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An old streetcar rounds a flat corner of radius 9.1m, at16km/h. What angle with the vertical will be made by the loosely hanging hand straps?

Short Answer

Expert verified

The vertical angle will be made by the loosely hanging hand straps is 12°.

Step by step solution

01

Given data

  • Radius=9.1 m
  • Velocity=16 km/hr
02

To understand the concept 

The problem deals with Newton’s laws of motion which describe the relations between the forces acting on a body and the motion of the body.

Formula:

|a|=v2/R

03

Calculate the angle with the vertical will be made by the loosely hanging hand straps

The free-body diagram (for the hand straps of mass m) is the view that a passenger might see if she was looking forward and the streetcar was curving towards the right (so it points rightwards in the figure).

We note that |a|=v2/R

Where,

v=16 km/hr=4.4 m/s

Applying Newton’s law to the axes of the problem (+x is rightward and +y is upward), we obtain,

Tsinθ=mv2/R

Tcosθ=mg

Solving these equations for the angle,

θ=tan1v2Rg

Substitute the values in the above equation, and we get,

θ=tan1(4.4 m/s)2(9.1 m)(9.8 m/s2)θ=tan1(4.4 m/s)2(9.1 m)(9.8 m/s2)θ=tan1(0.2170)θ=12°

Thus,the vertical angle will be made by the loosely hanging hand straps is 12°.

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