Question

Two cars are traveling at the same speed of 22 m/s on a curve that has a radius of 114 m. Car A has a mass of 1040 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) 4.25
`m/s^2`

(b) 4420 N

(c) 4.25
`m/s^2`

(d) 6842.5 N

Step-by-step explanation:

(a) Centripetal acceleration of car A,
`a_c`, is given as;

`a_c = (v^2)/(r)`

where v = velocity of car

r = radius of curve

`a_c = (22^2)/(114)\\ \\\\a_c = 4.25 m/s^2`

(b) Centripetal force of car A is given as:

`F_A = m_A*a_c = m_A*(v^2)/(r)`

`F_A = 1040 * 4.25 = \\\\\\F_A = 4420 N`

(c) Since car A and car B have the same speed, they have the same centripetal acceleration (
`a_c = 4.25 m/s^2`)

(d) Centripetal force of car A is given as:

`F_B = m_B*a_c = m_B*(v^2)/(r)`

`F_A = 1610 * 4.25 = \\\\\\F_A = 6842.5N`