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Physics: Post your doubts here!

janasalem

janasalem

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A cylindrical tube rolling down a slope of inclination θ moves a distance L in time T. The equation
relating these quantities is
L (3+a^2/P = QT^2sinθ
Where a is the internal radius of the tube and P and Q are constants.
Which line gives the correct units for P and Q?
 
Mahnoorfatima

Mahnoorfatima

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Anna Litical drops a ball from rest from the top of 78.4-meter high cliff. How much time will it take for the ball to reach the ground and at what height will the ball be after each second of motion?
I don't get the second part where the question says at what height will the ball be after each second of motion? The solution goes like:
At t = 1 s, y = 4.9 m (down) so height is 73.5 m (78.4 m - 4.9 m )

At t = 2 s, y = 19.6 m (down) so height is 58.8 m (78.4 m - 19.6 m )

At t = 3 s, y = 44.1 m (down) so height is 34.3 m (78.4 m - 45 m)

At t = 4 s, y = 78.4 m (down) so height is 0 m (78.4 m - 78.4 m)
Why are we subtracting 4.9 for the 1st second?
 
Mahnoorfatima

Mahnoorfatima

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A

Awesome12

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Mahnoorfatima said:
Physicsclassroom.com
A long jumper leaves the ground with an initial velocity of 12 m/s at an angle of 28-degrees above the horizontal. Determine the time of flight, the horizontal distance, and the peak height of the long-jumper. Could you please solve this one as well. I don't GET this at all! The same source.
Click to expand...
Are the answers :
t = 1.15 s
Horizontal distance = 12.2 m
Peak height: 9.1 m
 
A

Awesome12

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Mahnoorfatima said:
Last one's 1.6. First two are right. Can you please explain?
Click to expand...
Yeah sorry. A minor calculation error :D

Ok so basically a long jumper's jump's shape is that of a parabola, that is the same shape of the line of motion of an object in a projectile.

Form a right angle triangle whose angle with the horizontal is 28 degrees and whose hypotenuse is 12 (We are indirectly splitting the motion of the object in to horizontal and vertical components)



I)

Now the first question requires us to find the time the body is in the air. So we have to decide which component to use: Horizontal or Vertical?

Acceleration is a common term in each of the 4 or 5 formulas of motion. Acceleration is basically the force of gravity (9.81 m/s^2).

Since the body is moving upwards, the acceleration will be negative. (ie. -9.81 m/s^2).

Acceleration is a vertical component since gravity acts downwards. Therefore whatever formula we use, we have to use the vertical components only.

Now we know that the displacement is 0, since the body moves upwards and then returns to a level equal to the mean position.

Now find the VERTICAL COMPONENT of velocity. Why? Because like I said before, all terms should be the vertical components.
VERTICAL COMPONENT OF VELOCITY = 5.63 m/s


So far what we know:
Acceleration = -9.81
S/Displacement = 0
VERTICAL COMPONENT OF VELOCITY = 5.63 m/s

Time = ?


Now find a formula whose terms contains the things we know

One formula is

s = ut + 1/2 at^2

Substitute all the values to get t in the form of a QUADRATIC EQUATION:

Solve the quadrative equation. You wil get 1.15 and 0

Since the time cannot be 0, the ANSWER IS 1.15




II)

Now in part II, we need to find the HORIZONTAL DISTANCE. We already know the time.

What we can also derive is the HORIZONTAL COMPONENT OF SPEED, as like I said before, all the components should be the same either VERTICAL or Horizontal.

HORIZONTAL COMPONENT OF SPEED = 12 (Cos 28) = 10.6 m/s

Distance = 10.6 * 1.15

Distance = 12.2 m




III)

Now we need to find the peak position (that is the maximum VERTICAL DISTANCE)

Again like I said, to find the VERTICAL DISTANCE, the rest of the terms should also be VERTICAL COMPONENTS

We already know the VERTICAL COMPONENT OF INITIAL VELOCITY = 5.63 m/s

We also know the FINAL VELOCITY = 0
Why is it 0? Well, at the top, there is no velocity whatsoever, so we consider it to be 0.


What do we know so far

VERTICAL COMPONENT OF INITIAL VELOCITY = 5.63 m/s

FINAL VELOCITY = 0

ACCELERATION = -9.81 m/s

We need to find s/Displacement = ?


Formula to be used:

v^2 - u^2 = 2as

Substitute all the values and find s

s = 1.6 m



I hope this helps. :)
 
Mahnoorfatima

Mahnoorfatima

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