Download Chapter 5: Questions Mr. Kepple

Name: _______________________
Mr. Kepple
Chapter 5: Questions
Force – HW#1
Date: ___________ Period: _____
1. In the figure, forces ⃗ and ⃗ are applied to a lunchbox as it
slides at constant velocity over a frictionless floor. We are to
decrease angle without changing the magnitude of ⃗ . For
constant velocity, indicate below whether we should increase,
decrease, or maintain the magnitude of ⃗ .
___
X increase
___ decrease
___ maintain
Justify your answer:
As the angle decreases, the horizontal component of 𝐹 increases. At constant velocity
the net force must be zero. Therefore the magnitude of 𝐹 must increase in order to
balance out the increase in the horizontal component of 𝐹 .
2. The figure below shows overhead views of four situations in which forces act on a block that lies on
a frictionless floor. If the force magnitudes are chosen properly, in which situations is it possible…
(a) that the block is stationary? Justify your
answer.
(b) that the block is moving with a constant
velocity. Justify your answer.
2 and 4. Stationary means zero net
force. 1 and 3 have unbalanced upward
forces, so they will accelerate. Only 2
and 4 can be balanced.
2 and 4. For the block to be moving with
constant velocity, the net force acting
on the object must be zero. The answer
is the same as part (a).
3. The figure shows four choices for the direction of a force of
magnitude to be applied to a block on an inclined plane. The
directions are either horizontal or vertical. (For choices and ,
the force is not enough to lift the block off the plane.) Rank the
choices according to the magnitude of the normal force on the
block from the plane, greatest first. Justify your ranking.
d, c, a, b. The magnitude of the normal force can be found by the magnitude of the
component of the force that is perpendicular to the incline. 𝑑 and 𝑏 have the greatest
perpendicular component and 𝑎 and 𝑐 have the smallest perpendicular component.
However 𝑎 and 𝑏 point away from the surface so they will decrease the normal force
while 𝑑 and 𝑐 point into the surface which will increase the normal force.
4. The figure gives the free-body diagram for four situations in which an object is pulled by several
forces across a frictionless floor, as seen from overhead. For each situation, indicate whether the
object’s acceleration ⃗ has an component, a component, or both. Finally give the direction of ⃗ by
naming either a quadrant or a direction along an axis. (This should be done with mental calculations.)
___ 𝑥 component?
___
X 𝑥 component?
___
X 𝑥 component?
___
X 𝑥 component?
___
X 𝑦 component?
___ 𝑦 component?
___
X 𝑦 component?
___
X 𝑦 component?
What is the direction
of the acceleration?
What is the direction
of the acceleration?
What is the direction
of the acceleration?
What is the direction
of the acceleration?
+𝑦
+𝑥
Quadrant IV
Quadrant III
5. The figure to the right gives three graphs of the
velocity component
and three graphs of
the velocity component
. The graphs are not
to scale. Which graph best corresponds to the
following situations? Justify each answer.
(a) Situation 1 in question 4.
𝑎 and 𝑒. Situation 1 has zero
horizontal acceleration and positive
vertical acceleration.
(b) Situation 2 in question 4.
𝑏 and 𝑑. Situation 2 has zero vertical
acceleration and positive horizontal
acceleration.
(c) Situation 3 in question 4.
𝑏 and 𝑓. Situation 3 has positive
horizontal acceleration and negative
vertical acceleration.
(d) Situation 4 in question 4.
𝑐 and 𝑓. Situation 3 has negative
horizontal acceleration and negative
vertical acceleration.
Name: _______________________
Mr. Kepple
Newton’s Laws Problem Set
Force – HW#2
Date: ___________ Period: _____
1. Superman must stop a 120-km/h train in 150 m to keep it from hitting a stalled car on the tracks. If
the train’s mass is
kg, how much force must he exert? How much force does the train exert
on Superman?
2 km
h
m
=
m/s
h
s
km
𝑣 2 = 𝑣0 2 + 2𝑎𝑥
𝐹 = 𝑚𝑎
𝑣 2 − 𝑣0 2
𝑎=
2𝑥
𝑎=
− 𝑣0 2
2𝑥
𝐹𝑇𝑆
𝑣0 2
=𝑚 −
2𝑥
𝐹𝑇𝑆
𝑚𝑣0 2
=−
2𝑥
2
𝐹𝑇𝑆 = −
2 5
𝐹𝑇𝑆 ≈ −
6
N
𝐹𝑆𝑇 ≈ +
6
N
2. A 0.140-kg baseball traveling 35.0 m/s strikes the catcher’s mitt, which, in bringing the ball to rest,
recoils backward 11.0 cm. What was the average force applied by the ball on the glove?
𝐹𝐺𝐵
𝑚𝑣0 2
=−
2𝑥
𝐹𝐺𝐵 = −
4
5
2
2
𝐹𝐺𝐵 = −779 55 𝑁
𝐹𝐺𝐵 ≈ −78 N
3. What average force is required to stop a 950-kg car in 8.0 s if the car is traveling at 95 km/h?
𝑣 = 𝑣0 + 𝑎𝑡
𝑎=
𝑣 − 𝑣0
𝑡
95 km
h
𝐹 = 𝑚𝑎
𝐹=𝑚
h
s
𝑣 − 𝑣0
𝑡
𝐹 = 95
−2
8
9
=
8N
𝐹≈−
N
m
=2
km
9 m/s
4. A fisherman yanks a fish vertically out of the water with an acceleration of 2.5 m/s2 using very light
fishing line that has a breaking strength of 18 N (about 4 lb). The fisherman unfortunately loses the fish
as the line snaps. What can you say about the mass of the fish?
𝐹 = 𝑚𝑎
𝑇
𝑎
𝑚𝑔
𝑚=
𝑇 − 𝑚𝑔 = 𝑚𝑎
𝑚𝑎 + 𝑚𝑔 = 𝑇
𝑇
𝑚=
𝑎+𝑔
8
25+98
𝑚=
4
kg
𝑚≈
5 kg
In order to break the fishing line the fish
must have had a mass greater than 1.5 kg.
5. A 75-kg petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope
made of sheets tied together can support a mass of only 58 kg. What acceleration must the thief
descend with in order for the sheets to not break?
𝐹 = 𝑚𝑎
𝑇
𝑎
𝑚𝑔
𝑎=
𝑚𝑔 − 𝑇 = 𝑚𝑎
75 9 8 − 58 9 8
75
𝑎 = 2 22 m/s²
𝑚𝑔 − 𝑇
𝑎=
𝑚
𝑎 ≈ 2 2 m/s²
The rope can support his weight as long as he
maintains a downward acceleration of at least
2.2 m/s².
6. An elevator (mass 4850 kg) is to be designed so that the maximum acceleration is 0.0680 . What are
the maximum and minimum forces the motor should exert on the supporting cables?
𝑎max when elevator accelerates upward
𝐹 = 𝑚𝑎
𝑇
𝑎
𝑚𝑔
𝑇=𝑚 𝑔+
8 𝑔
𝑇 = 485
8
4
N
𝐹 = 𝑚𝑎
𝑇
𝑇 − 𝑚𝑔 = 𝑚𝑎
𝑇 =𝑚 𝑔+𝑎
𝑇=5 8
𝑎min when elevator accelerates downward
𝑚𝑔 − 𝑇 = 𝑚𝑎
𝑎
𝑚𝑔
𝑇 =𝑚 𝑔−𝑎
𝑇=𝑚 𝑔−
98
8 𝑔
𝑇 = 485
9 2
𝑇 = 44
4
N
98
Name: _______________________
Mr. Kepple
Free Body Diagrams
Force – HW #3
Date: ___________ Period: _____
1. Draw the free-body diagram for a basketball player
(a) just before leaving the ground on a jump
(b) while in the air
𝑁
𝑚𝑔
𝑚𝑔
2. Sketch the free-body diagram of a baseball
(a) at the moment it is hit by the bat
(b) after it has left the bat and is flying toward
the outfield.
𝑁
(if air resistance is ignored)
𝑚𝑔
𝑚𝑔
3. A box weighing 77.0 N rests on a table. A rope tied to the box runs
vertically upward over a pulley and a weight is hung from the other end
(see picture). Determine the force that the table exerts on the box if the
weight hanging on the other side of the pulley weighs (a) 30.0 N, (b) 60.0 N,
and (c) 90.0 N.
𝐹 = 𝑚𝑎
(a) 30 N hanging weight
𝑁 + 𝑇 − 𝑚1 𝑔 = 0
𝑁 = 𝑚1 𝑔 − 𝑚2 𝑔
𝑁 + 𝑚2 𝑔 = 𝑚1 𝑔
𝑁 = 77.0 − 30.0
𝑁 = 𝑚1 𝑔 − 𝑚2 𝑔
𝑁 = 47.0 N
(b) 60 N hanging weight
𝑁 = 𝑚1 𝑔 − 𝑚2 𝑔
𝑁 = 77.0 − 60.0
𝑁 = 17.0 N
(a) 90 N hanging weight
𝑁
𝑇
𝑁=0
The box is lifted up off
the table!
𝑚1 𝑔
𝑇
𝑚2 𝑔
4. At the instant a race began, a 65-kg sprinter exerted a force of 720 N on the starting block at a 22°
angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter? (b) If the
force was exerted for 0.32 s, with what speed did the sprinter leave the starting block?
(a) horizontal acceleration
(b) final speed
𝐹𝑥 = 𝑚𝑎𝑥
𝐹 cos 𝜃 = 𝑚𝑎
𝑎=
𝑎=
𝐹 cos 𝜃
𝑚
+𝑦
𝑣 = 𝑣0 + 𝑎𝑡
𝐹
𝑁
𝑣 = 0 + 10. 7 03
𝜃
𝑣 = 3. 86 m/s
𝑚𝑔
𝑣 ≈ 3.3 m/s
7 0 cos
65
+𝑥
𝑎 = 10. 7 m/s² ≈ 10 m/s²
5. The block shown in the picture has a mass of = 7.0 kg and lies on a
smooth frictionless plane tilted at an angle = .0 to the horizontal.
(a) Determine the acceleration of the block as it slides down the plane.
(b) If the block starts from rest 12.0 m up the plane from its base, what
will be the block’s speed when it reaches the bottom of the incline?
(a) acceleration
(b) speed at bottom
2
2
𝑣=
2
+𝑦
𝑣 = 𝑣0 + 𝑎𝑥
𝐹𝑥 = 𝑚𝑎𝑥
𝑚𝑔 sin 𝜃 = 𝑚𝑎
𝑎 = 𝑔 sin 𝜃
𝑎 = 9.80 sin
𝜃
𝑣=
.0
𝑁
𝑣0 + 𝑎𝑥
0+
3.67 1
𝜃 𝑚𝑔
𝑣 = 9.39 m/s
+𝑥
𝑎 = 3.67 m/s²
6. Suppose a block were given an initial speed of 4.5 m/s up the inclined plane from the previous
problem. Starting from the bottom, how far up the plane would the block go? Ignore friction.
Since the forces acting on the
block remain the same the
acceleration will remain
𝑎 = 3.67 m/s²
𝑣 2 = 𝑣0 2 + 𝑎𝑥
𝑣 2 − 𝑣0 2
𝑥=
𝑎
𝑥=
0
2
− 4.5
3.67
𝑥 = − .758 m
2
𝑥 ≈ .8 m
up the ramp
Mr. Kepple
Name: _______________________
Dynamics FRQ
Force – HW#4
Date: ___________ Period: _____
𝑚
𝑚
A block of mass
rests on a horizontal frictionless table, as shown above. It is connected to one end
of a string that passes over a massless pulley and has another block of mass
hanging from its other
end. The whole apparatus is released from rest. You may assume that the pulley is frictionless and the
mass of the string is negligible
(a) On the figure below, draw and label all the
forces that act on each block.
(b) Construct a free-body diagram for this
situation.
𝑁
𝑚
+𝑦
𝑇
𝑚
𝑇
𝑚 𝑔
𝑎
𝑁
𝑚
𝑇
𝑚 𝑔
𝑇
𝑚
+𝑥
𝑚 𝑔
𝑚 𝑔
(c) Calculate the acceleration of the system for
𝐹𝑥
𝑇
𝑚 𝑎𝑥
𝑚 𝑎
𝐹𝑥
and
𝑚 𝑎𝑥
𝑚 𝑔−𝑇
𝑚 𝑔− 𝑚 𝑎
𝑚 𝑎
𝑚 𝑎
𝑚 𝑎+𝑚 𝑎
𝑚 𝑔
𝑎 𝑚 +𝑚
𝑚 𝑔
𝑎
.
𝑚
𝑔
𝑚 +𝑚
𝑎
+
𝑎
𝑎
33𝑔
3 67 m/s²
𝑎 ≈ 3 3 m/s²
𝑔
(d) Calculate the tension in the string for
𝑎
and
𝑚
𝑔
𝑚 +𝑚
𝑇
𝑇
𝑚 𝑎
𝑚 𝑚
𝑔
𝑚 +𝑚
.
𝑇
+
𝑇
98
13 67 𝑁
𝑇 ≈ 13 N
𝑚
(e) Suppose instead of mass
being on a horizontal table, it is placed on the inclined plane shown
above. Indicate below whether the acceleration of the system would be greater than, less than, or
equal to the answer in part (c).
___ Greater than
___
X Less than
___ Equal to
Justify your answer.
When placed on an inclined plane, a component of the weight of block 1 will point
down the ramp, opposing the tension in the string. This results in a decrease in the
net force acting on block 1, which in response leads to a decrease in the acceleration
of the system.