Title : The similarities and differences of Chapter 14 (Kinetics of a Particle : Work and Energy) and Chapter 18 (Planar Kinetic of a Rigid Body : Work and Energy) The similarities 14 and 18
In chapter 14, we will analyse motion of a particle using the concepts of work and energy. The resulting equation will be useful for solving problems that involve force, velocity, and displacement. Before we do this, we must first define the work of a force. Force, F will do work on a particle only when the particle undergoes a displacement in the direction of the force.
In chapter 18, we will apply work and energy method to solve planar motion problems involving force, velocity, and displacement. But first it will be necessary to develop a means of
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If the particle acted upon by the force F undergoes a finite displacement along its path from r1 to r2 or s1 to s2 , Fig. 14-2a,the work of the force F is determined by the intergration. Provided F and and θ can be expressed as a function of the position,then
U_(1-2)= ∫_r1^r2▒〖F.dr〗= ∫_s1^s2▒〖F cosθ ds〗
Work of a Variable Force in Chapter 18.
If an external force F acts on a body, the work done by the force when the body moves along the path s, Fig. 18-5, is
U_F= ∫▒〖F.dr〗= ∫_s▒〖F cosθ ds〗
Here θ is the angle between the “tails” of the force and the differential displacement. The integration must account for the variation of the force’s direction and magnitude.
Work of a weight chapter 14
Consider a particle of weight W, which moves up along the path s shown in Fig,14-4 from position s1 to position s2. At an intermediate point, the displacement dr = dxi + dyj + dzk. Since W = -Wj, applying
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The kinetic energy is the sum of the both its rotational and translational parts. For the application, a free body diagram should be drawn in order to account for the work of all of the force and couple moments that acts on the body as it moves along the
For free falling objects, the net external force is just the weight of the object:
To begin with, there was friction between the marble and the wooden ramp, as the ramp was not very smooth, causing the marble’s velocity to decrease as the friction opposed the motion of the marble down the ramp. As a result, the initial velocity (vB) calculated using the test results would be slightly lower than the ideal value of vB, as the slightly lowered velocity would have caused teh marble to fall slightly closer to the lab bench. So since the horizontal displacement of the marble (dx ) decreased, this would have caused the initial velocity (vB) to decrease as well, because the vBx calculated using the slightly lower dx value would have also been slightly lower. Also, although the same person was used to release the marble down the ramp, it is possible that during some trials, the person responsible released the marble with an extra force on the marble, thus causing the initial velocity of the ramp to increase. All of the above have impacted the experimental values for vB in scenario 1 and 2, as these uncertainties impacted the horizontal displacement of the ball (dx ) as the ball fell off of the ramp. Therefore, in this case where the initial velocity has been slightly increased, the horizontal displacement of the ball would have increased slightly as well, causing the calculations to become less accurate in comparison to the ideal values of vB, which would have been slightly lower. Furthermore, in scenario 1, where the marble rolled off the ramp and onto the lab bench horizontally, before falling off the lab bench, the transition of the marble from the ramp to the lab bench caused a slight change in the velocity of the marble. When the marble bounced onto the lab bench from the ramp, it caused the
Vrock= Vcenter of mass + Wrock Where V is the translational velocity, and W is the angular velocity
2.Physics A World View. Larry D. Kirkpatrick, Gerald F. Wheeler. Harcourt College Publishers. 2001. P174.
The force exerted by object 1 onto object 2 is equal in magnitude and opposite in direction to the force exerted by object 2 onto object 1.
The file labeled “Newton’s 2nd Law” is to be opened. The cart’s mass along with the attachment of the sensor and the accelerometer are to be measured and recorded. Being carefully verified in order, the track is leveled and the Force Sensor is set to 10N and connected to...
The force in the previous equation can be calculated using Newton’s Second Law of Motion, F=ma (University of Tennessee, 2014).
The First Law of Motion (Law of Inertia) states that “A body at rest will remain at rest, and a body in motion will remain in motion unless it is acted upon by an external force”. The Second Law of Motion states that “The force acting on an object is equal to the mass of that object times its acceleration”. The Third Law of Motion states that “if a body exerts a force on a second body, the second body exerts a force that is equal in magnitude and opposite in direction to the first force. So for every action force there is always a reaction force” Sir Isaac Newton will be remembered today for his academic achievement and excellent Laws of Motion! Isaac Newton’s works was once accepted in Britain after half a century. Now, Isaac Newton’s work is widely distributed throughout the world and had been ranked among humanity’s greatest achievements in abstract
the length of the slope can be used to calculate the speed of the car
1.Kirkpatrick, L. D., & Wheeler, G. F. (2001). Physics: A World View. Orlando: Harcourt College Publishers.
Different collisions took place throughout the process of the Rube Goldberg Machine. This included Elastic and Inelastic collisions. An example of an Elastic Collision in our Rube Goldberg Machine is when the car went down the track and collided with another car. Elastic collisions are defined as collisions with conservation or no loss of momentum. This is proven by the first car which transferred its momentum to the second car thus momentum was perfectly conserved. An Inelastic Collision is seen in our project ...
This law can be expressed as the equation F= ma, where F is the net force, m is the mass and a is the acceleration. This equation can be used in different contexts and rearranged to solve numerous different calculations.
The motion direction of an object must be the same as the direction of net force that exert on it.
In the 1680s this mathematical approach to the mechanical physiology founded in Italy played a fundamental role for the embracement and acceptance of the mechanical philosophy in the