Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 10, Problem 75P
(a)
To determine
ToExplain: Whether the
(b)
To determine
ToExplain: Whether the energy of the object conserved
(c)
To determine
ToFind: Thespeed of the object when the unwrapped length has shortened to
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Problem Set #1: Topics: Work and Energy and Impulse, Momentum and Collision
1. A pendulum consisting of a bob with mass 3kg is attached to a 5m string. It is pulled aside so
that the string makes an angle of 35 degrees with the vertical and is released from rest. Find the
speed v at the bottom of the swing and the tension in the string at that time.
In this question you will use an energy approach to determine how the mass of a spring affects its motion. Normally we assume the spring has zero mass. But if we realize real springs have mass we can find the contribution to the kinetic energy of the system due to the motion of the spring. What makes this hard is that different parts of the spring move at different velocities. So, we must use a little calculus to find the result.Consider a vertical spring of mass m that has a mass M attached at its end. Let the position of the mass at the end of the spring relative to the point of attachment be given by Y and its velocity be given by V.
a)
What is the velocity of a small segment of the spring at the point of attachment?
b)
What is the velocity of a small segment of the spring right next to the moving mass?
c)
What is the velocity of a small segment of the spring that is exactly halfway between the top and the bottom?
d)
Now let the mass of the spring be m and…
Just a little something on momentum and kinetic energy. As a reminder, momentum is a vector and:
p = mv
K = 1/2 mv2 = 1/2 pv = p2/2m
In terms of the dot product: v2 = v⋅v, p2 = p⋅p, and pv = p⋅v.
Unlike speed vs. velocity, but like all other vectors, momentum may refer to the magnitude of the momentum vector.
Now, answers the following questions:
1) A 7-kg particle goes 96 m/s. Calculate its momentum in kg*m/s. (This requires an exact answer.)
2) A 7-kg particle's momentum is (392, 61) kg*m/s. Calculate its kinetic energy.
3) A pebble and a grapefruit have the same momentum. Which has the greater kinetic energy?
Chapter 10 Solutions
Physics for Scientists and Engineers
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- A fellow student tells you that she has both zero kinetic energy and zero potential energy. Is this possible? Explain.arrow_forwardA Vulcan spaceship has a mass of 6.50 × 104 kg and a Romulan spaceship is twice as massive. Both have engines that generate the same total force of 9.50 × 106 N. If each spaceship fires its engine for the same amount of time, starting from rest and ignoring any change in mass due to whatever is expelled by the engines, calculate the energy of the Vulcan spaceship if the engines are fired for 102 s.arrow_forwardGalactic Alliance Junior Mission Officer (GAJMO) Bundit Nermalloy is predicting the kinetic energy of a supply spacecraft, which is being moved in one dimension in the tractor beam of the ship named the Jadarian-Ruby, to ensure that the supply spacecraft doesn't damage the spaceport to which it is being delivered. GAJMO Nermalloy has been instructed to deliver the supply spacecraft with a kinetic energy less than 10¹0 J (where 1 J = 1 N·m). GAJMO Nermalloy knows that the change in kinetic energy of an object moving in one dimension is equal to the net work performed on it, where net work is the integral of the component of net force in the direction of motion with respect to the position of the of the object. That is: KE2 – KE₁ = 7² F(x) dx. x 1 The net force exerted by the tractor beam is supposed to be constant, Fo −3.5 × 106 N, but due to improper maintenance of the Jadarian-Ruby, the actual force exerted by the tractor beam as a function of position is given by F(x) = ax³ + ß,…arrow_forward
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