A simple accelerometer is constructed inside a car by suspending an object of mass m from a string of length L that is tied to the car's ceiling. As the car accelerates the string-object system makes a constant angle of 0 with the vertical. (a) Assuming that the string mass is negligible compared with m, derive an expression for the car's acceleration in terms of and show that it is independent of the mass m and the length L. (Use the following as necessary: 0 and g.) a = (b) Determine the acceleration of the car when = 23.6°. m/s² Need Help? Read It

A simple accelerometer is constructed inside a car by suspending an object of mass m from a string of length L that is tied to the car's ceiling. As the car accelerates the string-object system makes a constant angle of 0 with the vertical. (a) Assuming that the string mass is negligible compared with m, derive an expression for the car's acceleration in terms of and show that it is independent of the mass m and the length L. (Use the following as necessary: 0 and g.) a = (b) Determine the acceleration of the car when = 23.6°. m/s² Need Help? Read It

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Newton’s Third Law of Motion

The horse pulls the cart and the cart pulls the horse in response as per Newton third law. So the big question is, “Don’t the two forces cancel each other? How does the cart accelerate?”

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A simple accelerometer is constructed inside a car by suspending an object of mass m from a string of length L that is tied to the
car's ceiling. As the car accelerates the string-object system makes a constant angle of 0 with the vertical.
(a) Assuming that the string mass is negligible compared with m, derive an expression for the car's acceleration in terms
of and show that it is independent of the mass m and the length L. (Use the following as necessary: 0 and g.)
a =
(b) Determine the acceleration of the car when = 23.6°.
m/s²
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A simple accelerometer is constructed inside a car by suspending an object of mass m from a string of length L that is tied to the cars ceiling. As the car accelerates the stringobject system makes a constant angle of 0 with the vertical. (a) Assuming that the string mass is negligible compared with m, derive an expression for the cars acceleration in terms of u and show that it is independent of the mass m and the length L. (b) Determine the acceleration of the car when 0 = 23.0°.
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Subpart 2: Set up Newton's Second Law Equations (i) Newton's Second Law for m, in terms of weights of the blocks, m₁g, and m₂g, the tension in the string 7 and the normal reaction N₁ of the table on m, can be written as (use the coordinate axes for signs of different forces): ΣF= T ΣF= 10 =₁2₁₁x √=m₁a₁₁y (ii) Newton's Second Law for m₂ in terms of weights of the blocks, m₁g, and m₂g, the tension in the string T and the normal reaction N₁ of the table on m, can be written as: Note: The motion of m₂ is along the y-direction only. ΣF₁= m₂g-m₂a2y=m₂a2y