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Integrated Concept Problems
Unreasonable Results
Construct Your Own Problem
Appendices
WebAssign
Sapling Learning
1 INTRODUCTION: THE NATURE OF SCIENCE AND PHYSICS
- Physics: An Introduction
- Physical Quantities and Units
- Accuracy, Precision, and Significant Figures
- Approximation
In these subjects, all pertinent physical quantities can be expressed in terms of the fundamental units of length, mass and time. An important factor in the accuracy and precision of measurements involves the accuracy of the measuring instrument.
Glossary
The final estimate is much higher than the early estimate of 3 inches, but the other early estimate of 10 feet (120 inches) was more or less correct. Using mental math and your understanding of fundamental units, approximate the area of a regulation basketball court.
Section Summary
Conceptual Questions
Problems & Exercises
Can you estimate the number of atoms in each bacterium. credit: Rocky Mountain Laboratories, NIAID, NIH). 35.(a) Calculate the number of cells in a hummingbird, assuming that the mass of an average cell is ten times the mass of a bacterium. b) With the same assumption, how many cells are there in a human being.
2 KINEMATICS
Displacement
The +2.0 m displacement of the professor relative to Earth is represented by an arrow pointing to the right. The −4.0 m displacement of the passenger relative to the aircraft is represented by an arrow towards the rear of the aircraft.
Vectors, Scalars, and Coordinate Systems
It is important to note that the distance traveled, however, can be greater than the magnitude of the displacement (by magnitude we mean only the magnitude of the displacement regardless of its direction; that is, just a number with one unit). The distance traveled, however, is the total length of the path taken between the two markers.
Time, Velocity, and Speed
The minus sign indicates that the average speed is also towards the rear of the aircraft. What is (a) the average speed of the train and (b) the average speed of the train in m/s. a).
Note that the train travels 40 miles one way and 40 miles back, for a total distance of 80 miles.
Acceleration
It remains the same in the middle of the path (where there is no acceleration). The train has positive acceleration because it accelerates at the beginning of the journey.
It will be negative here, since the train is moving to the left and has a negative displacement. As in Example 2.5, this acceleration can be called a deceleration since it is in the direction opposite to the velocity.
Motion Equations for Constant Acceleration in One Dimension
We can use the equation x = x0+ v0t + 12at2 once we identify v0, a and t from the problem statement. Use the quadratic formula to solve for t. a) Rearrange the equation to get 0 on one side of the equation.
Problem-Solving Basics for One-Dimensional Kinematics
Check the answer to see if it makes sense: Does it make sense? This last step is extremely important - the goal of physics is to accurately describe nature. To check that an answer is reasonable, check its magnitude and sign next to the units.
Falling Objects
Since upward is positive, and the rock is thrown upward, the initial velocity must also be positive. Notice that when the rock is at its highest point (at 1.5 s), its velocity is zero, but its acceleration is still −9.80 m/s2. Another way of looking at it is the following: In Example 2.14, the rock is thrown up with an initial velocity of 13.0 m/s.
Graphical Analysis of One-Dimensional Motion
Furthermore, the slope of the velocity versus time graph is acceleration, as shown in Figure 2.48(c). Calculate the speed of the jet car at time 25 s by finding the slope of x vs . Taking this a step further, we notice that the slope of the graph is velocity versus time acceleration.
Section Summary 2.1 Displacement
What is the only case in which the magnitude of displacement and displacement are exactly the same. 16. If a subway train moves to the left (has a negative velocity) and then stops, what is the direction of its acceleration. 25. How many times higher can an astronaut jump on the Moon than on Earth if his ascent speed is the same in both places (gravitational acceleration on the Moon is about 1/6 of g on Earth).
Problems & Exercises 2.1 Displacement
Professional Application
What is its emergency deceleration in m/s2. 24. While entering the highway, the car accelerates from rest at speed. a) Draw a sketch of the situation. To solve this part, first identify the unknown and then discuss how you chose the appropriate equation to solve it. Solve this unknown in the same way as in part (c), explicitly showing all the steps. b) What is its final speed.
Professional Application
After solving the equation, show your steps in solving for the unknown, check your units, and discuss whether the answer makes sense.
Professional Application
45. A dolphin in a water show jumps straight out of the water at a speed of 13.0 m/s. a) List the known in this task. How much extra time will pass before the ball passes the tree branch on the way back. a) Calculate its vertical speed when it leaves the ground. 51. While standing at the foot of one of the cliffs of Mount Arapiles in Victoria, Australia, a hiker hears a rock fall from a height of 105 m. Verify that the acceleration of the jet is 5.0 m/s2 by measuring the slope of the curve at any point in Figure 2.61.
3 TWO-DIMENSIONAL KINEMATICS
Kinematics in Two Dimensions: An Introduction
The hypotenuse of the triangle is the rectilinear path, and so in this case its length in units of city blocks is The horizontal and vertical components of motion combine to give the straight path. The two-dimensional curved path of a horizontally thrown ball consists of two independent one-dimensional motions (horizontal and vertical).
Vector Addition and Subtraction: Graphical Methods
The length D of the arrow is proportional to the size of the vector and is measured along the line with a ruler. The tail of this vector must come from the head of the first vector pointing east. The length of the arrow is proportional to the size of the vector and is measured at 10.3 units.
Vector Addition and Subtraction: Analytical Methods
This method is called finding the components (or parts) of the displacement in the east and north directions, and is the reverse of the process followed to find the total displacement. For example, if Ax and Ay are 9 and 5 blocks respectively, then A blocks, again in line with the example of the person walking in a city. Similarly, the magnitudes of the vectors Ay and By add to give the magnitude of the resultant vector in the vertical direction.
Projectile Motion
This equation defines the maximum height of a projectile and depends only on the vertical component of the initial velocity. Often it is convenient to choose the initial position of the object as the origin, so that x0= 0 and y0= 0. Interestingly, for every starting angle except 45º, there are two angles that give the same area – the sum of these angles is 90º.
Addition of Velocities
Let's calculate the magnitude and direction of the boat's velocity relative to an observer on shore, vtot. 1. Find the following for path A in Figure 3.54: (a) the total distance traveled and (b) the magnitude and direction of the displacement from start to finish. 2. Find the following for path B in Figure 3.54: (a) the total distance traveled and (b) the magnitude and direction of the displacement from start to finish.
A player standing on the free-throw line throws the ball with an initial velocity of 7.15 m/s and releases it at a height of 2.44 m (8 ft) above the floor. At what angle above the horizontal should the ball be thrown to exactly hit the basket? What distance does the ball travel horizontally? 48.Prove that the trajectory of a projectile is parabolic and has the shape.
What is the speed of the swimmer relative to his stationary friend on the ground. At what angle must the speed of the puck be relative to the player (in his frame of reference) to hit the center of the goal. 280 m/s to the east and flying with a strong tailwind. a) What was the speed of the plane relative to the ground.
4 DYNAMICS: FORCE AND NEWTON'S LAWS OF MOTION
- Development of Force Concept
- Newton’s First Law of Motion: Inertia
- Newton’s Second Law of Motion: Concept of a System
- Newton’s Third Law of Motion: Symmetry in Forces
- Normal, Tension, and Other Examples of Forces
For example, in Figure 4.5(a) the interest system is the cart plus the child in it. Looking again at Figure 4.5(a), the force exerted by the child in the cart to hang on to the cart is an internal force between elements of the system of interest. Newton's second law states that the magnitude of the net external force on an object is Fnet= ma.
Note that the vertical tension in the wire acts as a normal force supporting the weight of the line roller. As we saw in the last example, the weight of the line roller acted as a force perpendicular to the rope. We saw that the tension in the rope was related to the weight of the line roller in the following way:
Problem-Solving Strategies
FT is no longer shown because it is not the force acting on the system of interest; Instead, FT acts on the outside world. It is almost always convenient to make one axis parallel to the direction of motion if this is known. Before writing the net force equations, it is crucial to determine whether the system is accelerating in a particular direction.
Further Applications of Newton’s Laws of Motion
Extended Topic: The Four Basic Forces—An Introduction
Draw a free-body diagram, which is a sketch that shows all the forces acting on an object. The normal force on an object is not always equal to the weight of the object. What is the scheme of interest if the acceleration of the child in the carriage is to be calculated. free body diagram, including all forces acting on the system.
What is the ratio between the strength of gravity and that of the strong nuclear force. What is the ratio between the strength of gravity and that of the weak nuclear force. 54.What is the ratio between the strength of the strong nuclear force and that of the electromagnetic force.
5 FURTHER APPLICATIONS OF NEWTON'S LAWS
FRICTION, DRAG, AND ELASTICITY
Friction
Part of the friction is due to the adhesive forces between the surface molecules of the two objects, which explain the dependence of friction on the nature of the substances. The magnitude of the friction force has two forms: one for static situations (static friction), the other when there is movement (kinetic friction). However, many parts of the body, especially the joints, have much lower coefficients of friction—often three or four times less than ice.
Drag Forces
The downward force of gravity remains constant regardless of the speed at which a person is moving. However, as the person's speed increases, the magnitude of the drag force increases until the magnitude of the drag force equals the gravitational force, resulting in a net force of zero. Because the resistance that air presents to movement is proportional to the surface area of the moving object.
Elasticity: Stress and Strain
In addition, the change in length is proportional to the original length L0 and inversely proportional to the cross-sectional area of the wire or rod. The force F on the nail (neglecting the nail's own weight) is the weight of the image w. FD, found to be proportional to the square of the velocity of the object; mathematically.
Section Summary 5.1 Friction
Fs= 6πrηv, where r is the radius of the object, η is the viscosity of the fluid, and v is the velocity deformation of the object perpendicular to the original length of the object. 20. The terminal velocity of a person falling into the air depends on the weight and surface area of the person facing the liquid. The clamping wire is attached to the top of the pole at an angle of 30º to the vertical.
6 UNIFORM CIRCULAR MOTION AND GRAVITATION
- Rotation Angle and Angular Velocity
- Centripetal Acceleration
- s = 7854 rad/s
- Centripetal Force
Note that the speed of a point on the rim of the tire is the same as the car's speed v. The direction of the centripetal acceleration is towards the center of curvature, but what is its magnitude. What is the magnitude of the centripetal acceleration of a car following a curve of radius 500 m at a speed of 25.0 m/s (about 90 km/h).