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Veseljchak [2.6K]

3 years ago

15

2. Calculate the slope of the line in your graph of the square of the period of the pendulum vs. length of the string .Galileo f

igured out the equation that describes the behavior of a pendulum. If you square both sides of the equation, you will find that the slope of the line is related to the acceleration due to gravity (g). Specifically, . Use your data to calculate g. How does it compare with the accepted value of ? Calculate the percent error and show your work.

1 answer:

Alla [95]3 years ago

4 0

The period is given by $T=2 \pi \sqrt{ \frac{l}{g} }$
Squaring this gives
$4 \pi ^{2} \frac{l}{g}$
Plotting this period as a function of length $l$ gives
$T=ml$
where the slope, m, is
$\frac{4 \pi ^{2} }{g}=4.0243$

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A cord of negligible mass runs around two massless, frictionless pulleys. A canister with mass m = 20 kg hangs from one pulley.

photoshop1234 [79]

(a) 196 N

The equation of the forces on the side of the cord where the force F is applied is:

$F-T=0$ (1)

where T is the tension in the cord.

On the other side of the cord, the equation of the forces on the canister is

$T-mg = ma$ (2)

where

m = 20 kg is the mass of the canister

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

a is the acceleration

From (1),

$T=F$

Substituting into (2),

$F-mg = ma\\F=m(g+a)$

We want the canister to move at constant speed, so

a = 0

And therefore:

$F=mg=(20)(9.8)=196 N$

b) 2.0 cm

The cord is inextensible, this means that the acceleration of its parts are the same. Therefore, the acceleration of the free end must be the same as the acceleration of the canister: and this means that the two parts also cover the same distance in the same time.

Therefore, the free end of the cord must be moved exactly the same as the canister, by 2.0 cm.

c) 3.92 J, the same

The work done by the tension in the cord is

$W_T = T d$

where

T is the tension

d = 2.0 cm = 0.02 m is the displacement

As we said in part (a), the tension in the cord is equal to the force applied to the free end:

T = F

So

T = 196 N

Therefore, the work done by the tension is

$W=(196)(0.02)=3.92 J$

And since the force applied (F) is the same, then the work done by you when pulling the cord is exactly the same.

(d) -3.92 J

The weight of the canister is

$F_g = mg =(20 kg)(9.8 m/s^2)=196 N$

However, the direction of the force of gravity is opposite to the displacement. Therefore, the work done by gravity is negative:

$W_g = - F_g d$

And substituting,

$W_g=-(196)(0.02)=-3.92 J$

(e) Zero

The net work done on the canister can be simply calculated by adding the work done by the tension in the cord and the weight of the canister:

$W=W_T+W_g = 3.92 + (-3.92 ) = 0$

This is in agreement with the work-energy theorem, which states that the work done on an object is equal to its change in kinetic energy. In this situation, the canister is moving at constant speed, so its kinetic energy is not change: therefore,

$\Delta K = 0$ (change in kinetic energy = 0)

and so, the work done on it is also zero.

(f) The pulley system changes the direction of the force applied

This is a simple pulley system, which means that the system does not multiply the force applied in input. In fact, the mechanical advantage of the system is

$MA=\frac{F_{out}}{F_{in}}$

where:

$F_{out}$ is the output force, which is the weight of the canister

$F_{in}$ is the force in input, which is F

So, the mechanical advantage is 1:

$MA=\frac{196 N}{196 N}=1$

From a point of view of energy, therefore, there is no advantage in this system.

However, the advantage offered by the pulley system concerns the direction of the force: in fact, it changes the direction of the applied force (which is F, downward) into the tension of the cord (which is upward on the canister).

6 0

3 years ago

Consider two wires made of copper. They have the same diameter but one of them has three times the length of the other. Choose t

boyakko [2]

Answer:

a. Both wires have the same resistivity

Explanation:

For the resistance of a wire , following formula holds good .

R = ρ l / S , R is resistance , l is length , S is cross sectional area and ρ is resistivity of the material that the wire is made of. Resistance is dependent on length and cross sectional area but resistivity does not depend upon length or cross sectional area . It only depends upon the type of material.

If we replace copper wire with aluminium wire , then resistivity will change .

Hence , since the wire remains made of copper , resistivity will not change.

6 0

3 years ago

You leave on a 450 miles trip in order to attend a meeting that will start 10.8 hours after you begin your trip. Along the way y

Lorico [155]

Answer:2.6 h

Explanation:

Given

Total Trip distance=450 miles

Meeting starts after 10.8 hours

safe Fastest speed is 55 mi/h

so if he drives all the to the meeting with max speed then it takes $=\frac{450}{55}=8.181 h$

and total allowable time is 10.8

Therefore longest time he can spend over dinner is $10.8-8.181 \approx 2.6 hours$

5 0

3 years ago

When an unbalanced force acts on an object,

Gwar [14]

When balanced forces follow up on an object, the object won't move. If you push against a wall, the wall pushes back with an equal but opposite force. Neither you nor the wall will move. Forces that cause a change in the motion of an object are unbalanced forces.

6 0

3 years ago

Read 2 more answers

What factor affects weight( what force causes weight to change)

Alex Ar [27]

Answer:

Gravitational force affects weight, weight changes with change in gravity

Hope it helped u,

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3 0

3 years ago