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3 years ago

An object is dropped from a platform 400 ft high. Ignoring wind resistance, how long will it take to reach the ground?

1 answer:

8 0

Let's convert the initial height from feet to meters first:
$h=400 ft=121.9 m$

The object is in free fall, so it is moving by uniformly accelerated motion with constant acceleration $g=9.81 m/s^2$ (gravitational acceleration) from initial height h=121.9 m. Its vertical position at time t is given by
$y(t)=h- \frac{1}{2}gt^2$

We want to know how long it will take to reach the ground, therefore we should calculate the time t at which the vertical position y(t) becomes zero:
$0=h- \frac{1}{2}gt^2$
rearranging,
$t= \sqrt{ \frac{2h}{g} }= \sqrt{ \frac{2(121.9 m)}{9.81 m/s^2} }=4.98 s$

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Answer:

Explanation:

option A is correct

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3 years ago

A 0.18-kg turntable of radius 0.32 m spins about a vertical axis through its center. A constant rotational acceleration causes t

borishaifa [10]

Answer:

Angular acceleration will be $18.84rad/sec^2$

Explanation:

We have given that mass m = 0.18 kg

Radius r = 0.32 m

Initial angular velocity $\omega _i=0rev/sec$

And final angular velocity $\omega _f=24rev/sec$

Time is given as t = 8 sec

From equation of motion

We know that $\omega _f=\omega _i+\alpha t$

$24=0+\alpha \times 8$

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So angular acceleration will be $18.84rad/sec^2$

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4 years ago

A planet orbits a star along an elliptical path from point X to point Y, as shown in the figure. In which of the following syste

8090 [49]

Answer:

The correct answer is Option D, the closed system containing the planet and the star.

Explanation:

To start, we need to define mechanical energy: the energy an object has from its motion and position.

The fundamental principle in physics is that the total energy in a closed system stays constant, even if it transforms. By saying "closed system," we refer to a system isolated from its surroundings. Energy never leaves the system; it only moves from one part to another.

This statement only applies to closed systems, however. An open system that interacts with its environment works differently. Energy may enter and leave the system through interaction with external forces, and this includes mechanical energy. For this reason, Option A and Option B are incorrect.

The remaining two options, C and D, only vary with the objects in the closed system. Option D includes the star; Option C does not.

However, we should take a closer look at Option C. Can an object have potential energy with itself? No, it cannot. It only has potential energy with other bodies. If the system is defined as the planet only, the only type of energy present is kinetic energy. We know a planet orbiting a star has more kinetic energy near and more gravitational potential energy further from its star. Thus it has less kinetic energy further from its star and less mechanical energy. Because of this, Option C is incorrect.

The only answer left is Option D. If we define the planet and star as a closed system, we find no net external force acting on it. Consequently, it obeys the law of conservation of energy. From prior reasoning, we know mechanical energy includes potential energy and kinetic energy and that the amounts of these energies vary with its orbit. As a result, mechanical energy is always conserved and always the same. In the end, the correct answer is Option D.

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3 years ago

A uniform thin rod of mass ????=3.41 kg pivots about an axis through its center and perpendicular to its length. Two small bodie

vivado [14]

Answer:

The length of the rod for the condition on the question to be met is $L = 1.5077 \ m$

Explanation:

The Diagram for this question is gotten from the first uploaded image

From the question we are told that

The mass of the rod is $M = 3.41 \ kg$

The mass of each small bodies is $m = 0.249 \ kg$

The moment of inertia of the three-body system with respect to the described axis is $I = 0.929 \ kg \cdot m^2$

The length of the rod is L

Generally the moment of inertia of this three-body system with respect to the described axis can be mathematically represented as

$I = I_r + 2 I_m$

Where $I_r$ is the moment of inertia of the rod about the describe axis which is mathematically represented as

$I_r = \frac{ML^2 }{12}$

And $I_m$ the moment of inertia of the two small bodies which (from the diagram can be assumed as two small spheres) can be mathematically represented as