Chapter 9 Applications of Newton’s Second Law Fnet = ma
page 9-2 Addition of Forces
Often you must find Fnet when more than one force is present. This will require vector addition techniques when the individual force vectors are not parallel.
If the mass in Figure 2 is not accelerating, what is true concerning FS and mg ?
page 9-3 Spring Forces
Figure 4 is accurate as long as the spring is not stretched to a point that it will not return to its original length when the mass is removed.
Hooke’s Law FS = kX
This gives the magnitude of the spring force. k is the spring constant (or force constant). X is the distance the spring has stretched from its relaxed position.
From figure 4, calculate k using the units of Newtons for the force and meters for X.
Write Hooke’s Law as a vector equation. Let X be in the direction the end of the spring is stretched.
page 9-4 The Spring Pendulum
Why does FS always point back towards the nail?
What is the direction of mg ?
Does mg change much from point -1 to point 15 in Figure 7?
At what point in Figure 7 is FS > mg by the largest amount?
At what point in Figure 7 is FS < mg by the largest amount?
We will not compute the net force as is done on pages 9-6 and 9-7.
What questions do you have about the drawing of the net Force vectors on pages 9-6 and 9-7?
Is Figure 8c exact?
On the right margin of this page,
make an approximately accurate sketch
of the net Force at point 3 in Figure 7.
Skip pages 9-8 to 9-9
page 9-10 The Inclined Plane
Demo We will see an inclined air track in class and discuss the motion of the cart.
*Does the air track exert any force on the cart while the cart is moving down the track?
Describe the force.
If the cart experiences a gravitational force of 4.9 Newtons, does the cart feel a pull of 4.9 Newtons down the air track in our demonstration?
Make a sketch of an air track and cart
at a 30 degree angle. Draw the mg
vector. Let the X axis be aligned
with the air track. Draw the X and
Describe the magnitude of the
normal force, FP .
What is the magnitude of the
acceleration of the cart? Express a
as a function of the angle of the
air track.
We will calculate and then make a measurement of the time required for a cart to move 1 meter along an air track that is inclined at a known angle.
page 9-12 Friction
The force of friction is a result of the microscopic interaction of surfaces. We will not explore the details of this interaction. We will use the simplifying assumptions stated in the text.
Let’s consider friction first for the case of an object sliding on a horizontal surface. What is the magnitude of the normal force if the object has a mass, m?
Recall from you memory watching some object slide across a horizontal surface that is not slick. Describe the velocity as a function of time.
Was the acceleration zero or non-zero?
Was the net force zero or non zero for the object?
Can mg act in a horizontal direction?
How do you explain the presence of acceleration of the object in the horizontal direction?
There are two categories of friction: static friction and kinetic friction. Static friction applies when the velocity is zero. Kinetic friction applies when the velocity is not zero.
True or False The force of friction always opposes motion.
Ff < m S FNormal Ff = m K FNormal
I agree with the text that the measurement of the coefficient of friction is approximate at best in an introductory physics lab. But, we can discern a difference between static friction and kinetic friction.
Typical values of m are less than 1.0.
True or False The force of static friction is usually larger than the force of kinetic friction.
Why is the force of static friction variable?
Is the force of friction in the same direction as the normal force?
*What force allows you to walk?
We will work this problem in class: A string is used to pull a 3 kg object across a horizontal surface which has a coefficient of kinetic friction of 0.5. The coefficient of static friction is 0.6. The acceleration of the object is 0.3 m/s2. What is the value of the tension in the string?
Make a drawing that shows a 5 kg object on a frictionless plane which is inclined at 25 degrees to the horizontal. Show all of the forces that act on the object. a) Find the magnitude of the normal force and the magnitude of the force acting on the object in a direction of "down the plane". b) Now suppose that a 3 kg object is connected with a string at the upward side of the 5 kg object. The string passes over a pulley at the top of the ramp and the 3 kg object hangs vertically from the string. The 3 kg object does not touch the ground. The system starts at rest. Calculate the acceleration of the 3 kg object. Let the up-the-plane direction be the positive direction. c) Calculate the tension in the string.
page 9-15 String Forces
Have you ever seen a string pull something at an angle of 90 degrees away from the direction of the string?
Do you agree that mrope arope = F1 + F2 ?
Why aren’t the masses of the people included in this equation?
*If the rope has no mass what do you conclude about the two forces?
Demo We will put some spring scales together and see what they read when the ends of the scales are pulled similar to Figure 17.
Write one sentence that describes the force person one applies to the rope and the force the rope applies to person one.
Have you ever heard Newton’s Third Law described as "action reaction?"
Why is that description misleading?
page 9-16 The Atwood’s Machine
Do you agree with both equations (29) ?
Refer to Figure 19a. What is the net force on the system of m1 and m2?
What is the total mass of the system?
Write Newton’s Second Law for this system.
Can the equation you wrote above be transformed into equation 33 on page 9-17?
Can Atwood’s Machine be used to measure "g?"
If the sum of the two masses is held constant how could data be collected such that a graph of m1 - m2 vs. acceleration allow you to calculate "g?"
page 9-18 to 9-20 Skip
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