The discussion clarifies the correct approach to calculating the acceleration of a train using a pendulum. The acceleration is determined using the tangent function, specifically the formula atrain = g * tan(θ), where g represents gravitational acceleration and θ is the angle of the pendulum from the vertical. The vector triangle formed by the gravitational force and the train's acceleration is essential for understanding the relationship between these forces. Misconceptions regarding the use of sine versus tangent in this context were addressed and corrected.
PREREQUISITESPhysics students, educators, and anyone interested in understanding the dynamics of pendulum motion in accelerating frames, particularly in relation to trigonometric applications in physics.
So was I right. I searched for it over internet which says about using tan instead of sin but it seemed unreasonable to meBystander said:See, you're understanding vectors, and which components mean what.
My bad. What you found about tan is correct. The gravitational force is perpendicular to the train's acceleration. The force acting on the pendulum mass is the vector sum of the gravitational force and the train's acceleration.shayan haider said:using tan instead of sin
What did you mean by that. I want to learn which is correct gsintheta or gtantheta.Bystander said:My bad. What you found about tan is correct. The gravitational force is perpendicular to the train's acceleration. The force acting on the pendulum mass is the vector sum of the gravitational force and the train's acceleration.
Mea culpa.
The vector triangle to be examined has three sides: 1) the hypotenuse, which is the resultant of gravitational force on the pendulum, and the train's acceleration (pulling the mass toward rear of train); 2) the vertical leg, which is mg of the pendulum; and 3) the horizontal leg, which is atrainm. The relationship between the two legs of the triangle is "opposite" (horizontal) over "adjacent" (vertical), or tangent, since the angle of the resultant is measured from the vertical.shayan haider said:gtantheta.
Oh sorry, I have got your point. You are right. Thanks for correction.Bystander said:The vector triangle to be examined has three sides: 1) the hypotenuse, which is the resultant of gravitational force on the pendulum, and the train's acceleration (pulling the mass toward rear of train); 2) the vertical leg, which is mg of the pendulum; and 3) the horizontal leg, which is atrainm. The relationship between the two legs of the triangle is "opposite" (horizontal) over "adjacent" (vertical), or tangent, since the angle of the resultant is measured from the vertical.
I mistook that first. g is not the resultant. It is component.Bystander said:The vector triangle to be examined has three sides: 1) the hypotenuse, which is the resultant of gravitational force on the pendulum, and the train's acceleration (pulling the mass toward rear of train); 2) the vertical leg, which is mg of the pendulum; and 3) the horizontal leg, which is atrainm. The relationship between the two legs of the triangle is "opposite" (horizontal) over "adjacent" (vertical), or tangent, since the angle of the resultant is measured from the vertical.
You and me both, but it's straightened out now.shayan haider said:I mistook that first. g is not the resultant. It is component.