Ask question

Ask question

All categories

3 years ago

12

When you whirl a small rubber stopper on a cord in a vertical circle, you find a critical speed at the top for which the tension

in the cord is zero. At this speed. the force of gravity on the object 1S itselfisufficient to supply the necessary centripetal force. How slowly can you swing a 15-g stopper like this so that It will just follow a circle with a radius of m?

1 answer:

Sauron [17]3 years ago

6 0

Answer:

√(9.8/m) radians per second

Explanation:

The centripetal acceleration required for a radius of m is ...

a = mω²

so, the angular speed required is ...

ω = √(a/m) = √(g/m) . . . . . where g is the acceleration due to gravity

ω = √(9.8/m) . . . radians per second

__

The speed is independent of the mass. For a 1 m radius, the speed is about 29.9 RPM.

You might be interested in

Irina finds an unlabeled box of fine needles, and wants to determine how thick they are. A standard ruler will not do the job, a

Vsevolod [243]

Answer:

$d=\frac{1.22\times 640\times 10^{-9}\times 21.7}{7.35\times 10^{-2}}=2305.21\times 10^{-7}m$

Explanation:

The expression which represent the first diffraction minima by a circular aperture is given by $d sin\Theta =1.22\lambda$ --------eqn 1

The angle through which the first minima is diffracted is given by $tan\Theta =\frac{y_1}{D}$ ---------eqn 2

As $\Theta$ is very small so we can write $sin\Theta =tan\Theta$

So from eqn 1 and eqn 2 we can write

$y_1=\frac{1.22\lambda D}{d}$ --------eqn 3

Here $y_1$ is the position of first maxima D is the distance of screen from the circular aperture d is the diameter of aperture

It is given that diameter of circular aperture is 14.7 cm so $y_1=\frac{14.7}{2}=7.35 \ cm$

Now putting all these value in eqn 3

$d=\frac{1.22\lambda D}{y_1}$

$d=\frac{1.22\times 640\times 10^{-9}\times 21.7}{7.35\times 10^{-2}}=2305.21\times 10^{-7}m$

8 0

3 years ago

A baseball pitcher throws the ball towards the batter at 90 mph. His bat connects with the ball for a line drive, after which th

forsale [732]

Answer:

$F=-18412.9N$ , where the minus indicates the direction is opposite to that of the throw.

Explanation:

a)

Since MKS stands for meter-kilogram-second and we know that:

$1\ hour = 3600\ seconds$

$1\ mile = 1600\ meters$

$1000g = 1kg$

We can write that:

$\frac{1\ hour}{3600\ seconds}=1$

$\frac{1600\ meters}{1\ mile}=1$

$\frac{1kg}{1000g}=1$

These are conversion factors, equal to 1, so multiplying our results by them won't change their value, only their units.

So we have that:

$90 mph=90 \frac{miles}{hour}(\frac{1\ hour}{3600\ seconds})(\frac{1600\ meters}{1\ mile})=40m/s$

$110 mph=110 \frac{miles}{hour}(\frac{1\ hour}{3600\ seconds})(\frac{1600\ meters}{1\ mile})=48.89m/s$

$145 g=145 g(\frac{1kg}{1000g})=0.145kg$

b)

Newton's 2nd Law tells us that F=ma, and the definition of acceleration is $a=\frac{\Delta v}{\Delta t}$ , so we have:

$F=m\frac{\Delta v}{\Delta t}=m\frac{v_f-v_i}{t}$

Taking the throw direction as the positive one, for our values we have:

$F=m\frac{v_f-v_i}{t}=(0.145kg)\frac{(-48.89m/s)-(+40m/s)}{0.0007s}=-18412.9N$

4 0

3 years ago

A wire along the z axis carries a current of 6.8 A in the z direction Find the magnitude and direction of the force exerted on a

Alexeev081 [22]

Answer:

Force is 14.93N along positive y axis.

Explanation:

We know that force 'F' on a current carrying conductor placed in a magnetic field of intensity B is given by

$\overrightarrow{F}=\overrightarrow{Il}\times \overrightarrow{B}$

where L is the length of the conductor

Applying values in the equation we have force F =

$\overrightarrow{F}=6.8\times 6.1\widehat{k}\times 0.36\widehat{i}\\\\\overrightarrow{F}=41.48\widehat{k}\times 0.36\widehat{i}\\\\\therefore \overrightarrow{F}=14.93N\widehat{j}$

Thus force is 14.93N along positive y axis.

3 0

3 years ago

A 873-kg (1930-lb) dragster, starting from rest completes a 401.4-m (0.2509-mile) run in 4.945 s. If the car had a constant acce

Delvig [45]

To solve this problem it is necessary to apply the kinematic equations of motion.

By definition we know that the position of a body is given by

$x=x_0+v_0t+at^2$

Where

$x_0 =$ Initial position

$v_0 =$ Initial velocity

a = Acceleration

t= time

And the velocity can be expressed as,

$v_f = v_0 + at$

Where,

$v_f = Final velocity$

For our case we have that there is neither initial position nor initial velocity, then

$x= at^2$

With our values we have $x = 401.4m, t=4.945s$ , rearranging to find a,

$a=\frac{x}{t^2}$

$a = \frac{ 401.4}{4.945^2}$

$a = 16.41m/s^2$

Therefore the final velocity would be

$v_f = v_0 + at$

$v_f = 0 + (16.41)(4.945)$

$v_f = 81.14m/s$

Therefore the final velocity is 81.14m/s

8 0

3 years ago

A tennis ball is tossed up off a building with a velocity of 22m/s. It takes 6.4s to reach the ground. How high is the building

Amanda [17]

The height of the tennis ball,relative to the ground is H=h max+h-->h max-the maximum height that the tennis ball reaches relative to the roof of the building; h-the height of the building;h max =v0^2/2g=24,2m(g=10m/s^2).H=gt^2/2=>24,2+h=gt^2/2=>h=gt^2/2-24,2=180,6m

4 0

3 years ago