Question

Interactive LearningWare 5.2 illustrates good problem-solving techniques for this type of problem. Two cars are traveling at the same speed of 21 m/s on a curve that has a radius of 127 m. Car A has a mass of 1010 kg, and car B has a mass of 1610 kg. Find (a) the magnitude of the centripetal acceleration and (b) the magnitude of the centripetal force for Car A, (c) the magnitude of the centripetal acceleration and (d) the magnitude of the centripetal force for Car B.

Answer 1

(a)
`a_(cA)=3.47(m)/(s^(2))`

(b)
`F_(cA)=3507N`

(c)
`a_(cB)=3.47(m)/(s^(2))`

(d)
`F_(cB)=5587N`

Step-by-step explanation:

(a) Find the magnitude of the centripetal acceleration for Car A:

`a_(cA)=(v^(2))/(r)`

`a_(cA)=((21(m)/(s))^(2))/(127m)`

`a_(cA)=3.47(m)/(s^(2))`

(b) Find the magnitude of the centripetal force for Car A:

`F_(c)=m.a_(c)`

`F_(cA)=m_(A).a_(c)`

`F_(cA)=1010kg*3.47(m)/(s^(2))`

`F=3507N`

(c) Find the magnitude of the centripetal acceleration for Car B:

As the centripetal acceleration depends of the velocity and the radius, the magnitude of the centripetal acceleration for the Car B is the same as the centripetal acceleration for the Car A.

`a_(cB)=3.47(m)/(s^(2))`

(d) Find the magnitude of the centripetal force for Car B:

`F_(cB)=m_(B).a_(c)`

`F_(cB)=1610kg*3.47(m)/(s^(2))`

`F=5587N`