MasteringPhysics: Assignment Print View
Uniform Circular Motion
Learning Goal: To find the velocity and acceleration vectors for uniform circular motion and to recognize that this acceleration is the centripetal acceleration. Suppose that a particle's pos
MasteringPhysics: Assignment Print View
Reading Quiz 3.1
Part A What is a vector? ANSWER: A quantity having both size and direction The rate of change of velocity A number defined by an angle and a magnitude The difference between initial and final displa
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Reading Quiz 2.1
Part A The slope at a point on a position-versus-time graph of an object is ANSWER: the object's speed at that point. the object's average velocity at that point. the object's instantaneous velocity
14.1. Solve: The frequency generated by a guitar string is 440 Hz. The period is the inverse of the frequency, hence
T= 1 1 = = 2.27 10 -3 s = 2.27 ms f 440 Hz
14.2. Solve: Your pulse or heart beat is 75 beats per minute. The frequency of your heart's osc
13.1. Model: The crankshaft is a rotating rigid body.
Solve: The crankshaft at t = 0 s has an angular velocity of 250 rad/s. It gradually slows down to 50 rad/s in 2 s, maintains a constant angular velocity for 2 s until t = 4 s, and then speeds up to 200
12.1.
Solve: (b)
Model: Model the sun (s), the earth (e), and the moon (m) as spherical. (a)
Fs on e =
Gms me (6.67 10 -11 N m 2 / kg 2 )(1.99 10 30 kg)(5.98 10 24 kg) = 3.53 10 22 N = (1.50 1011 m ) 2 rs2 e -
Fm on e =
GMm Me (6.67 10 -11 N m 2 / kg 2 )(
11.1. Visualize:r Please refer to Figure Ex11.1. r
Solve: (b) (c)
(a) A B = AB cos = ( 4)(5)cos 40 = 15.3. r r C D = CD cos = (2)( 4)cos120 = -4.0. r r E F = EF cos = (3)( 4)cos 90 = 0.
11.2. Visualize:r Please refer to Figure Ex11.2. r
Solve: (b) (c)
(a)
10.1. Model: We will use the particle model for the bullet (B) and the bowling ball (BB).
Visualize:
Solve:
For the bullet,
KB =
For the bowling ball,
1 1 2 mB vB = (0.01 kg)(500 m /s) 2 = 1250 J 2 2 1 1 2 mBB vBB = (10 kg)(10 m / s) 2 = 500 J 2 2
K BB =
Solve: (a) The momentum p = mv = (1500 kg)(10 m /s) = 1.5 10 4 kg m /s . (b) The momentum p = mv = (0.2 kg)( 40 m /s) = 8.0 kg m /s .
9.1. Model: Model the car and the baseball as particles.
9.2. Model: Model the bicycle and its rider as a particle. Also
8.1. Visualize:
Solve: Figure (i) shows a weightlifter (WL) holding a heavy barbell (BB) across his shoulders. He is standing on a rough surface (S) that is a part of the earth (E). We distinguish between the surface (S), which exerts a contact force, and
7.1. Solve: (a) From t = 0 s to t = 1 s the particle rotates clockwise from the angular position +4 rad to -2 rad. Therefore, = -2 - ( +4 ) = -6 rad in one sec, or = -6 rad s . From t = 1 s to t = 2 s, = 0 rad/s. From t = 2 s to t = 4 s the particle rotat
6.1. Model: We will assume motion under constant-acceleration kinematics in a plane.
Visualize:
Instead of working with the components of position, velocity, and acceleration in the x and y directions, we will use the kinematic equations in vector form. S
5.1.
Model: We can assume that the ring is a single massless particle in static equilibrium. Visualize:
Solve:
Written in component form, Newton's first law is
( Fnet ) x = Fx = T1x + T2 x + T3 x = 0 N
T1 x = - T1
T1y = 0 N Using Newton's first law: T2x =
4.1. Solve: A force is basically a push or a pull on an object. There are five basic characteristics of forces. (i) A force has an agent that is the direct and immediate source of the push or pull. (ii) Most forces are contact forces that occur at a point
3.1. Solve: (a) If one component of the vector is zero, then the other component must not be zero (unless the whole vector is zero). Thus the magnitude of the vector will be the value of the other component. For example, if Ax = 0 m and Ay = 5 m, then the
2.1.
Solve:
Model: The car is represented by the particle model as a dot. (a) Time t (s) Position x (m) 0 1200 1 975 2 825 3 750 4 700 5 650 6 600 7 500 8 300 9 0
(b)
2.2. Solve:
Diagram (a) (b) (c)
Position Negative Negative Positive
Velocity Positive Ne
1.1.
Solve:
1.2.
Solve:
Solve: (a) The basic idea of the particle model is that we will treat an object as if all its mass is concentrated into a single point. The size and shape of the object will not be considered. This is a reasonable approximation of
MasteringPhysics: Assignment Print View
Vector Cross Product
Let vectors , , and .
Calculate the following, expressing your answers as ordered triples (three comma-separated numbers). Part A Hint A.1 The cross product Hint not displayed ANSWER: Part B ANS
Precarious Lunch
A uniform steel beam of length and mass is bolted to the side of a building. The beam is
supported by a steel cable attached to the end of the beam at an angle , as shown. The wall exerts an unknown force, , on the beam. A workman of mass
MasteringPhysics: Assignment Print View
PSS 13.1: Let's Go for a Spin
Learning Goal: To practice Problem-Solving Strategy 13.1 for problems involving rotational dynamics. A uniform board of mass and length is pivoted on one end and is supported in the hor
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A Matter of Some Gravity
Learning Goal: To understand Newton's law of gravitation and the distinction between inertial and gravitational masses. In this problem, you will practice using Newton's law of gravitation.
MasteringPhysics: Assignment Print View
Introduction to Potential Energy
Learning Goal: Understand that conservative forces can be removed from the work integral by incorporating them into a new form of energy called potential energy that must be added to
MasteringPhysics: Assignment Print View
PSS 10.1: College Bored
Learning Goal: To practice Problem-Solving Strategy 10.1 for problems involving conservation of mechancial energy. A bored college student decides to try bungee jumping. He attaches an elasti
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Conservation of Momentum in Inelastic Collisions
Learning Goal: To understand the vector nature of momentum in the case in which two objects collide and stick together. In this problem we will consider a collision o
MasteringPhysics: Assignment Print View
Newton's 3rd Law Discussed
Learning Goal: To understand Newton's 3rd law, which states that a physical interaction always generates a pair of forces on the two interacting bodies. In Principia, Newton wrote: To ever
MasteringPhysics: Assignment Print View
Projectile Motion Tutorial
Learning Goal: Understand how to apply the equations for 1-dimensional motion to the y and x directions separately in order to derive standard formulae for the range and height of a projec
MasteringPhysics: Assignment Print View
Applying Newton's 2nd Law
Learning Goal: To learn a systematic approach to solving Newton's 2nd law problems using a simple example. Once you have decided to solve a problem using Newton's 2nd law, there are steps t
MasteringPhysics: Assignment Print View
Free-Body Diagrams: Introduction
Learning Goal: To learn to draw free-body diagrams for various real-life situations. Imagine that you are given a description of a real-life situation and are asked to analyze the mo
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Vector Addition and Subtraction
In general it is best to conceptualize vectors as arrows in space, and then to make calculations with them using their components. (You must first specify a coordinate system in order
MasteringPhysics: Assignment Print View
Given Positions, Find Velocity and Acceleration
Learning Goal: To understand how to graph position, velocity, and acceleration of an object starting with a table of positions vs. time. The table shows the x coordina