a
SPH4U
1. Objects in equilibrium
2.3 Application of Newton’s Laws Home Fun 2.3-page 83 Q 2, 3, 4, 5
Zeroer
2[x
14
= Zero
Equilibrium: Obj will balance T
be in
,
[F = Zero - 25y-zero constant Inters
A sled has a mass of 14 kg and is on a hill that is inclined 25° to the horizontal, as shown to the right. The hill is very icy
0
=
=>
(negligible friction), and the sled is held at rest by a rope attached to a post. The rope is parallel to the hill as shown.
=
-
Draw a FBD. V = Zero at incline
NX .
a Zero Wy = ewos Oins
·
Et = wx Sin Dina
Zero =
EW
to be balanced
Turbieched
&todirectio
e
wx = T ~ "
w
Wy =
Ef = Zero w = m9
Calculate the magnitude of the tension in the rope. = 14 9 81
.
EFx Zero
34N/
· =
T 137
wither
=
wX - -
=
.
I
T= WS in O
T =
137 .
34 Sin 25
= 58 067
.
NE
Calculate the magnitude of the normal force acting on the sled.
-
Wy -W Cos Pin
[fy
=
= Zero
137 34 Cos 25
=
.
N- Wy =
Zero
= 124 .
53N34
N = Wy
Your car is stuck in the snow. You tie a rope to it, then you and your friend pull the rope with a force of 103 N, but it doesn’t
=>
move. Then you try tying the free end of the rope to a tree, and pulling on the rope in the middle, as shown in the diagram.
The car just starts to move! What tension force does the car experience, and why does this work?
=
EFx = Zero
Tcos 10 = T cos 10 X Cancel
↑ sin 10
Ety =
Zero
Tsin 10
T
↑ Sin (10) +T Sin (10) =
Fa Zero
=
To
. T
2 Sin (10) =
1000
Fa
287938
=
T =
both guys
free will be a support to
2. Accelerating objects
amax every aia
nd
Newton’s 2 Law: El = m . it self
#
Positive x-axis:
O
A sled is at the top of a hill, which makes an angle of 18° with the horizontal. The height
of the hill is 25 m. Calculate the speed of the sled as it reaches the bottom of
Assume that no friction acts on the sled. ... the hill.
usin
X-axis
Vi = Zero
Wos
If :?
Ada = 80 1 .
·
3 03
at
.
↓ er2aAd
= (3 .
02)(80 % .
o
Sin 18 =
The 22 . 031
mis,
9 8)
1
Op hap =
80
A= .
same as
incline
9 %1
ax =
a sind >
- Ax =
.
sin 12
=
3 . 031
a
an - cost
ay =
= a 81
.
Cos 18
9
-
329
=
.
A crate with a mass of 32.5 kg sits on a frictionless surface and is connected to a second crate by a string that passes over a
pulley. The second crate has a mass of 40.0 kg. The pulley is frictionless and has no mass. The string also has no mass.
Determine the acceleration of the system of crates and the magnitude of the tension in the string.
SPH4U 2.3 Application of Newton’s Laws Home Fun 2.3-page 83 Q 2, 3, 4, 5
Q2. Determine the tensions in all three cables in Figure 12.
Figure 12
Q3. A flag of mass 2.5 %& is supported by a single rope as shown in Figure 13. A strong horizontal wind exerts a force of
12 ( on the flag. Calculate the tension in the rope and the angle, ), the rope makes with the horizontal.
Figure 13
SPH4U 2.4 Forces of Friction Home Fun 2.4-page 90 Q 1, 2, 5, 6
Coefficient of friction
1. Types of friction is called M >
-
u or
Tls
Kinetic Friction:
Ex : Friction for bodies that are in motion
[s] Ek
Static Friction: As : "that prevent bodies from moving
matering
Tables of Friction Values
Friction depend on
material every
A worker must move a crate that can be either pushed or pulled, as shown to the
right. The worker can exert a force of 3.6 x 102 N, and the crate has a mass of 45
kg. The worker can push or pull the crate at an angle of 25°, and the coefficient
-
of kinetic friction between the floor and the crate is 0.36.
152
-
Calculate the acceleration when pushing the1 crate. .
NIsin 25
[app 3 6x10
Big
= .
= = 3 . 6x102
m = 45 Ag
[Cos Is
-
A = 250
326 .
3
MK = 0 .
36
TNine depends on Ex
Fy =
= 326
152 .
.
3
↑
-
Calculate the acceleration when pulling the crate.
Mac
35)
Si-Mr .
N = 0 .
36 (269 .
104 . 166
=
ZEx = ma N +
Esin2s -W = 0
-fis 45 A N + 152 ) 45(9 81)
= co12s 0
.
= = .
326 3- 104 166
. .
=
Which is faster (pushing or pulling), or are both the same?
439- N = 289 35N4 .
A crate is placed on an inclined board as shown to the right. One end of the board is hinged
so that the angle θ is adjustable. The coefficient of static friction between the crate and the
board is 0.30. Determine the angle at which the crate just begins to slip.
Two blocks are joined with a rope that runs over a pulley. The mass of m2 is 5.0 kg, and the
incline is 35°. The coefficient of static friction between m1 and the inclined plane is 0.25.
Determine the largest mass for m1 such that both blocks remain at rest.
SPH4U 2.4 Forces of Friction Home Fun 2.4-page 90 Q 1, 2, 5, 6
Q1. A car is moving with a speed of 20 $/& when the brakes are applied. Th e wheels lock (stop spinning). Aft er travelling
40 $, the car stops. Determine the coefficient of kinetic friction between the tires and the road.
Q2. A hockey puck slides with an initial speed of 50.0 $/& on a large frozen lake. Th e coefficient of kinetic friction between
the puck and the ice is 0.030. Determine the speed of the puck aft er 10.0 &.
Q5. Friction can be helpful in some situations but cause problems in other situations.
(a) Describe two situations in which friction is helpful for an object moving on a horizontal surface.
(b) Describe two situations in which it would be ideal if there were no friction when an object moves across a
horizontal surface.
Q6. Two blocks are connected by a massless string that passes over a frictionless pulley (Figure 7). The coefficient of static
friction between , ! and the table is 0.45. Th e coefficient of kinetic friction is 0.35. Mass , ! is 45 -., and , " is 12 -..
(a) Is this system in static equilibrium? Explain.
(b) Determine the tension in the string.
(c) A mass of 20.0 -. is added to , " . Calculate the acceleration.
Figure 7
Q4. A car is parked on a slippery hill (Figure 14). The hill is at an angle of 15° to the horizontal. To keep it from sliding down
the hill, the owner attaches a cable at the back of the car and to a post. The mass of the car is 1.41 × 10! )*.
(a) Draw an FBD showing the forces on the car.
(b) Write the equations for the conditions for static equilibrium along the horizontal and vertical directions.
(c) Calculate the tension in the cable. Assume there is no friction between the road and the tires.
Figure 14
Q5. A student pushes on a lawn mower from rest parallel to the handle of the mower. The student pushes with a force of
magnitude 42 ,. The handle makes an angle of 35° to the horizontal. The mower accelerates across a level driveway with
negligible friction on the mower toward the lawn, 5.0 . away. The mass of the lawn mower is 18 )*.
(a) Draw the FBD of the mower.
(b) Calculate the acceleration of the mower.
(c) Calculate the normal force acting on the mower.
(d) Calculate the velocity of the mower when it reaches the lawn.
