Physics for Scientists and Engineers With Modern Physics
9th Edition
ISBN: 9781133953982
Author: SERWAY, Raymond A./
Publisher: Cengage Learning
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Chapter 7, Problem 58AP
To determine
The work done on an object to displace from
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Given the points M(0.1, -0.2, -0.1), N(-0.2, 0.1, 0.3), and P(0.4, 0, 0.1), find: (a) the vector RMN; (b)the dot product RMN. RMP ; (c) the scalar projection of RMN on RMP; (d) the vector projection of RMN on RMP; (e) the angle between RMN on RMP.
The work done on an object is equal to the integral of the force on that object dotted with its displacent.
This looks like W=∫(F.ds) (W is work, F is force, and ds is the infinitesimally small displacement vector). For a force whose direction is the line of motion, the equation becomes W=∫(Fdx).
If the force on an object as a function of displacement is F(x)=3x2+x, what is the work as a function of displacement (using calculus application) W(x)? Assume W(0)=0 and the force is in the direction of the object's motion.
The mass m is attached to a spring of free length b and stiffness k. The coefficient of friction
between the mass and the horizontal rod is u. The acceleration of the mass can be shown to be
x=-f(x), where
k
f(x) = ug+(b + x) 1–-
m
b² +x²
If the mass is released from rest at x = b, its speed at x = 0 is given by
1. Compute vo by numerical Simpson's 1/3 and 3/8 integration and compare between them
with different step size, using the data m = 0.9 kg. b = 0.6 m, =0.3, k = 100 N/m, and g
= 9.81 m/s.
2. Develop a MATLAB code to solve the equation for both methods.
3. Plot the acceleration of the mass versus x, and find the area under the curve by MATLAB
built-in function.
4. Can we find an exact solution??Try it.
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Chapter 7 Solutions
Physics for Scientists and Engineers With Modern Physics
Ch. 7.2 - Prob. 7.1QQCh. 7.2 - shows four situations in which a force is applied...Ch. 7.3 - Which of the following statements is true about...Ch. 7.4 - A dart is inserted into a spring-loaded dart gun...Ch. 7.5 - A dart is inserted into a spring-loaded dart gun...Ch. 7.6 - Choose the correct answer. The gravitational...Ch. 7.6 - A ball is connected to a light spring suspended...Ch. 7.8 - What does the slope of a graph of U(x) versus x...Ch. 7 - Prob. 1OQCh. 7 - If the net work done by external forces on a...
Ch. 7 - Prob. 3OQCh. 7 - A cart is set rolling across a level table, at the...Ch. 7 - Let N represent the direction horizontally north,...Ch. 7 - Prob. 6OQCh. 7 - Prob. 7OQCh. 7 - As a simple pendulum swings back and forth, the...Ch. 7 - Bullet 2 has twice the mass of bullet 1. Both are...Ch. 7 - Prob. 10OQCh. 7 - If the speed of a particle is doubled, what...Ch. 7 - Prob. 12OQCh. 7 - Prob. 13OQCh. 7 - A certain spring that obeys Hookes law is...Ch. 7 - A cart is set rolling across a level table, at the...Ch. 7 - Prob. 16OQCh. 7 - Can a normal force do work? If not, why not? If...Ch. 7 - Object 1 pushes on object 2 as the objects move...Ch. 7 - Prob. 3CQCh. 7 - (a) For what values of the angle u between two...Ch. 7 - Prob. 5CQCh. 7 - Discuss the work done by a pitcher throwing a...Ch. 7 - Prob. 7CQCh. 7 - Prob. 8CQCh. 7 - Prob. 9CQCh. 7 - Prob. 10CQCh. 7 - Prob. 11CQCh. 7 - Prob. 12CQCh. 7 - Prob. 13CQCh. 7 - Cite two examples in which a force is exerted on...Ch. 7 - A shopper in a supermarket pushes a cart with a...Ch. 7 - Prob. 2PCh. 7 - In 1990, Walter Arfeuille of Belgium lifted a...Ch. 7 - The record number of boat lifts, including the...Ch. 7 - A block of mass m = 2.50 kg is pushed a distance d...Ch. 7 - Spiderman, whose mass is 80.0 kg, is dangling on...Ch. 7 - Prob. 7PCh. 7 - Vector A has a magnitude of 5.00 units, and vector...Ch. 7 - Prob. 9PCh. 7 - Find the scalar product of the vectors in Figure...Ch. 7 - Prob. 11PCh. 7 - Using the definition of the scalar product, find...Ch. 7 - Prob. 13PCh. 7 - Prob. 14PCh. 7 - A particle is subject to a force Fx that varies...Ch. 7 - In a control system, an accelerometer consists of...Ch. 7 - When a 4.00-kg object is hung vertically on a...Ch. 7 - Prob. 18PCh. 7 - Prob. 19PCh. 7 - Prob. 20PCh. 7 - Prob. 21PCh. 7 - Prob. 22PCh. 7 - Prob. 23PCh. 7 - Prob. 24PCh. 7 - A small particle of mass m is pulled to the top of...Ch. 7 - The force acting on a particle is Fx = (8x 16),...Ch. 7 - When different loads hang on a spring, the spring...Ch. 7 - Prob. 28PCh. 7 - Prob. 29PCh. 7 - Review. The graph in Figure P7.20 specifies a...Ch. 7 - Prob. 31PCh. 7 - Prob. 32PCh. 7 - A 0.600-kg particle has a speed of 2.00 m/s at...Ch. 7 - A 4.00-kg particle is subject to a net force that...Ch. 7 - A 2 100-kg pile driver is used to drive a steel...Ch. 7 - Review. In an electron microscope, there is an...Ch. 7 - Review. You can think of the workkinetic energy...Ch. 7 - Prob. 38PCh. 7 - Review. A 5.75-kg object passes through the origin...Ch. 7 - A 1 000-kg roller coaster car is initially at the...Ch. 7 - A 0.20-kg stone is held 1.3 m above the top edge...Ch. 7 - Prob. 42PCh. 7 - A 4.00-kg particle moves from the origin to...Ch. 7 - Prob. 44PCh. 7 - A force acting on a particle moving in the xy...Ch. 7 - Prob. 46PCh. 7 - Prob. 47PCh. 7 - Prob. 48PCh. 7 - Prob. 49PCh. 7 - Prob. 50PCh. 7 - Prob. 51PCh. 7 - For the potential energy curve shown in Figure...Ch. 7 - A right circular cone can theoretically be...Ch. 7 - The potential energy function for a system of...Ch. 7 - Prob. 55APCh. 7 - A particle moves along the xaxis from x = 12.8 m...Ch. 7 - Prob. 57APCh. 7 - Prob. 58APCh. 7 - Prob. 59APCh. 7 - Why is the following situation impossible? In a...Ch. 7 - Prob. 61APCh. 7 - Prob. 62APCh. 7 - An inclined plane of angle = 20.0 has a spring of...Ch. 7 - Prob. 64APCh. 7 - Prob. 65APCh. 7 - A particle of mass m = 1.18 kg is attached between...Ch. 7 - Prob. 67CP
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