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Andrews [41]
3 years ago
14

The period of a simple pendulum, defined as the time necessary for one complete oscillation, is measured in time units and is gi

ven by
T = 2π×square root of l/g

where ℓ is the length of the pendulum and g is the acceleration due to gravity, in units of length divided by time squared. Show that this equation is dimensionally consistent.
Physics
1 answer:
Oksana_A [137]3 years ago
7 0

The task is to show that the right side of the equation has units of [Time], just like the left side has.

The right side of the equation is . . . 2 π √(L/G) .

We can completely ignore the  2π since it has no units at all, so it has no effect on the units of the right side of the equation.  Now the task is simply to find the units of  √(L/G) .

L . . . meters

G . . . meters/sec²

(L/G) = (meters) / (meters/sec²)

(L/G) = (meters) · (sec²/meters)

(L/G) = (meters · sec²) / (meters)

(L/G) = sec²

So  √(L/G) = seconds = [Time]

THAT's what we were hoping to prove, and we did it !

You might be interested in
Newtons laws of motion
Viktor [21]

Answer:

Law 1. A body continues in its state of rest, or in uniform motion in a straight line, unless acted upon by a force.

Law 2. A body acted upon by a force moves in such a manner that the time rate of change of momentum equals the force.

Law 3. If two bodies exert forces on each other, these forces are equal in magnitude and opposite in direction.

7 0
2 years ago
Right Hand Rule 1 requires you to put the thumb of your right hand in the direction of current and your curled fingers will indi
Jet001 [13]
Answer: false
explanation: magnetic field does that
3 0
2 years ago
Read 2 more answers
At an altitude of 5000 m the rocket's acceleration has increased to 6.9 m/s2 . What mass of fuel has it burned?
sergey [27]

1) Initial upward acceleration: 6.0 m/s^2

2) Mass of burned fuel: 0.10\cdot 10^4 kg

Explanation:

1)

There are two forces acting on the rocket at the beginning:

- The force of gravity, of magnitude F_g = mg, in the downward direction, where

m=1.9\cdot 10^4 kg is the rocket's mass

g=9.8 m/s^2 is the acceleration of gravity

- The thrust of the motor, T, in the upward direction, of magnitude

T=3.0\cdot 10^5 N

According to Newton's second law of motion, the net force on the rocket must be equal to the product between its mass and its acceleration, so we can write:

T-mg=ma (1)

where a is the acceleration of the rocket.

Solving for a, we find the initial acceleration:

a=\frac{T-mg}{m}=\frac{3.0\cdot 10^5-(1.9\cdot 10^4)(9.8)}{1.9\cdot 10^4}=6.0 m/s^2

2)

When the rocket reaches an altitude of 5000 m, its acceleration has increased to

a'=6.9 m/s^2

The reason for this increase is that the mass of the rocket has decreased, because the rocket has burned some fuel.

We can therefore rewrite eq.(1) as

T-m'g=m'a'

where

m' is the new mass of the rocket

Re-arranging the equation and solving for m', we find

m'=\frac{T}{g+a}=\frac{3.0\cdot 10^5}{9.8+6.9}=1.8\cdot 10^4 kg

And since the initial mass of the rocket was

m=1.9 \cdot 10^4 kg

This means that the mass of fuel burned is

\Delta m = m-m'=1.9\cdot 10^4 - 1.80\cdot 10^4 = 0.10\cdot 10^4 kg

3 0
3 years ago
The units of force in science is the
Liono4ka [1.6K]
The correct answer is D. Newton
4 0
3 years ago
Read 2 more answers
If a racquet ball hits the wall with 20 N of force, how much force will it bounce back with?
loris [4]

Answer:

-20N

Explanation:

The racquet ball will bounce back with the same force.

This is in compliance with newton's third law of motion:

  "action and reaction are equal but opposite"

If the ball hits the wall with an action force of 20N, the reaction force will be -20N.

The negative indicates an oppositely directed force.

8 0
3 years ago
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