Question

A 14000N car traveling at 25m/s rounds a curve of radius 200m. Find the following: a. The centripetal acceleration of the car.

Answer 1

Answer:

Explanation:

weight of car, W = 14000 N

radius, r = 200 m

velocity, v = 25 m/s

(a) Centripetal acceleration is given by

a = v²/r

a = 25 x 25 / 200 = 3.125 m/s²

(b) Centripetal force, F = mass x centripetal acceleration

mass = weight / acceleration due to gravity

m = 14000 / 9.8 = 1428.57 kg

So, F = 1428.57 x 3.125

F = 4464.28 N

(c) Let μ be the coefficient of friction

So, F = μ mg

4464.28 = μ x 14000

μ = 0.32

Answer 2

Answer:

Explanation:

Given

Weight of car $W=14,000\ N$

mass of car $m=\frac{14,000}{9.8}=1428.57\ N$

velocity of car $v=25\ m/s$

radius $r=200\ m$

(a)Centripetal acceleration is given by

$a_c=\frac{v^2}{r}$

$a_c=\frac{25^2}{200}$

$a_c=3.125\ m$

(b)Force that provide centripetal acceleration

$F=F_c=\frac{mv^2}{r}$

$F=\frac{1428.57\times 25^2}{200}$

$F=4464.285\ N$

(c)Friction force between car and tires is given by

$=\mu N$

where $\mu$=coefficient of static friction

N=normal reaction

Centripetal force will balance the friction force

$F_c=F_r$

$4464.285=\mu \times 1428.57\times 9.8$

$\mu =0.318$