All categories

3 years ago

What is the best definition of vectors?

Physics

1 answer:

mariarad [96]3 years ago

8 0

Answer:

Number value and direction

Explanation:

Vectors are quantities that can be identified by value and direction . Examples are velocity and acceleration

You might be interested in

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

Read 2 more answers

What will happen if you heat a liquid to high temperatures?

WARRIOR [948]

It’s c hope this helps :)

5 0

3 years ago

1. An astronaut is getting ready to explore. If his mass is 60 kg, what is his weight<br> on Earth?

kifflom [539]

Answer:

<h3>The mass of an object is the same on Earth, in orbit, or on the surface of the Moon. ... 1N=1kg ⋅m/s2. 1 N = 1 kg · m/s 2 . ... The gravitational force on a mass is its weight. ... </h3>

Explanation:

3 0

3 years ago

Read 2 more answers

Index fossils are used to determine the relative ages of rock and fossils and are also used to

kolbaska11 [484]

Index fossils are used to determine the relative ages of rock and fossils and are also used to define the boundaries between geologic periods.

<u>Option: A</u>

<u>Explanation:</u>

The fossils which are recognized as fossils guides or indicator fossils are used to classify and recognize geological or faunal periods, termed as index fossils. It must be of short vertical reach, wide geographic distribution and swift patterns in evolution. It helps to assess the rock layers ' age and helps to date other fossils found close and around them. For an instance, Ammonites were abundant in the Mesozoic period between 245 to 65 mya, they have not been found after the Cretaceous era, as they became endangered during the K-T extinction (65 mya).

3 0

3 years ago

Why can gases be compressed

Keith_Richards [23]

Gases can be compressed, because they just take up the space surrounding them. The attractive forces between the particles in a gas are very weak, so the particles are free to move in random direction. They just move along until they collide, either with the walls of the container or with each other. Moreover, gases can be compressed because the particles are far apart and they have space to move into.

5 0

3 years ago