Find the acceleration and tension for a horizontal mass pulley system with no friction.
2.6 هزار بار بازدید -
10 ماه پیش
-
In this problem, we find
In this problem, we find the acceleration and tension for a horizontal Atwood machine with no friction.
We begin with a discussion of the direction of acceleration and the critical need to define the acceleration consistently. We choose to call the actual direction of acceleration the positive direction for the force analysis of each mass in the horizontal mass pulley system, and this is important because "a" needs to represent the same value in each of our equations. If one "a" stands for a negative quantity while the other stands for a positive quantity, then the system of equations for tension and acceleration will not work!
Next, we show all the force vectors for the mass and pulley system. The mass on the track feels the force of gravity downward, the normal force upward and the tension pulling to the right on the mass. The hanging mass feels the force of gravity pulling downward and the tension pulling upward.
We set up the general equations for the mass and pulley system by applying Newton's second law to each mass. Next, we solve the system of equations by using elimination and we solve for the acceleration of the Atwood machine in general. Plugging in the numbers, we find the acceleration of the system. Finally, we plug our general acceleration for the mass pulley system back into our first equation, obtain a general expression for tension in the string, then plug numbers in to solve for the tension in the string.
We begin with a discussion of the direction of acceleration and the critical need to define the acceleration consistently. We choose to call the actual direction of acceleration the positive direction for the force analysis of each mass in the horizontal mass pulley system, and this is important because "a" needs to represent the same value in each of our equations. If one "a" stands for a negative quantity while the other stands for a positive quantity, then the system of equations for tension and acceleration will not work!
Next, we show all the force vectors for the mass and pulley system. The mass on the track feels the force of gravity downward, the normal force upward and the tension pulling to the right on the mass. The hanging mass feels the force of gravity pulling downward and the tension pulling upward.
We set up the general equations for the mass and pulley system by applying Newton's second law to each mass. Next, we solve the system of equations by using elimination and we solve for the acceleration of the Atwood machine in general. Plugging in the numbers, we find the acceleration of the system. Finally, we plug our general acceleration for the mass pulley system back into our first equation, obtain a general expression for tension in the string, then plug numbers in to solve for the tension in the string.
10 ماه پیش
در تاریخ 1402/06/13 منتشر شده
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