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2 years ago

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A turntable, with a mass of 1.5 kg and diameter of 20 cm, rotates at 70 rpm on frictionless bearings. Two 540 g blocks fall from

above, hit the turntable simultaneously at opposite ends of a diameter, and stick to it.
Required:
What is the turntable's angular speed, in rpm, just after this event?

1 answer:

ivann1987 [24]2 years ago

3 0

Answer:

The turntable's angular speed after the event is 28.687 revolutions per minute.

Explanation:

The system formed by the turntable and the two block are not under the effect of any external force, so we can apply the Principle of Conservation of Angular Momentum, which states that:

$I_{T}\cdot \omega_{o} = (2\cdot r^{2}\cdot m +I_{T})\cdot \omega_{f}$ (1)

Where:

$I_{T}$ - Moment of inertia of the turntable, in kilogram-square meters.

$r$ - Distance of the block regarding the center of the turntable, in meters.

$m$ - Mass of the object, in kilograms.

$\omega_{o}$ - Initial angular speed of the turntable, in radians per second.

$\omega_{f}$ - Final angular speed of the turntable-objects system, in radians per second.

In addition, the momentum of inertia of the turntable is determined by following formula:

$I_{T} = \frac{1}{2}\cdot M\cdot r^{2}$ (2)

Where $M$ is the mass of the turntable, in kilograms.

If we know that $\omega_{o} \approx 7.330\,\frac{rad}{s}$ , $M = 1.5\,kg$ , $m = 0.54\,kg$ and $r = 0.1\,m$ , then the angular speed of the turntable after the event is:

$I_{T} = \frac{1}{2}\cdot M\cdot r^{2}$

$I_{T} = 7.5\times 10^{-3}\,kg\cdot m^{2}$

$I_{T}\cdot \omega_{o} = (2\cdot r^{2}\cdot m +I_{T})\cdot \omega_{f}$

$\omega_{f} = \frac{I_{T}\cdot \omega_{o}}{2\cdot r^{2}\cdot m +I_{T}}$

$\omega_{T} = 3.004\,\frac{rad}{s}$ ( $28.687\,\frac{rev}{min}$ )

The turntable's angular speed after the event is 28.687 revolutions per minute.

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A 59.31 kg rock is sitting at the top of a cliff that is 300 m tall. What is the gravitational potential energy of that rock?

Diano4ka-milaya [45]

Answer:

The gravitational potential energy of that rock is 174371.4 J.

Explanation:

Given

Mass m = 59.31 kg

Height h = 300 m

To determine

We need to find the gravitational potential energy of the rock

We know that the potential energy of a body is termed as the stored energy due to its position.

One kind of energy comes from Earth's gravity — Gravitational potential energy (GPE).

Gravitational potential energy (GPE) can be determined using the formula

$GPE = mgh$

where

$m$ is the mass

$g$ is the gravitational acceleration which is equal to g = 9.8 m/s²

$h$ is the height

GPE is the Gravitational potential energy

now substituting m = 59.31, h = 300 and g = 9.8

$GPE = mgh$

$=59.31\times 9.8\times 300$

$=174371.4$ J

Therefore, the gravitational potential energy of that rock is 174371.4 J.

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3 years ago

Dominik [7]

Answer:

a. All the laboratory equipment given are very basic equipment used in all the laboratories. Name of each equipment is as follows:

V refers to the tape measure.
W refers to dropper.
X refers to an inoculating loop.
Y refers to a stopwatch.
Z refers to the microscope.

b. Use of each laboratory equipment identified is:

Tape measures (V) is used to measure the length of objects or distance in a laboratory.
Dropper (W) is used to measure unit of drop required to dispensed as one drop or several drops in any experiment.
Inoculating loop (X) is used by microbiologists to cultivate microbes on plates and retrieving an inoculum from a culture of microorganisms.
Stopwatch (Y) is used to measure the time of any experiment.
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3 years ago

If light intensity obeyed an inverse square law you would expect to find the intensity of light to decrease as the square of the

Reptile [31]

Inverse square law: $\frac{I_{2} }{I_{1}}= (\frac{d{2} }{d_{1}})^2$
where
$I_{1}$ is the intensity at distance 1
$I_{2}$ is the intensity at distance 2
$d_{1}$ is distance 1
$d_{2}$ is distance 2

The inverse squared law state that intensity decreases in inverse proportion to the distance squared. So if light obeyed that rule, it will decreases its intensity as the square of the distance increases.

We can conclude that the correct answer is: true.

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3 years ago

Read 2 more answers

)If a force of 5.00 N is needed to open a 90.0 cm wide door when applied at the edge opposite the hinges, what force must be app

masha68 [24]

Answer:

A force of 12.857 newtons must be applied to open the door.

Explanation:

In this case, a force is exerted on the door, a moment is performed and the door is opened. If moment remains constant, the force is inversely proportional to distance respect to axis of rotation passing through hinges. That is:

$F \propto \frac{1}{r}$

$F = \frac{k}{r}$ (Eq. 1)

Where:

$F$ - Force, measured in newtons.

$k$ - Proportionality ratio, measured in newton-meters.

$r$ - Distance respect to axis of rotation passing through hinges, measured in meters.

From (Eq. 1) we get the following relationship and clear the final force within:

$F_{A}\cdot r_{A} = F_{B}\cdot r_{B}$

$F_{B}=\left(\frac{r_{A}}{r_{B}} \right)\cdot F_{A}$ (Eq. 2)

Where:

$F_{A}$ , $F_{B}$ - Initial and final forces, measured in newtons.

$r_{A}$ , $r_{B}$ - Initial and final distances, measured in meters.

If we know that $F_{A} = 5\,N$ , $r_{A} = 0.9\,m$ and $r_{B} = 0.35\,m$ , then final force is:

$F_{B}= \left(\frac{0.9\,m}{0.35\,m} \right)\cdot (5\,N)$

$F_{B} = 12.857\,N$

A force of 12.857 newtons must be applied to open the door.

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3 years ago

A city planner needs to make a model of the city. In real life, the tallest tree in the city is 40 feet tall. The shortest tree

Verdich [7]

To solve this you must set up what is called a proportion. A proportion is a way of comparing two comparing values where one of the four values is missing. In your problem the missing value is the height of the smallest tree in the model.

To set up a proportion, you need all of your values. The easiest way to do this is to list them:

Highest tree in real life: 40ft
Highest tree in model: 10ft
Smallest tree in real life: 4ft
Smallest tree in model: x

So know you can set your proportion like this:

40/4 = 4/x

(When setting up a proportion, you always want to have the values belong to each other. For example don't put the height of the small tree in the model underneath the value of the highest tree in real life.)

So know to find what the x values equals, we need to cross multiply. And then all that's left after that is to solve for x.

40 times x = 4 times 4

40x = 16

x = 2.5

The smallest tree in the model should equal 2.5 feet.

Hope this helps! :)

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3 years ago