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 θ 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 θ and show that it is independent of the mass m and the length L. (Use the following as necessary: θ and g.)(b) Determine the acceleration of the car when θ = 22.6°.

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 θ 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 θ and show that it is independent of the mass m and the length L. (Use the following as necessary: θ and g.)(b) Determine the acceleration of the car when θ = 22.6°.

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter2: Newtonian Mechanics-single Particle

Section: Chapter Questions

Problem 2.51P: Let us make the (unrealistic) assumption that a boat of mass m gliding with initial velocity v0 in...

See similar textbooks

Similar questions

Let us make the (unrealistic) assumption that a boat of mass m gliding with initial velocity v0 in water is slowed by a viscous retarding force of magnitude bv2, where b is a constant, (a) Find and sketch v(t). How long does it take the boat to reach a speed of v0/l000? (b) Find x(t). How far does the boat travel in this time? Let m = 200 kg, v0 = 2 m/s, and b = 0.2 Nm-2s2.
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 block with mass m1 = 9.2 kg rests on the surface of a horizontal table which has a coefficient of kinetic friction of μk = 0.58. A second block with a mass m2 = 10.8 kg is connected to the first by an ideal string passing over an ideal pulley such that the second block is suspended vertically. The second block is released from rest, and motion occurs. Using the variable T to represent tension, write an expression for the sum of the forces in the y-direction, ΣFy, for block 2. Using the variable T to represent tension, write an expression for the sum of the forces in the x-direction, ΣFx for block 1. Block 1 accelerates along the tabletop, in the horizontal direction, while block 2 moves vertically. With the coordinate system provided in the drawing, we may write a⃗ 1=a1i^a→1=a1i^ and a⃗ 2=a2y^a→2=a2y^. Write an expression that relates the vertical component of the acceleration of block 2 to the horizontal component of the acceleration of block 1. Write an expression using the…
A block with mass m1 = 9.2 kg rests on the surface of a horizontal table which has a coefficient of kinetic friction of μk = 0.58. A second block with a mass m2 = 10.8 kg is connected to the first by an ideal string passing over an ideal pulley such that the second block is suspended vertically. The second block is released from rest, and motion occurs. Using the variable T to represent tension, write an expression for the sum of the forces in the y-direction, ΣFy, for block 2. Using the variable T to represent tension, write an expression for the sum of the forces in the x-direction, ΣFx for block 1. Block 1 accelerates along the tabletop, in the horizontal direction, while block 2 moves vertically. With the coordinate system provided in the drawing, we may write a⃗ 1=a1i^a→1=a1i^ and a⃗ 2=a2y^a→2=a2y^. Write an expression that relates the vertical component of the acceleration of block 2 to the horizontal component of the acceleration of block 1. Write an expression using the…
A block with mass m1 = 8.6 kg rests on the surface of a horizontal table which has a coefficient of kinetic friction of μk = 0.74. A second block with a mass m2 = 10.2 kg is connected to the first by an ideal string passing over an ideal pulley such that the second block is suspended vertically. The second block is released from rest, and motion occurs. 1. Using the variable T to represent tension, write an expression for the sum of the forces in the y-direction, ΣFy, for block 2. 2. Using the variable T to represent tension, write an expression for the sum of the forces in the x-direction, ΣFx for block 1. 3. Block 1 accelerates along the tabletop, in the horizontal direction, while block 2 moves vertically. With the coordinate system provided in the drawing, we may write a1=a1i and a2=a2y. Write an expression that relates the vertical component of the acceleration of block 2 to the horizontal component of the acceleration of block 1. 4. Write an expression using the variables…
An object of mass mm is initially at rest. After a force of magnitude F acts on it for a time T, the object has a speed v. Suppose the mass of the object is doubled, and the magnitude of the force acting on it is quadrupled. In terms of T, how long does it take for the object to accelerate from rest to a speed v now?
Two blocks, of weights 2.5 N and 5.6 N, are connected by a massless string and slide down a 30° inclined plane. The coefficient of kinetic friction between the lighter block and the plane is 0.081; that between the heavier block and the plane is 0.40. Assuming that the lighter block leads, find (a) the magnitude of the acceleration of the blocks and (b) the tension in the string.
A person in a kayak starts paddling, and it accelerates from 0 to 0.8 mile/hour in adistance of 0.8km. If the combined mass of the person and the kayak is 80kg, whatis the magnitude of the net force acting on the kayak?
A spaceship lifts off vertically from the Moon, where g = 1.6 m/s2. If the ship has an upward acceleration of 1.0 m/s2 as it lifts off, what is the magnitude of the force exerted by the ship on its pilot, who weighs 735 N on Earth?
There are two forces on the 1.19 kg box in the overhead view of the figure but only one is shown. For F1 = 15.7 N, a = 14.7 m/s2, and θ = 34.1°, find the second force (a) in unit-vector notation and as (b) a magnitude and (c) a direction. (State the direction as a negative angle measured from the +x direction.)
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).
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.