o) Instructions show ALL your work in detail T#: write all answers legibly and c

Question

o) Instructions show ALL your work in detail T#: write all answers legibly and clearly use UNITS for all final answers no collaboration, no talking to each other you can use your book and your calculator, but nothing else (1) 10 points car goes over a hill with the speed of 20 miles/hour. The radius of curvature of the hill at its top is 20m. Calculate the normal force that acts on the car. At what speed would the normal be zero, when car loses contact with the ground? (2) 10 points What is the angular speed of the hour clock hand?

Explanation / Answer

1)

20miles/hour = 1609*20/3600 = 8.93 m/s

mg-N = mv^2/r

mg-N = m8.93^2/20

N = m(9.8 - 3.98)

=5.81m ; where m is the mass of the car

normal force ,N=0 when , mg = mv^2/r

so v= sqrt(rg) = sqrt(20*9.8) = 14 m/s

2) angular velocity of hour clock : 2pie/3600*12 = 0.0001453 radians per second

3)using work energy theorem :

mg*6*sin30 = friction force *length of ramp + 0.5mv^2

120 = 36 +0.5mv^2

v= 6.41m/s

4) no it is not possible for both of them to be at rest because there was some initial momentum of the two body system so there must be some momemtum of the system after the collision .

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