The formula F=mv^2/r gives the centripetal force F of an object of mass m moving along a circle of radius r, where v is the tangential velocity of the object. Solve the formula for v. Rationalize the denominator. Calculate the tangential velocity of a 100kg object with a force of 50 Newton, moving along a circular path with a diameter of 150 meters.

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freckledspots freckledspots · Answer 1 · 2019-06-11T03:33:04+02:00

Answer: (It didn't say what to have the units in so I assumed as is)

(pm) 5sqrt(6)/2

(pm) 6.12372 (rounded version)

Step-by-step explanation:

F=mv^2/r (Given)

rF=mv^2 (Multiply both sides by r)

rF/m=v^2 (Divide both sides by m)

v=(pm) sqrt(rF/m) (Square root both sides)-(pm means plus or minus)

v=(pm) sqrt(rF)/sqrt(m)

v=(pm) sqrt(rF)sqrt(m)/m (I had multiply top and bottom by sqrt(m))

v=(pm) sqrt(rFm)/m

*sqrt( ) means square root of whatever is in the ( ) that follows the sqrt

Now find v if F=50, m=100 kg, and r=150/2=75 so plug in

v=(pm) sqrt(75*50*100)/100

v=(pm) sqrt(375000)/100 OR

v=(pm) sqrt(100*25*3*25*2)/100

v=(pm) 10*5*sqrt(3)*5*sqrt(2)/100

v=(pm) 250sqrt(6)/100

v=(pm) 2.5sqrt(6)

v=(pm) 5sqrt(6)/2

Or if you want a decimal number rounded, it would be (pm) 6.12372