A rake is a simple machine. Thus, the correct option is D.
A simple machine is a mechanical device which changes the direction or magnitude of an applied force. In general, these machines can be defined as the simplest mechanisms which uses mechanical advantage also called as leverage to multiply the force. Usually the term refers to the six classical simple machines which were defined by Renaissance scientists including lever, wheel and axle, pulley, inclined plane, wedge, and screw.
A simple machine uses a single applied force to do the work against a single load force or friction. Ignoring the friction losses, the work done on the load force is equal to the work done by the applied force.
Therefore, the correct option is D.
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Jeremy wants to buy some snacks. He walks four blocks east and two blocks south to get to the closest convience store to his house. How far away is store from his house, directly?
2)A slanted vector has a magnitude of 41 N and is at an angle of 23 degrees north of east. What are the magnitude and direction of the horizontal and vertical components of this vector?
3)A horizontal component vector has a magnitude of 11 m. If the resultant vector forms and angle with this component of 19 degrees, what is the magnitude of the resultant vector?
1) The distance of the store from the house is 4.47 blocks
2) The horizontal component of the vector is 37.7 N, the vertical component is 16.0 N
3) The magnitude of the resultant vector is 11.6 m
Explanation:
1)
Jeremy's motion is divided into two parts:
- First, a motion of 4 blocks east
- Then, a motion of 2 blocks south
Here we want to measure the distance between the initial and final position of Jeremy.
We notice that the two displacements are perpendicular to each other, so they correspond to the sides of a right triangle, of which the hypothenuse is the distance between the initial and final point. Therefore, the distance can be found by using Pythagorean's theorem:
So, 4.47 blocks.
2)
The horizontal and vertical components of the vector can be calculated as
where
v = 41 N is the magnitude of the vector
is the angle between the direction of the vector and the x-axis (which corresponds to the east direction)
Substituting numbers into the equations, we find
3)
In the previous part, we said that the horizontal component of a vector is given by
where
v is the magnitude of the vector
is the angle
In this problem we know that:
is the horizontal component
is the angle
Therefore, we can re-arrange the equation to find v, the magnitude of the resultant vector:
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The reason why the moon can't be eclipsed when it's halfway between the nodes of the orbit because the moon's orbit is at it's maximum deviation, meaning that it is leaving it's course from the sun's path, which would make the shadow fall way below or above the moon. Because of that, the moon can't eclipsed.
The Moon cannot be eclipsed when it is halfway between the nodes of its orbit due to its 5° tilt relative to the ecliptic. Eclipses can only happen during 'eclipse season' when the Moon's path crosses the ecliptic. The apparent varying sizes of the Moon and Sun from Earth also factor into whether an eclipse can occur.
The Moon cannot be eclipsed when it is halfway between the nodes of its orbit because of the tilt in its orbit relative to the ecliptic, or the path of the Sun on the celestial sphere. The Moon's orbit is tilted by about 5° relative to the ecliptic. So, if you imagine two hula hoops with a common center, representing the orbits of the Moon and Sun, they are tilted slightly towards each other. This means that most months, the Moon is above or below the ecliptic plane and thus cannot enter into Earth's shadow for an eclipse to occur.
Only when the path of the Moon crosses the ecliptic, during what's known as an 'eclipse season', can eclipses occur. This happens twice a year. In other words, an eclipse can only happen if the Moon is at or very near to one of the nodes of its orbit when it is at full for a lunar eclipse or new for a solar eclipse.
An additional factor causing the Moon to avoid being eclipsed is the varying apparent sizes of the Sun and the Moon from our viewpoint. At times, the Moon appears smaller than the Sun, meaning it can't entirely cover the Sun even with perfect alignment for a total solar eclipse to occur. This is known as an 'annular eclipse' that leaves a ring of sunlight visible around the Moon.
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