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Alinara [238K]
3 years ago
8

A Car with drives into a solid object with 70 km/h, from which height would it fall if it was in free fall?​

Physics
1 answer:
Ilya [14]3 years ago
8 0

Answer:

18.9 m.

Explanation:

From the question given above, the following data were obtained:

Initial velocity (u) = 0 m/s

Final velocity (v) = 70 km/h

Height (h) =?

Next, we shall convert 70 km/h to m/s. This can be obtained as follow:

3.6 km/h = 1 m/s

Therefore,

70 km/h = 70 km/h × 1 m/s / 3.6 km/h

70 km/h = 19.44 m/s

Finally, we shall determine the height. This can be obtained as follow:

Initial velocity (u) = 0 m/s

Final velocity (v) = 19.44 m/s

Acceleration due to gravity (g) = 10 m/s²

Height (h) =?

v² = u² + 2gh

19.44² = 0² + (2 × 10 × h)

377.9136 = 0 + 20h

377.9136 = 20h

Divide both side by 20

h = 377.9136 / 20

h = 18.9 m

Thus, the car will fall from a height of 18.9 m

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A heavy flywheel is accelerated (rotationally) by a motor that provides constant torque and therefore a constant angular acceler
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Answer:

a)t_1=\frac{w_1-w_o}{\alpha}=\frac{w_1}{\alpha}sec

b)\theta_1=\frac{w_1^2}{2\alpha}rad

c)t_2=\frac{\alpha t_1}{5\alpha}=\frac{t_1}{5}sec

Explanation:

1) Basic concepts

Angular displacement is defined as the angle changed by an object. The units are rad/s.

Angular velocity is defined as the rate of change of angular displacement respect to the change of time, given by this formula:

w=\frac{\Delat \theta}{\Delta t}

Angular acceleration is the rate of change of the angular velocity respect to the time

\alpha=\frac{dw}{dt}

2) Part a

We can define some notation

w_o=0\frac{rad}{s},represent the initial angular velocity of the wheel

w_1=?\frac{rad}{s}, represent the final angular velocity of the wheel

\alpha, represent the angular acceleration of the flywheel

t_1 time taken in order to reach the final angular velocity

So we can apply this formula from kinematics:

w_1=w_o +\alpha t_1

And solving for t1 we got:

t_1=\frac{w_1-w_o}{\alpha}=\frac{w_1}{\alpha}sec

3) Part b

We can use other formula from kinematics in order to find the angular displacement, on this case the following:

\Delta \theta=wt+\frac{1}{2}\alpha t^2

Replacing the values for our case we got:

\Delta \theta=w_o t+\frac{1}{2}\alpha t_1^2

And we can replace t_1from the result for part a, like this:

\theta_1-\theta_o=w_o t+\frac{1}{2}\alpha (\frac{w_1}{\alpha})^2

Since \theta_o=0 and w_o=0 then we have:

\theta_1=\frac{1}{2}\alpha \frac{w_1^2}{\alpha^2}

And simplifying:

\theta_1=\frac{w_1^2}{2\alpha}rad

4) Part c

For this case we can assume that the angular acceleration in order to stop applied on the wheel is \alpha_1 =-5\alpha \frac{rad}{s}

We have an initial angular velocity w_1, and since at the end stops we have that w_2 =0

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w_2 =w_1 +\alpha_1 t_2

Since w_2=0 if we solve for t_2 we got

t_2=\frac{0-w_1}{\alpha_1}=\frac{-w_1}{-5\alpha}

And from part a) we can see that w_1=\alpha t_1, and replacing into the last equation we got:

t_2=\frac{\alpha t_1}{5\alpha}=\frac{t_1}{5}sec

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