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2 years ago

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A bored student makes a poor life decision and decides to go do donuts in a school parking lot. The student jumps into his/her 1

500kg car and heads to the lot. Assume he/she drives in circles with a 10 meter radius and the coefficient of friction is 0.7 between the tires and the dry road. A) What is the maximum speed car can go before it starts to slide?

1 answer:

DerKrebs [107]2 years ago

7 0

Answer:

The maximum speed the car can go before it star to slide is

$v=8.2 m/s$

Explanation:

Using the conservation of energy the force in motion is

$F=m*a$

$F_k=u*F_N$

$F_N=m*g$

$F_k=m*a_c$

$u*m*g=m*a_c$

$a_c=\frac{V^2}{r}$

$u*g=\frac{V^2}{r}$

Solve to v'

$v=\sqrt{u*r*g}=\sqrt{10m*0.7*9.8m/s^2}=\sqrt{68.6 m^2/s^2}$

$v=8.2 m/s$

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A 150 g particle at x = 0 is moving at 8.00 m/s in the +x-direction. As it moves, it experiences a force given by Fx=(0.850N)sin

krok68 [10]

Answer:

9.98 m/s

Explanation:

The force acting on the particle is defined by the equation:

$F=(0.850) sin (\frac{x}{2.00})$ [N]

where x is the position in metres.

The acceleration can be found by using Newton's second law:

$a=\frac{F}{m}$

where

m = 150 g = 0.150 kg is the mass of the particle. Substituting into the equation,

$a=\frac{0.850}{0.150}sin (\frac{x}{2.00})=5.67 sin(\frac{x}{2.00})$ [m/s^2]

When x = 3.14 m, the acceleration is:

$a=5.67 sin(\frac{3.14}{2.00})=5.67 m/s^2$

Now we can find the final speed of the particle by using the suvat equation:

$v^2-u^2=2ax$

where

u = 8.00 m/s is the initial velocity

v is the final velocity

$a=5.67 m/s^2$

x = 3.14 m is the displacement

Solving for v,

$v=\sqrt{u^2+2ax}=\sqrt{8.00^2+2(5.67)(3.14)}=9.98 m/s$

And the speed is just the magnitude of the velocity, so 9.98 m/s.

4 0

2 years ago

Margy is trying to improve her cardio endurance by performing an exercise in which she alternates walking and running 100.0 m ea

madreJ [45]

In order to answer this exercise you need to use the formulas

S = Vo*t + (1/2)*a*t^2

Vf = Vo + at

The data will be given as

Vf = final velocity = ?

Vo = initial velocity = 1.4 m/s

a = acceleration = 0.20 m/s^2

s = displacement = 100m

And now you do the following:

100 = 1.4t + (1/2)*0.2*t^2

t = 25.388s

and

Vf = 1.4 + 0.2(25.388)

Vf = 6.5 m/s

So the answer you are looking for is 6.5 m/s

7 0

2 years ago

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A graduated cylinder contains 17.5 ml of water. When a metal cube is placed onto the cylinder, its water level rises to 20.3 ml

pogonyaev

If you are asking what the volume of the cube is it would be 20.3 - 17.5 ml so 2.8 ml.

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2 years ago

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The U.S. Department of Energy had plans for a 1500-kg automobile to be powered completely by the rotational kinetic energy of a

navik [9.2K]

Answer:

230

Explanation:

$\omega$ = Rotational speed = 3600 rad/s

I = Moment of inertia = 6 kgm²

m = Mass of flywheel = 1500 kg

v = Velocity = 15 m/s

The kinetic energy of flywheel is given by

$K=\dfrac{1}{2}I\omega^2\\\Rightarrow K=\dfrac{1}{2}6\times 3600^2\\\Rightarrow K=38880000\ J$

Energy used in one acceleration

$K=\dfrac{1}{2}mv^2\\\Rightarrow K=\dfrac{1}{2}1500\times 15^2\\\Rightarrow K=168750\ J$

Number of accelerations would be given by

$n=\dfrac{38880000}{168750}\\\Rightarrow n=230.4$

So the number of complete accelerations is 230

8 0

2 years ago

If you find an igneous rock which has 450 radioactive isotopes and 3,150 stable daughter isotopes, how many half-lifes of this i

slavikrds [6]

Answer:

$3t_{1/2}$

Explanation:

To find the half-lifes of the isotope we need to use the following equation:

$N_{t} = N_{0}2^{-\frac{t}{t_{1/2}}}$ (1)

<em>where Nt: is the amount of the isotope that has not yet decayed after a time t, N₀: is the initial amount of the isotope, t: is the time and </em> $t_{1/2}$ <em>: is the half-lifes.</em>

By solving equation (1) for t we have:

$\frac{t}{t_{1/2}} = - \frac{Ln(Nt/N_{0})}{Ln(2)}$

<u>Having that:</u>

Nt = 450

N₀ = 3150 + 450 = 3600,

The half-lifes of the isotope is:

$t = - \frac{Ln(450/3600)}{Ln(2)} \cdot t_{1/2} = 3t_{1/2}$

Therefore, 3 half-lives of the isotope passed since the rock was formed.

I hope it helps you!

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2 years ago