A certain mass of a gas occupies 2 litres at 27 °C and 100

An object with a mass m slides down a rough 370 inclined plane where the coefficient of kinetic friction is 0.20. If the plane i

Svetllana [295]

Answer:

$v \approx 9.312\,\frac{m}{s}$

Explanation:

The Free Body Diagram of the system is presented in the image attached below. The final speed is determined by means of the Principle of Energy Conservation and the Work-Energy Theorem:

$K_{A} + U_{g,A} = K_{B} + U_{g,B} + W_{loss}$

$K_{B} = K_{A} + U_{g,A}-U_{g,B} - W_{loss}$

$\frac{1}{2}\cdot m \cdot v^{2} = m\cdot g \cdot s\cdot \sin \theta - \mu_{k}\cdot m \cdot g \cdot s \cos \theta$

$\frac{1}{2}\cdot v^{2} = g\cdot s \cdot (\sin \theta - \mu_{k}\cdot \cos \theta)$

$v = \sqrt{2\cdot g \cdot s \cdot (\sin \theta - \mu_{k}\cdot \cos \theta)}$

$v = \sqrt{2\cdot (9.807\,\frac{m}{s^{2}} )\cdot (10\,m)\cdot (\sin 37^{\textdegree} - 0.2\cdot \cos 37^{\textdegree})}$

$v \approx 9.312\,\frac{m}{s}$

3 0

3 years ago

A diver jumps off a cliff 50m high and needs to clear the rock that extend outward 5.0m from the base of the cliff. The diver ju

igor_vitrenko [27]

Answer:

He should run at least at 1.5 m/s

The diver will enter the water at an angle of 87° below the horizontal.

Explanation:

Hi there!

The position and velocity of the diver are given by the following vectors:

r = (x0 + v0x · t, y0 + v0y · t + 1/2 · g · t²)

v = (v0x, v0y + g · t)

Where:

r = position vector at time t

x0 = initial horizontal position

v0x = initial horizontal velocity

t = time

y0 = initial vertical position

v0y = initial vertical velocity

g = acceleration due to gravity (-9.8 m/s² considering the upward direction as positive)

v = velocity vector at time t

Please, see the attached figure for a description of the problem. Notice that the origin of the frame of reference is located at the jumping point so that x0 and y0 = 0.

We know that, to clear the rocks, the position vector r final (see figure) should be:

r final = ( > 5.0 m, -50 m)

So let´s find first at which time the y-component of the vector r final is - 50 m:

y = y0 + v0y · t + 1/2 · g · t²

-50 m = 2.1 m/s · t - 1/2 · 9.8 m/s² · t²

0 = -4.9 m/s² · t² + 2.1 m/s · t + 50 m

Solving the quadratic equation

t = 3.4 s

Now, we can calculate the initial horizontal velocity using the equation of the x-component of the position vector knowing that at t =3.4 the horizontal component should be greater than 5.0 m:

x = x0 + v0x · t (x0 = 0)

5.0 m < v0x · 3.4 s

v0x > 5.0 m / 3.4 s

v0x > 1.5 m/s

The initial horizontal velocity should be greater than 1.5 m/s

To find the angle at which the diver enters the water, we have to find the magnitude of the final velocity (vector vf in the figure). We already know the magnitude of the x-component of the vector vf, since the horizontal velocity is constant. So:

vfx > 1.5 m/s

Now, let´s calculate vfy:

vfy = v0y + g · t

vfy = 2.1 m/s - 9.8 m/s² · 3.4 s

vfy = -31 m/s

Let´s calculate the minimum magnitude that the final velocity will have if the diver safely clears the rocks. Let´s consider the smallest value allowed for vfx: 1.5 m/s. Then:

$|v| = \sqrt{(1.5 m/s)^{2} + (31m/s)^{2}} = 31 m/s$

Then the final velocity of the diver will be greater or equal than 31 m/s.

To find the angle, we have to use trigonometry. Notice in the figure that the vectors vf, vfx and vy form a right triangle in which vf is the hypotenuse, vfx is the adjacent side and vfy is the opposite side to the angle. Then:

cos θ = adjacent / hypotenuse = vfx / vf = 1.5 m/s / 31 m/s

θ = 87°

The diver will enter the water at an angle of 87° below the horizontal.

8 0

3 years ago

Please do all of i will give you brainlest and thanks to best answer plz do it right

Sergeu [11.5K]

Answer:

winter solstice i think

Explanation:

8 0

2 years ago

Read 2 more answers

Is it possible for one ray to be shorter in length than another?

8090 [49]

Yes, even light rays can vary in wavelength and frequency, if the length of the ray is sorter, it becomes more energetic and has a higher frequency. If you're talking about a ray tracing diagram for lenses or mirrors, the length of the ray doesn't really matter unless you're finding the path length but there are some procedures for that too. Let me know if I missed what you were asking.

8 0

3 years ago

Imagine a system where a block rests on an inclined plane. The block is then given an initial push so that it starts sliding dow

katen-ka-za [31]

Answer:

the correct affirmation is the 3

Explanation:

Let's analyze the problem with Newton's second law before looking at the claims.

X axis parallel to the plane, positive down

F -fr + Wₓ = ma

Y Axis perpendicular to the plane

N -Wy = 0

With trigonometry

Wₓ = W sin θ

Wy = w cos θ

Let's multiply by the displacement along the plane, to relate to the work, which has as expression W = F d

F d -fr d + Wx d = ma d

Push W₁ = Fd

frictional force W₂ = -fr d

gravity W₃ = Wx d

W₁ + W₃ -W₂ = m a d

Analysis affirmations:

R1) false. The work of gravity is the subtraction

R2) false. Each force contributes according to its magnitude

R3) true. In the equation we see that, if the acceleration is zero, W2 = W1 + W3

R4) False. It equals the difference

the correct affirmation is the 3

6 0

3 years ago