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Evgen [1.6K]
2 years ago
5

A car accelerates uniformly from rest and reaches a speed of 21.9 m/s in 8.99 s. Assume the diameter of a tire is 57.5 cm. (a) F

ind the number of revolutions the tire makes during this motion, assuming that no slipping occurs.
Physics
1 answer:
Marat540 [252]2 years ago
7 0

Answer:

Explanation:

initial velocity, u = 0 m/s

time, t = 8.99 s

final velocity, v = 21.9 m/s

diameter of tyre, D = 57.5 cm

(a) Let a is the acceleration, and n be the number f revolutions made by the tyre.

Use first equation of motion

v = u + at

21.9 = 0 + a x 8.99

a = 2.44 m/s²

Use third equation of motion

v² = u² + 2 a s

21.9 x 21.9 = 0 + 2 x 2.44 x s

s = 98.28 m

Circumference of wheel, S = π x D = 3.14 x 0.575 = 1.8055 m

number of revolutions, n = distance / circumference

n = 98.28 / 1.8055

n = 54.4

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Answer:

The final velocity of the cars is 8.38 m/s at an angle 39.1° south of west.

Explanation:

Given that,

Mass of first car = 1100 kg

Velocity of first car = 8.5 m/s

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Velocity of second car = 17.5 m/s

Suppose we need to find the final velocity of the cars and direction of the cars.

We need to calculate the velocity of the car in west direction

Using conservation of momentum in west direction

m_{f}v_{f}+m_{s}v_{s}= (m_{f}+m_{s})v_{x}

v_{x}=\dfrac{m_{f}v_{f}+m_{s}v_{s}}{(m_{f}+m_{s})}

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v_{x}=6.5\ m/s

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Using conservation of momentum in south direction

m_{f}v_{f}+m_{s}v_{s}= (m_{f}+m_{s})v_{y}

v_{y}=\dfrac{m_{f}v_{f}+m_{s}v_{s}}{(m_{f}+m_{s})}

Put the value into the formula

v_{y}=\dfrac{1100\times8.5+650\times0}{1100+650}

v_{y}=5.3\ m/s

We need to calculate the final velocity of the cars

Using formula of velocity

v_{eq}=\sqrt{(6.5)^2+(5.3)^2}

v_{eq}=8.38\ m/s

We need to calculate the direction

Using formula of direction

\tan\theta=\dfrac{v_{y}}{v_{x}}

Put the value into the formula

\tan\theta=\dfrac{5.3}{6.5}

\theta=\tan^{-1}(\dfrac{5.3}{6.5})

\theta=39.1^{\circ}

Hence, The final velocity of the cars is 8.38 m/s at an angle 39.1° south of west.

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