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

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter4: The Laws Of Motion

Section: Chapter Questions

Problem 27P

See similar textbooks

Similar questions

An object of mass m1= 5.0 kg placed on a frictionless, horizontal table is connected to a string thatpasses over a pulley and then is fastened to a hanging object of mass m2 = 9.0 kg as shown in theFigure. Find:(a) The magnitude of the acceleration of the objects and(b) The tension T in the string.
A constant horizontal force F of magnitude 0.1 N is applied to m1. If m1 = 1.0 kg and m2 = 0.33 kg, find the magnitude of the acceleration of the system of two blocks.
According to legend, Galileo Galilei dropped two balls of different mass from the top of the leaning tower of Pisa in 1589. Whether or not this public experiment ever took place, Galileo was able to demonstrate that, contrary to Aristotle’s teaching, all bodies fall at the same rate regardless of mass, assuming that one is not so tenuous that it is slowed by air resistance. In this experiment, an equation is presented relating the acceleration of gravity at Earth’s surface, g, to the height that an object falls from, h, and the time it takes the object to reach the ground, t. Gravity acceleration at Earth’s surface has been measured many times. In British Imperial Units, Small Metric Units, and Large Metric Units, the standard values of g are: g = 32 feet per second-squared (ft/s2) g = 980 centimeters per second-squared (cm/s2) g = 9.8 meters per second-squared (m/s2). Theory Newton succeeded in explaining gravitational acceleration using his Laws of…
A particle of mass m is located at the origin. It is at rest and in equilibrium. A time-dependent force of F → (t) is applied at time t = 0 , and its components are Fx(t) = pt and Fy(t) = n + qt where p, q, and n are constants. Find the position r → (t) and velocity v → (t) as functions of time t.
Show that the acceleration of any object down an incline where friction behaves simply (that is, where fk=μkN)fk=μkN) is a=g(sinθ−μkcosθ).a=g(sinθ−μkcosθ). Note that the acceleration is independent of mass and reduces to the expression found in the previous problem when friction becomes negligibly small (μk=0).(μk=0).
The effective force acting on the bob of focault's pendulum is the resultant of a) weight of the bob and tension in the string. b) tension in string and coriolis force. c) weight of the bob and coriolis force. d) weight of bob, tension in the string and the coriolis force.
Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg, a) just after it is dropped from the window of a stationary train, b) just after it is dropped from the window of a train running at a constant velocity of 36 km/h,
If a block of mass m lies on a wedge of mass M, here all surfaces are smooth, and the block slips on the wedge, will the wedge have any acceleration? If yes, explain why and of what magnitude?
A 2.8 kg mass is initially at rest while upon a horizontal surface. An applied force of 17 N is exerted on the mass in the =x direction. If the acceleration produced is 2.3 m/s² in the +x direction, what is the coefficient of kinetic friction between the mass and the surface?
Two thieves want to steal a 1mx1mx1m Lazada Mystery Box worth of 1million pesos that is placed on a warehouse with a cemented floor. When they successfully break into the warehouse using a bobby pin they realize that they both cannot carry the 400 lb package, so they decided to push it out of the warehouse. If the untouched package and the cemented floor has a coefficient of friction of 0.400, what is the maximum amount of force they first need to exert in order to make the package move when they will: A) push the package with their hands 90 degree with the vertical wall of the box. B) push the package with their hands in 120 degree with the vertical wall of the package. C) When they decided to pull the box instead and their hands are in 120 degree with the top edge of the box. ASAP
At the end of a roller coaster ride, the cars must slow to a stop, but the magnitude of the acceleration cannot exceed 1.3 g's. Given a car with a mass of 1,700 kg (including the passengers), what is the magnitude of the maximum allowable force (in N)?
In which of the following situations do the forces on the body sum to zero?