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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%