Transcript 01 Newtons 2nd

Ch 12: Newton’s Second
Law, Fnet = ma
M Sittig
AP Physics B
Summer Course 2012
2012年AP物理B暑假班
Four-Step Problem Solving for
Newton’s 2nd (force) Problems
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1. Draw a proper free-body diagram.
2. Resolve vectors into their components.
3. For each axis, set up an expression for
Fnet, and set it equal to ma.
4. Solve your system of equations.
Key points to remember
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A net force causes an acceleration, and an
acceleration means there is a net force.
Net force and acceleration must be in the
same direction.
Only Fnet is equal to ma, setting single forces
= ma is playing with fire.
Types of problems
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Blocks on planes
Blocks on inclines
Pulleys/strings
Atwood machines
Elevator rides
Blocks on planes
Example Problem
Practice Problem
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Two blocks are in contact on a frictionless
table. A horizontal force F is applied to M2. If
M1 = 2 kg, M2 = 4 kg and F = 6 N, find the size
of the contact force between the two blocks.
Practice Problem
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Two blocks are in contact on a frictionless
table. A horizontal force F is applied to M1. If
M1 = 2 kg, M2 = 4 kg and F = 6 N, find the size
of the contact force between the two blocks.
Practice Problem
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Two blocks of equal masses are placed on a
horizontal table as shown. The bottom block is
then pulled with a slowly increasing horizontal
force F. The coefficients of static friction for
both surfaces are greater than zero and equal
to each other.
Select the correct description of the motion of
the blocks. (continued…)
Practice Problem
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The top block begins to move as soon as F reaches a certain minimum value; the bottom
block does not move at that instant but would begin to move as F increases further.
The top block begins to move as soon as F reaches a certain minimum value; the bottom
block would never move even as F increases further.
Both blocks begin to move simultaneously as reaches a certain minimum value; as F
increases further, both blocks always have the same acceleration.
The bottom block begins to move as soon as F reaches a certain minimum value; the top
block does not move at that instant but would begin to move as F increases further.
Both blocks begin to move simultaneously as F reaches a certain minimum value; as F
increases further, the acceleration of the bottom block exceeds the acceleration of the top
block.
The bottom block begins to move as soon as F reaches a certain minimum value; the top
block would never move even as F increases further.
Both blocks begin to move simultaneously as F reaches a certain minimum value; as F
increases further, the acceleration of the top block exceeds the acceleration of the bottom
block.
Practice Problem
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Two blocks of equal masses are placed on a
horizontal table as shown. The top block is
then pulled with a slowly increasing horizontal
force . The coefficients of static friction for both
contact surfaces are greater than zero and
equal to each other
Select the correct description of the motion of
the blocks. (continued…)
Practice Problem
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Two blocks of equal masses are placed on a
horizontal table as shown. The top block is
then pulled with a slowly increasing horizontal
force . The coefficients of static friction for both
contact surfaces are greater than zero and
equal to each other
Select the correct description of the motion of
the blocks. (continued…)
Practice Problem
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The top block begins to move as soon as F reaches a certain minimum
value; the bottom block would never move even as F increases further.
Both blocks begin to move simultaneously as F reaches a certain
minimum value; as F increases further, the acceleration of the top block
exceeds the acceleration of the bottom block.
The top block begins to move as soon as F reaches a certain minimum
value; the bottom block does not begin to move at that instant but
would begin to move as F increases further.
Both blocks begin to move simultaneously as F reaches a certain
minimum value; as F increases further, the acceleration of the bottom
block exceeds the acceleration of the top block.
Both blocks begin to move simultaneously as F reaches a certain
minimum value; as F increases further, both blocks always have the
same acceleration.
Blocks on inclines
Example Problem
Practice Problem
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If an automobile’s braking distance from
100 km/hr is 60 m on level pavement,
determine the automobile’s braking
distance when it is going up a 6° incline.
Hint: What force causes the braking auto to
decelerate?
Pulleys/strings
Example Problem
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A frictionless pulley with zero
mass is attached to the ceiling,
in a gravity field of 9.81 m/s2.
Mass m1 = 0.15 kg is
accelerating downward at 1.1
m/s2. Find M2.
Practice Problem
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A 1.97 kg mass is suspended from a string
which is pulled upward. The mass
accelerates upwards with an acceleration of
2.30 m/s2. What is the tension in the string?
Atwood machines
Example Problem
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M1 and M2 are connected by a string
over a massless, frictionless pulley.
Describe the motion of M2 when:
A) the table is frictionless.
B) the coefficient of kinetic friction
between the table and M1 is mu.
Practice Problem
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Block m1 goes up on an inclined plane (θ =
15o) with acceleration a = 3.49 m/s2. It is
connected with m2 = 4 kg by a string that
passes over a frictionless pulley. Knowing
that the pulley is massless and the
coefficient of friction on the inclined plane is
μk = 0.5, find m1.
Super Challenge Problem
More Challenge Problem
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Two prisms are placed as shown. Angle θ (see the diagram)
is given. The coefficient of static friction between the
touching surfaces of the prisms is μ. The bottom prism is
pushed along a horizontal surface. What is the range of
accelerations of the bottom prism that allows the top prism
to remain at rest relative to the bottom one?
Elevator rides
Example Problem
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Daniel weights himself in an elevator that
accelerates downward with constant
acceleration a = 2 m/s2. If Daniel's mass is m
= 65 kg, find what the scale from the
elevator will show.
Elevator Demo
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Let’s take a ride in the elevator! On a scale!
Practice Problem
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Starting from rest, an elevator
accelerates uniformly between the 1st
and 2nd floors, and decelerates
uniformly between the 5th and 6th
floors, coming to a stop at the 6th
floor. Between the 2nd and 5th floors,
the elevator covers the 6 meter
distance between two adjacent floors
in 1 second. Inside, Liz (who is about
to graduate) is standing on a scale that
reads 800 N when the elevator isn’t
moving. What was her minimum scale
reading during the trip? Use g = 10
m/s2.
Practice Problem
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A student is riding an elevator in the Acme
Building, and the elevator is moving a
constant upward speed. Which plot shows
the tension T in the elevator cable as a
function of time?
Practice Problem
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A student steps onto a bathroom scale in a
stationary elevator on the first floor of the Acme
Building. The elevator accelerates until it reaches
the second floor and then continues at constant
speed until the 5th floor, where it starts slowing and
stops on the 6th floor. Which sketch of the apparent
weight (reading of the scale) vs. time during the
entire process is most likely to be correct?
Newton’s 3rd Law
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Forces come in pairs.
If Fm,E, then FE,m.
Why don’t N3 pairs cancel out?
Example: I kick a ball, there is a force of
foot-on-ball and a force of ball-on-foot, why
does the ball move?