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4 years ago

Explain how to determine the volume of an irregularly shaped object such as a rock

1 answer:

6 0

If you have no way to accurately measure all of the object's bumps and dimples, then the only way to measure its volume is by means of fluid displacement.

-- Put some water into a graduated (marked) container, read the amount of water, drop the object into the container, and read the new volume in the container. The volume of the object is the difference between the two readings.

-- Alternatively, stand an unmarked container in a large pan, and fill it to the brim. Slowly slowly lower the object into the unmarked container, while the pan catches the water that overflows from it. When the object is completely down in the container, carefully remove the container from the pan, and measure the volume of the water in the pan. It's equal to the volume of the object.

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A cylinder of radius R, length L, and mass M is released from rest on a slope inclined at angle θ. It is oriented to roll straig

inna [77]

Answer:

$\mu_s=\frac{1}{3}\tan \theta$

Explanation:

Let the minimum coefficient of static friction be $\mu_s$ .

Given:

Mass of the cylinder = $M$

Radius of the cylinder = $R$

Length of the cylinder = $L$

Angle of inclination = $\theta$

Initial velocity of the cylinder (Released from rest) = 0

Since, the cylinder is translating and rolling down the incline, it has both translational and rotational motion. So, we need to consider the effect of moment of Inertia also.

We know that, for a rolling object, torque acting on it is given as the product of moment of inertia and its angular acceleration. So,

$\tau =I\alpha$

Now, angular acceleration is given as:

$\alpha = \frac{a}{R}\\Where, a\rightarrow \textrm{linear acceleration of the cylinder}$

Also, moment of inertia for a cylinder is given as:

$I=\frac{MR^2}{2}$

Therefore, the torque acting on the cylinder can be rewritten as:

$\tau = \frac{MR^2}{2}\times \frac{a}{R}=\frac{MRa}{2}------ 1$

Consider the free body diagram of the cylinder on the incline. The forces acting along the incline are $mg\sin \theta\ and\ f$ . The net force acting along the incline is given as:

$F_{net}=Mg\sin \theta-f\\But,\ f=\mu_s N\\So, F_{net}=Mg\sin \theta -\mu_s N-------- 2$

Now, consider the forces acting perpendicular to the incline. As there is no motion in the perpendicular direction, net force is zero.

So, $N=Mg\cos \theta$

Plugging in $N=Mg\cos \theta$ in equation (2), we get

$F_{net}=Mg\sin \theta -\mu_s Mg\cos \theta\\F_{net}=Mg(\sin \theta-\mu_s \cos \theta)--------------3$

Now, as per Newton's second law,

$F_{net}=Ma\\Mg(\sin \theta-\mu_s \cos \theta)=Ma\\\therefore a=g(\sin \theta-\mu_s \cos \theta)------4$

Now, torque acting on the cylinder is provided by the frictional force and is given as the product of frictional force and radius of the cylinder.

$\tau=fR\\\frac{MRa}{2}=\mu_sMg\cos \theta\times R\\\\a=2\times \mu_sg\cos \theta\\\\But, a=g(\sin \theta-\mu_s \cos \theta)\\\\\therefore g(\sin \theta-\mu_s \cos \theta)=2\times \mu_sg\cos \theta\\\\\sin \theta-\mu_s \cos \theta=2\mu_s\cos \theta\\\\\sin \theta=2\mu_s\cos \theta+\mu_s\cos \theta\\\\\sin \theta=3\mu_s \cos \theta\\\\\mu_s=\frac{\sin \theta}{3\cos \theta}\\\\\mu_s=\frac{1}{3}\tan \theta............(\because \frac{\sin \theta}{\cos \theta}=\tan \theta)$

Therefore, the minimum coefficient of static friction needed for the cylinder to roll down without slipping is given as:

$\mu_s=\frac{1}{3}\tan \theta$

3 0

3 years ago

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NEED HELP ASAP, ILL GIVE YOU BRAINLIEST IF CORRECT (30POINTS)

Vera_Pavlovna [14]

Answer:

the bar is the top and bottem. the nucleas in the middle and the Spiral arm is the last space

Explanation:

5 0

3 years ago

Consider a horizontal layer of the dam wall of thickness dx located a distance x above the reservoir floor. What is the magnitud

adoni [48]

Answer:

Explanation:

Attached is the solution

6 0

3 years ago

Jobisdone [24]

Hey!!

here is your answer >>>

We know that, acids and strong bases are good conductors of electricity!. And gold conducts electricity , while the best is silver and niext comes gold!. And H20 which is water contains less ions , so it is not a good conductors , it is a conductors but not a good conductor!. Salt in it's solid for cannot produce ions, hence, it cannot conduct electricity , but when this salt is mixed with water or when it is in it's molten state it can conduct electricity!. So now,the answer for the question is ,

B) III and IV only!.

Hope my answer helps!

7 0

3 years ago

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.<br> What happens to the average kinetic energy of water molecules as water freezes?

leva [86]

Answer:molecules slow down

Explanation:

because science

6 0

4 years ago