Circular Motion Problems
Last updated on July 17th, 2023 at 04:51 pm
Here goes a set of Circular Motion Problems. This set contains Physics numerical problems on centripetal force and uniform circular motion for class 11. Solutions are also appended in this post for our students.
Formulas Used
Centripetal force Fc = mv2/r
Centripetal acceleration ac = v2/r
Circular Motion Problems [for class 11]
1 ) A rock of mass 250 g is attached to the end of a 1.5 m long string and whirled in a horizontal circle at 15 m/s. Calculate the centripetal force and acceleration of the rock.
2) A car of mass 1450 kg is driven around a bend of radius 70.0 m. Determine the frictional force required between the tires and the road in order to allow the car to travel at 70.0 km/h.
3) A 400 g rock is tied to the end of a 2 m long string and whirled until it has a speed of 12.5 m/s. Calculate the centripetal force and acceleration experienced by the rock.
4) A 900 kg motorcycle, traveling at 70 km/h, rounds a bend in the road with a radius of 17.5 m. Calculate the centripetal force required from the friction between the tires and the road.
Solution
1] Centripetal force Fc = mv2/r = (0.25×152) /1.5 = 37.5 N
Centripetal acceleration can be found using its formula or, more simply, using Newton’s Second Law.
ac=Fc / m = 37.5/0.25 = 150 m/s2
2 ] The frictional force between the tyres and the road must provide sufficient centripetal force for the circular motion involved.
v = 70 kmph = 70×1000/3600 m/s = 19.4 m/s
Centripetal force Fc = mv2/r = 1450 x 19.42 / 70 = 7800 N.
That is, the total frictional force provided by the tyres must be at least 7800 N or an average force of 1950 N per tyre.
Problem #3 ] Same solution steps to be followed as described in the solution for problem #1.
Problem #4 ] Same solution steps to be followed as described in the solution for problem #2.