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What angle does the string make with the vertical?

  • Thread starter PerpetuallyFrustrate
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PerpetuallyFrustrate

[SOLVED] Help with a few problems

A pair of fuzzy dice is hanging by a string from your rearview mirror. While you are accelarting from a stoplight to 20 m/s (in 5 seconds), what angle does the string make with the vertical?

A train traveling at a constant speed rounds a curve of radius 275 m. A chandelier suspended from the ceiling swings out to an angle of 17.5º throughout the turn. What is the speed of the train?

Help on where to start and how to solve the problems would be appreciated.
 
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For the first problem Identify the acceleration of the system, and the weight of the dice. Find the angle using trigonometry. [hint: draw a force diagram]

For the second problem: Use the similar method as to the first problem, except this time is the centripetal force.
 
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Start by drawing a free-body diagram to depict the forces acting on the object.

You are not given the mass, so let mass = M. In the case of the dice, you can find the acceleration just by doing a bit of arithmetic. So, in terms of M, what are the forces acting on the dice, and in which directions do these forces act? You are asked to find θ (the angle the string makes from the vertical), so figure out how to write equations to represent the horizontal and vertical components of these forces in terms of θ. Now see how you can manipulate these expressions in order to solve for θ.

In the second case, by a similar approach, you can use the angle of the chandelier (which is given) to find the angular acceleration, and then use the angular acceleration and the radius of curvature to solve for the speed.

Give it a try.
 

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