1. Most of the gasoline that is used to power a car is burned during acceleratio
ID: 1881159 • Letter: 1
Question
1. Most of the gasoline that is used to power a car is burned during acceleration. Answer the following questions related to this process, neglecting any drag or friction on the car, and assuming a car has a mass of 1000 kg (a little over 1 ton) How much energy is required for a car to accelerate from 0 to 100 km/h over a distance of 100 m in kJ? (5 pts) a. How much energy is required for a car to accelerate from 0 to 100 km/h on an incline of 30° over a distance of 100 m in kJ? (5 pts) b. c. The energy density of gasoline is ~50 MJ/kg. If the density of gasoline is 700 kg/m3, how many liters (L) of gasoline are burned in the above two cases (no incline AND incline of 30°)? (Hint: 1 m#1000 L) (5 pts)Explanation / Answer
Given,
m = 1000 kg ;
a)u = 0 ; v = 100 km/h = 27.78 m/s ; d = 100 m
we know that
v^2 = u^2 + 2 a s
27.78^2 = 0^2 + 2 x a x 100
a = 27.78^2/200 = 3.86 m/s^2
F = ma = 1000 x 3.86 = 3860 N
E = F d = 3860 x 100 = 386,000 = 386 kJ
Hence, E = 386 kJ
b)till F it remains same
E = F d cos(theta)
E = 3860 x 100 x cos30 = 334,000 J
Hence, E = 334 kJ
c)E' = E/V = E rho/m
m = E rho/E'
for first case
m = 386 x 10^3 x 700/50 x 10^6 = 5.404 kg
m' = 334 x 10^3 x 700/50 x 10^6 = 4.68 kg
Hence, m = 5.404 kg ; m' = 4.68 kg
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