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PHYS 101 Lecture 14: Momentum,​ ​Energy,​ ​and​ ​Work

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School
McGill University
Department
Physics
Course
PHYS 101
Professor
Kenneth J Ragan

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PHYS 101 Full Course Notes
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PHYS 101 Full Course Notes
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Document Summary

Example #2 (continued from lecture 13) : a block (mass m) slides frictionlessly along a looped track. What is the minimum height h to release it from so that it stays on the track at the top of the loop of radius r. We have to be careful with non-conservative forces: We do not define pe for a non-conservative force. But we can now modify our work-energy principle from w net . Object moving in a circular path? generalized form that includes potential energy . The conservation of mechanical energy is only true if there are acting. We know that we have to apply a force on the spring) Of course, the spring pushes back with an equal and opposite force. (units: n/m) and varies from spring to . Be careful ! the force (f=-kx) is changing as x changes. Power = rate at which work is done. = rate at which energy is expended.

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Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

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Related Questions

Hint:

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.

1) An object is moving with constant velocity. Which of thefollowing statements is true?
a) A constant force is being applied in the direction ofmotion.
b) A constant force is being applied in the direction opposite ofmotion.
c) There are no forces acting on the object.
d) The net force on the object is zero.
e) There is no frictional force acting on the object.


2) You apply the same force to two objects. Object 1 has mass M andobject 2 has mass 5M.
a) ten times that of object 1 b) five times that of object 1
c) the same as that of object 1 d) 1/5 as that of object 1


3) An object of weight W is in free-fall close to the surface ofEarth. What is the force that the object exerts on Earth?
a) a force greater than W b) a force less than W
c) a force equal to W d) no force at all


4) A parking crate slides down an inclined ramp at constantvelocity. Thus we can deduce that _
a) a frictional force is acting on it
b) a net downward force is acting on it
c) a net upward force is acting on it
d) it is not acted on by appreciable normal force
e) it is not acted on by appreciable gravitational force

5) A person applies a constant force of 20N to a rock of mass1000kg for a total of 20 seconds. What is the work done by thisperson if the person does not move at all by this appliedforce?
a) 1000J b) 2000J c) 20,000J d) 0J e) 400J

6) If the net work done on an object is positive, then theobject's kinetic energy.
a) decreases b) remains the same c) increases d) is zero

7) You throw a ball straight up. Compare the sign of the workdone by gravity while the ball goes up with the sign of the workdone by gravity while it goes down.
a) Work is + on the way up and + on the way down
b) Work is + on the way up and - on the way down
c) Work is - on the way up and + on the way down
d) Work is - on the way up and - on the way down