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Chapter 8: Q. 58 (page 202)

Elm Street has a pronounced dip at the bottom of a steep hill before going back uphill on the other side. Your science teacher has asked everyone in the class to measure the radius of curvature of the dip. Some of your classmates are using surveying equipment, but you decide to base your measurement on what you’ve learned in physics. To do so, you sit on a spring scale, drive through the dip at different speeds, and for each speed record the scale’s reading as you pass through the bottom of the dip. Your data are as follows:

Speed m/sec

Scale Reading N

5

599

10

625

15

674

20

756

25

834

Short Answer

Expert verified

The curvature of dip is 150 m.

Step by step solution

01

Given information

The reading is given as below:

Speed m/sec

Scale Reading N

5

599

10

625

15

674

20

756

25

834

02

Explanation

Lets draw the free body diagram as below

The figure shows forces in a circular motion,
T= tension, Centripetal force = mv2/r and gravitational force = mg .

Consider the bottom point

TBottom=mv2r+mg

When v=0 we have T=mg=588 N .

We can find mass

m=588N9.81m/s2=60kg

The equation become

T=(60kgv2r)+588N

The equation y=- mx +C

Where C=588 N and m=60/r

lets draw the graph with given data

Here , from the graph we can get

60r=0.4

This means r = 150 m.

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