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3 years ago

8

What is the slope of the line plotted below?

1 answer:

lubasha [3.4K]3 years ago

6 0

Answer:

Slope is in fact -2

Explanation:

Rise over Run

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m_a_m_a [10]

Answer:

Driving force increases, friction forces increase, the driving force is bigger than friction 12.

Explanation:

4 0

2 years ago

A rock is thrown upward from the level ground in such a way that the maximum height of its flight is equal to its horizontal ran

marshall27 [118]

Answer

a) For the rock

$\dfrac{v_t^2sin 2\theta}{g} = \dfrac{v_t^2sin^2\theta}{2g}$

$2sin\thetacos\theta = \dfrac{sin^2\theta}{2}$

$2cos\theta = \dfrac{sin\theta}{2}$

$tan\theta = 4$

$\theta = tan^{-1} 4$

$\theta = 76^0$

b) $\theta = 45^0$ for maximum range

$\dfrac{d_{max}}{d}=\dfrac{(v_tcos 45^0)(2v_tsin 45^0)g}{(v_tcos 76^0)(2v_tsin 76^0)g}$

$\dfrac{d_{max}}{d}=\dfrac{0.707\times 0.707)}{0.97\times 0.242}$

$\dfrac{d_{max}}{d}=2.129$

$d_{max}=2.129 d$

c) The value of θ is the same on every planet as g divides out.

5 0

3 years ago

A nebula, or swirling cloud of interstellar dust and gases, is seen. What happens next in the star formation process?

AVprozaik [17]

Atoms begin to gravitate together to form a center

5 0

3 years ago

Read 2 more answers

Explain the relationship between resistance and the velocity of shortening.

butalik [34]

The velocity of shortening refers to the speed of the contraction from the muscle shortening while lifting a load. The relationship between the resistance and velocity of shortening is inverse. The greater the resistance, the shorter the velocity of shortening and the smaller the resistance, the larger the velocity of shortening.

Hopefully this help :)

7 0

3 years ago

Two uniform, solid cylinders of radius R and total mass M are connected along their common axis by a short, light rod and rest o

sveta [45]

Explanation:

A) To prove the motion of the center of mass of the cylinders is simple harmonic:

System diagram for given situation is shown in attached Fig. 1

We can prove the motion of the center of mass of the cylinders is simple harmonic if

$a_{x} = -\omega^{2} x$

where aₓ is acceleration when attached cylinders move in horizontal direction:

<h3>PROOF:</h3>

rotational inertia for cylinders is given as:

$I=\frac{1}{2}MR^{2}$ -----(1)

Newton's second law for angular motion is:

∑τ = Iα ------(2)

For linear motion in horizontal direction it is:

∑Fₓ = Maₓ ------ (3)

By definition of torque:

τ = RF --------(4)

Put (4) and (1) in (2)

$RF=\frac{1}{2}MR^{2}\alpha$

$RF=\frac{1}{2}MR^{2}\alpha$

from Fig 3 it can be seen that fs is force by which the cylinders roll without slipping as they oscillate

So above equation becomes

$f_{s}=\frac{1}{2}MR\alpha$ ------ (5)

As angular acceleration is related to linear by:

$a= R\alpha$

Eq (5) becomes

$f_{s}=\frac{1}{2}Ma_{x}$ ---- (6)

aₓ shows displacement in horizontal direction

From (3)

∑Fₓ = Maₓ

Fₓ is sum of fs and restoring force that spring exerts:

$\sum F_{x} = f_{s} - kx$ ----(7)

Put (7) in (3)

$f_{s} - kx = Ma_{x}$ [/tex] -----(8)

Using (6) in (8)

$\frac{1}{2}Ma_{x} - kx =Ma_{x}$

$a_{x} = \frac{2k}{3M} x$ --- (9)

For spring mass system

$a= -\omega^{2} x$ ----- (10)

Equating (9) and (10)

$\omega^{2} = \frac{2k}{3M}$

$\omega = \sqrt{ \frac{2k}{3M}}$

then (9) becomes

$a_{x} = - \omega^{2}x$

(The minus sign says that x and aₓ have opposite directions as shown in fig 3)

This proves that the motion of the center of mass of the cylinders is simple harmonic.

<h3 /><h3>B) Time Period</h3>

Time period is related to angular frequency as:

$T=\frac{2\pi }{\omega}$

$T = 2\pi \sqrt{\frac{3M}{2k}$

5 0

3 years ago