PHLB09H3 Lecture : Lecture notes

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maroonarmadillo957

22 Apr 2011

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Suppose two people are in a lifeboat with no food. If one dies soon enough, the other can eat him. Not straightforwardly t rue that you can kill him. Problem: our intuitions about abortion tell us o o o. Abortion where fetus threatens life of mother is ok. The mother has prior right to the property which the fetus didn"t have. If you invite someone into your house and they start to grow uncontrollable, do they have the right to stay? o. Note, the question here is whether or not this person has a right to your stuff o. The invitation is conditional upon your guess that they wouldn"t turn around and t ry to kill you when you got there o. If you knew about this before hand, then you"d have every right to throw them out o. We wouldn"t give this right to the ordinary person, so why give it to the fetus? (thomson)

Related Questions

How fast can a racecar travel through a circular tum without skidding and hitting the wall? The answer could depend on several factors:

The weight of the car;
The friction between the tires and the road;
The radius of the circle;
The “steepness” of the turn.

In this project, we investigate this question for NASCAR racecars at the Bristol Motor Speedway in Tennessee. Before considering this track in particular, we use vector functions to develop the mathematics and physics necessary for answering questions such as this.

A car of mass m moves with constant angular speed to around a circular curve of radius R (Figure 3.20). The curve is banked at an angle . If the height of the car off the ground is h, then the position of the car at time t is given by the function

As the car moves around the curve, three forces act on it: gravity, the force exerted by the road (this force is perpendicular to the ground), and the friction force (Figure 3.21). Because describing the frictional force generated by the tires and the road is complex, we use a standard approximation for the frictional force. Assume that for some positive constant . The constant is called the coefficient of friction.

Let denote the maximum speed the car can attain through the curve without skidding. In other words, is the fastest speed at which the car can navigate the turn. When the car is navigate at this speed, the magnitude of the centripetal force is

The next three questions deal with developing a formula that relates the speed to the banking angle .

Now that we have a formula relating the maximum speed of the car and the banking angle, we are in a position to answer the questions like the one posed at the beginning of the project.

The Bristol Motor Speedway is a NASCAR short track in Bristol, Tennessee. The track has the approximate shape shown in Figure 3.22. Each end of the track is approximately semicircular, so when cars make turns they are traveling along an approximately circular curve. If a car takes the inside track and speeds along the bottom of turn 1, the car travels along a semicircle of radius approximately with a banking angle of . If the car decides to take the outside track and speeds along the top of turn 1, then the car travels along a semicircle with a banking angle of . (The track has variable angle banking.)

The coefficient of friction for a normal fire in Elly conditions is approximately . Therefore, we assume the coefficient for a NASCAR tire in dry conditions is approximately .

Before answering the following questions, note that it is easier to do computations in terms of feet and seconds, and then convert the answers to miles per hour as a final step.

11. Suppose the measured speed of a car going along the outside edge of the turn is . Estimate the coefficient of friction for the car’s tires.

goldpug777

Good Vibes: Introduction to Oscillations

The conditions that lead to simple harmonic motion are as follows:

There must be a position of stable equilibrium.

There must be a restoring force acting on the oscillating object. The direction of this force must always point toward the equilibrium, and its magnitude must be directly proportional to the magnitude of the object's displacement from its equilibrium position. Mathematically, the restoring force F⃗ is given by ⃗, where is the displacement from equilibrium and k is a constant that depends on the properties of the oscillating system.

The resistive forces in the system must be reasonably small.

Consider a block of mass m attached to a spring with force constant k, as shown in the figure(Figure 1) . The spring can be either stretched or compressed. The block slides on a frictionless horizontal surface, as shown. When the spring is relaxed, the block is located at x=0. If the block is pulled to the right a distance A and then released, A will be the amplitude of the resulting oscillations.

Assume that the mechanical energy of the block-spring system remains unchanged in the subsequent motion of the block.

Part A

After the block is released from x=A, it will

(a) remain at rest

(b) move to the left until it reaches equilibrium and stop there.

(d) move to the left until it reaches x=−A and then begin to move to the right.

The time it takes the block to complete one cycle is called the period. Usually, the period is denoted T and is measured in seconds.

The frequency, denoted f, is the number of cycles that are completed per unit of time: f=1/T. In SI units, f is measured in inverse seconds, or hertz (Hz).

Part B

If the period is doubled, the frequency is

(a) unchanged

(b) doubled

Part C

An oscillating object takes 0.10 s to complete one cycle; that is, its period is 0.10 s. What is its frequency f?

Express your answer in hertz.

Part D

If the frequency is 40 Hz, what is the period T?

Express your answer in seconds.

The following questions refer to the figure (Figure 2) that graphically depicts the oscillations of the block on the spring.

Note that the vertical axis represents the x-coordinate of the oscillating object, and the horizontal axis represents time.

Part E

Which points on the x-axis are located at a distance A from the equilibrium position?

(a) R only

(b) Q only

Part F

Suppose that the period is T. Which of the following points on the t-axis are separated by the time interval T?

(a) K and L

(b) K and M

(d) L and N

(e) M and P

Now assume for the remaining Parts G - J, that the x coordinate of point R is 0.12 m and the t coordinate of point K is 0.0050 s.

Part G

What is the period T?

Express your answer in seconds.

Part H

How much time t does the block take to travel from the point of maximum displacement to the opposite point of maximum displacement?

Express your answer in seconds.

Part I

What distance d does the object cover during one period of oscillation?

Express your answer in meters.

Part J

What distance d does the object cover between the moments labeled K and N on the graph?

Express your answer in meters.

emeraldyak680

PHLB09H3 Lecture : Lecture notes

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