Question

A car at the Indianapolis 500 accelerates uniformly from the pit area, going from rest to 330 km/h in a semicircular arc with a radius of 230 m

A) Determine the tangential and radial acceleration of the car when it is halfway through the arc, assuming constant tangential acceleration.

B) If the curve were flat, what would the coefficient of static friction would be necessary between the tires and the road to provide this acceleration with no slipping or skidding?

Answer #1

Here,

initial speed , u = 0 m/s

final speed , v = 330 km/hr = 91.7 m/s

Now , for the tangential acceleration at

total distance , d = pi * R = pi * 230

using third equation of motion

v^2 - u^2 = 2 *at * d

91.7^2 - 0 = 2 * at * (pi * 230)

at = 5.82 m/s^2

**the tangential acceleration of the car is 5.82
m/s^2**

Now, for the speed at half way

again using third equation of motion

v^2 - u^2 = 2 *at * d

v^2 - 0 = 2 * 5.82 * (pi * 230/2)

v = 64.84 m/s

radial acceleration = v^2/R

radial acceleration = 64.84^2/230

radial acceleration = 18.27 m/s^2

the radius acceleration is 18.27 m/s^2

**the radial acceleration is 18.27 m/s^2**

B)

net acceleration = sqrt(18.27^2 + 5.82^2)

net acceleration = 19.2 m/s^2

now, for the coefficient of friction u

u * g = 19.2

u = 19.2/.9.8

**u = 1.96**

**the coefficient of friction needed is 1.96**

a
car accelerates uniformly from rest to 24.1 m/s in 9 s along a
level stretch of road. Ignoring friction , determine the average
power required to accelerate the car if the mass of the car is
1,131 kg

A curve of radius 20 m is banked so that a 1100 kg car traveling
at 30 km/h can round it even if the road is so icy that the
coefficient of static friction is approximately zero. The
acceleration of gravity is 9.81 m/s 2 .
Find the minimum speed at which a car can travel around this
curve without skidding if the coefficient of static friction
between the road and the tires is 0.3. Answer in units of m/s.

10.4-5-6)
A)
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uniformly from rest with a tangential acceleration of 2.10
m/s2. The car makes it one quarter of the way around the
circle before it skids off the track. From these data, determine
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________
(Hint: You are not given a value of the radius of the track.
Think through the problem using the symbol R for this
value and...

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(a) Find the maximum linear speed of a person sitting on the
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(b) Find the person's maximum radial acceleration.
(c) Find the angular acceleration of the merry-go-round.
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A curve of radius 20 m is banked so that a 1000 kg car traveling
at 60 km/h can round it even if the road is so icy that the
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