moves from its initial position to a point
that is displaced 20 meters horizontally and 15 meters above
its initial position. How much work is done by the
gravitational force on the projectile?
AP Physics
(
)
W = F " y = (2kg) $9.8 kgN (15m)
Chapter 7 Review
W = $294J
!
4
1. A constant force of 12N in the positive x direction acts on a
4.0kg object as it moves from the origin to the point (6i - 8j)
meters. How much work is done by the given force during
this displacement?
4. A 2.5-kg object falls vertically downward in a viscous
m
medium at a constant speed of 2.5sec
. How much work is
done by the viscous force on the object as it falls 80 cm?
(
!
(
)
W = F " y = (2.5Kg) $9.8 KgN (0.8m) = $20J
W = F " x = (12iN ) " 6iˆ m = 72J
)
!
!
2
5
2. A 5.0-kg object is pulled along a horizontal surface at a
constant speed by a 15N force acting 20° above the
horizontal. How much work is done by this force as the
object moves 6.0 meters?
m
5. A 2.0-kg particle has an initial velocity of (5i - 4j) sec
. Some
m
time later, its velocity is (7i + 3j)sec
. What work was done
by the resultant force during this time interval, assuming no
energy is lost in the process?
!
!
W = F " x = Fx cos# =15N (6m) cos20° = 84.6J
2
2
m
v o = 5 + 4 = 41 sec
m
v = 72 + 32 = 58 sec
W = %K
15N
!
!
1
1
W = m(v 2 $ v o2 ) = (2Kg)(58 $ 41) =17J
2
2
5.0 kg
!
!
3
6
!
7. A force acting on an object moving along the x axis is given
by F ( x ) = (14 x $ 3.0x 2 ) N where x is in meters. How much
work is done by this force as the object moves from
x = -1 m to x = +2 m?
!
W=
0
F(N) 4
4
8
x(m)
12
-4
2
& (14 x $ 3x ) dx
2
Slope =
$1
W = (7x 2 $ x
3 2m
)
At 8m F = (0.6 Nm ) x $ 2N = $0.8N
= (28 $ 8) $ (7 + 1) = 12J
-1m
%F [ 4N $ ($2N )]
=
= 0.6 Nm
%x
10m
-
!
1
W = Area = ($2 + ($0.8)) J " (2m ) = $2.8J
2
!
10
7
!
!
8. An object moving along the x axis is acted upon by a force
Fx that varies with position as shown. What work is done
by this force as the object moves from x = 2 m to x = 8 m?
9. A block is pushed across a rough horizontal surface from
point A to point B by a force P as shown in the figure. The
magnitude of the force of friction acting on the block
between A and B is 1.2N and points A and B are 0.5 meters
apart. If the kinetic energies of the block at A and B are 4.0 J
and 5.6 J, respectively, how much work is done on the block
by the force P between A and B?
F(N)
0
4
4
8
12
x(m)
W P $ W f = %K
-4
W P = %K + W f
W P = (5.6J $ 4J ) + (1.2N )(0.5m)
W P = 2.2J
11
8
!
10. A 1.4-kg block is pushed up a frictionless 14° incline from
point A to point B by a force P as shown in the figure. Points
A and B are 1.2 m apart. If the kinetic energies of the block at
A and B are 3 J and 4 J, respectively, how much work is
done on the block by the force P between A and B?
B
F(N)
0
4
4
8
12
x(m)
W P $ W par = %K
-4
W P = %K + W par
P
1.4 Kg
A
14°
W P = %K + mgsin #d
These two areas cancel out!
(
)
W P = (4J $ 3J ) + (1.4kg) 9.8 kgN (sin14°)1.2m
W P = 4.98J
12
9
!
11. The force an ideal spring exerts on an object is given by
F(x) = - kx, where x measures the displacement of the
object from its equilibrium (x = 0) position. If k = 60 Nm ,
how much work is done by this force as the object
moves from x = - 0.20 m to x = 0?
15. A 2.0-kg body moving along the x axis has a velocity vx =
m
5.0 sec
at x = 0. The only force acting on the object is given
by F(x) = (-4.0x) N, where x is in meters. For what value of
x will this object first come (momentarily) to rest?
!
x
!
W = & F ( x ) dx = $ & (4x )dx = $2x 2
1
W = %U = $ & F ( x )dx = $ &$0.2m ($kx)dx = kx 2
2
0
0
%K = K $ K o = $25J
1
2
60 Nm )(0.2m) = 1.2J
(
2
W =
2x 2 = 25
!
x = 3.5m
!
!
16
13
!
12. A 3.0-kg block is dragged over a rough horizontal surface by
a constant force of 15 N acting at an angle of 37° below the
horizontal as shown. The speed of the block increases from
m
m
4.0 sec
to 6.0 sec
in a displacement of 5.0 m. What work was
done by the friction force during this displacement?
W = & F ( x ) dx =
!
!
16. The only force acting on a 0.50-kg object as it moves along
the x axis is given by F(x) = ( 4x 3 ) N where x is measured in
m
meters. If the speed at x = 0 is equal to 3.5sec
, what is its
speed at x = 2.0 meters?
FH = F cos# =15N (cos37°) =12.0N
1
2
2
(3Kg) (6 secm ) $ (4 secm ) = 30J
2
$ %K = W f
W H $W f = %K =
WH
!
(
)
(12N )(5m) $ 30J = W f
!
2m
4 2m
& ( 4x )dx = ( x )
3
0
0
=16J
%K = 12 mv 2 $ 12 mv o2 = 16J
1
2
!
v=
= 30J
mv 2 = 16J + 12 mv o2 = 16J + 3.0625J
2(19.0625J )
m
= 8.73 sec
0.5Kg
17
14
!
!
m
20. The speed of a 4.0-kg object is given by v = (2t ) sec
, where
t is in seconds. At what rate is the resultant force on this
object doing work at t = 3 sec?
14. The horizontal surface on which a 2-kg block slides is
frictionless. The
speed of the block before it touches the
m
spring is 6.0 sec . How fast is the block moving at the instant
the spring has been compressed 15 cm? k = 2.0 KN
m
Ko = K f + US
!
v o2 $
Ko $ US = K f
1
2
a=
k 2
x =v
m
mv o2 $ 12 kx 2 = 12 mv 2
2
o
2
mv $ kx = mv
2
!
m 2
sec
(6 )
2000 Nm
2
$
(0.15m)
2Kg
dv d (2t )
=
= 2 secm 2
dt
dt
!
P = Fv
P = ( ma)v
(
)
m
P = ( 4kg) 2 secm 2 (6 sec
)
m
v = (2t ) sec
"m
P = 48 Nsec
at t = 3sec,
P = 48w
m
v = 6 sec
m
v = 3.67 sec
15
!
!
!
!
18