The 1400-kg{\ m kg} mass of a car includes four tires, each of mass (including w
ID: 1293340 • Letter: T
Question
The 1400-kg{ m kg} mass of a car includes four tires, each of mass (including wheels) 32kgkg and diameter 0.80 m{ m m}. Assume each tire and wheel combination acts as a solid cylinder.Determine the fraction of the kinetic energy in the tires and wheels.
What percent error would you make in part C if you ignored the rotational inertia of the tires and wheels?
The 1400-kg{ rm kg} mass of a car includes four tires, each of mass (including wheels) 32kgkg and diameter 0.80 m{ rm m}. Assume each tire and wheel combination acts as a solid cylinder. Determine the fraction of the kinetic energy in the tires and wheels. If the car is initially at rest and is then pulled by a tow truck with a force of 1400N ^N, what is the acceleration of the car? Ignore frictional losses. What percent error would you make in part C if you ignored the rotational inertia of the tires and wheels?Explanation / Answer
M = 1400 kg
m = 32 kg
d = 0.80 m, r = 0.40 m
I = mr^2/2
= 32 *0.40^2/2
= 2.56 kg.m2
rotational energy = 4 *1/2 *I*(v/r)^2
= 2 *2.56 *V^2/0.40^2
= 32*V^2
K.E = 1/2 *M*V^2
= 0.5 *1400 *V^2
= 700 v^2
Fraction = 32/700
= 0.0457 or 4.57 %
F = M*a + 4 *I*alpha
= M*a + 4 *I*a/r
= (1400 + 4*2.56/0.40 ) *a
= 1425.6 *a
a = 0.982 m/s2
Ignoring rotational inertia
a = F/M
= 1 m/s2
error = 0.98-1/1
= 0.02
= 2%
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