Physics. Pendulum Lab What is the relationship between the length and the period of a pendulum?

Physics

Pendulum Lab

• What is the relationship between the length and the period of a pendulum?

Pendulum Lab

• What is the relationship between the length and the period of a pendulum?

• (Draw a picture)

Pendulum Lab

• What is the relationship between the length and the period of a pendulum?

• (Draw a picture)

Define:LengthPeriod=time for one full swing, forward and back

Pendulum Lab

• What is the relationship between the length and the period of a pendulum?

• Data:• Measure and record a length, measure and

record its period

• Length (cm) Period (s)

Length (cm) Period (s)

• A few thoughts:– Find many data points – Use the full range– Repeat trials to reduce uncertainty– Control your protocol

Length (cm) Period (s)

• A few thoughts:– Find many data points – Use the full range– Repeat trials to reduce uncertainty– Control your protocol

Length (cm)Period (s) Length (cm) Period x 10 (s)42.3 13.3240.5 12.9436.5 12.3634.4 12.0731.6 11.7128.8 11.0425.9 10.5822.5 9.7919.4 9.2617.0 8.7914.6 8.1910.2 6.878.3 6.206.8 5.49

Pendulum Lab

• What is the relationship between the length and the period of a pendulum?

• Graph it. Independent variable on the bottom

0 5 10 15 20 25 30 35 40 450

0.2

0.4

0.6

0.8

1

1.2

1.4

Length (cm)

Perio

d (s

)

Pendulum Lab

• Do you see the parabola?

0 5 10 15 20 25 30 35 40 450

0.2

0.4

0.6

0.8

1

1.2

1.4

Length (cm)

Perio

d (s

)

Pendulum Lab

• Write a relationship:

• Length is related to the period squared.(Period is related to the square root of the length)

Pendulum Lab

Period is related to the square root of the length• Write an equation

T=k√L

Calculate and graph Square root of length Period

6.504 1.3326.364 1.2946.042 1.2365.865 1.2075.621 1.1715.367 1.1045.089 1.0584.743 0.9794.405 0.9264.123 0.8793.821 0.8193.194 0.6872.881 0.622.608 0.549

0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.0000

0.2

0.4

0.6

0.8

1

1.2

1.4

Square Root of length (cm)

Peri

od (s

)

Slope = 2.1 s/√cm

Pendulum Lab

Period is related to the square root of the length• Write a conclusion

T=(2.1s/√cm)√L

Measurement Lab

• Measure carefully.• Estimate one digit• Include a unit with each value.

• Show all of your work in the calculations(see pp 18 and 22 of your planner for equations)– Consider significant figures at each step– Include units at each step

At 30 km/h

At 75 km/h

Velocity

• --a vector, including a speed and a direction• --units are meters/second (m/s)

• Common speeds:• --walking pace ~2 m/s• --highway speed ~30 m/s

Position/Time graph

Position/Time graph

Velocity/Time graph

Velocity/Time graph

Acceleration/Time graph

Kinematics

Constant motion

1) A sprinter runs at 10.0 m/s for 3.5 s. How far does he travel?

2) A car travels 1500 m in 45 s. What is its speed?

3) An airplane flies at 240 m/s from Denver to Kansas City, a distance of 1,000,000 m. How long does the flight take?

10 m/s for 10 s

0 5 10 15 20 25 30 350

5

10

15

20

25

30

35

Time (s)

Spee

d (m

/s)

10 m/s for 10 s

0 5 10 15 20 25 30 350

5

10

15

20

25

30

35

Time (s)

Spee

d (m

/s)

That’s 100 m total!

5 m/s for 20 s

0 5 10 15 20 25 30 350

5

10

15

20

25

30

35

Time (s)

Spee

d (m

/s)

5 m/s for 20 s

0 5 10 15 20 25 30 350

5

10

15

20

25

30

35

Time (s)

Spee

d (m

/s)

That’s also 100 m total!

Accelerated motion

1) A sprinter reaches 10.0 m/s in 2.95 s after the start of a race. What is his acceleration?

2) An airplane accelerates from rest to 180 m/s at an acceleration of 6.0 m/s2. How long does this take-off last?

3) A car accelerates at 3.0 m/s2 for 12 s. What is its change in speed?

10 m/s for 10 s

0 5 10 15 20 25 30 350

5

10

15

20

25

30

35

Time (s)

Spee

d (m

/s)

That’s 100 m total!

From rest to 20 m/s in 10 s

0 5 10 15 20 25 30 350

5

10

15

20

25

30

35

Time (s)

Spee

d (m

/s)

From rest to 20 m/s in 10 s

0 5 10 15 20 25 30 350

5

10

15

20

25

30

35

Time (s)

Spee

d (m

/s)

That’s 100 m total!

Accelerated motion

1) A sprinter reaches 10.0 m/s in 2.95 s after the start of a race. What is his acceleration?

2) An airplane accelerates from rest to 180 m/s at an acceleration of 6.0 m/s2. How long does this take-off last?

3) A car accelerates from rest at 3.0 m/s2 for 12 s. What is its change in speed?

What distance is covered in each of these cases?

…is dropped from a height of…

• Two things are given here!

1) vi=0 m/s and

2) a=-9.8 m/s2

…is thrown vertically…

1) a=-9.8 m/s2

2) The object rises as long as v>0 m/s, then it turns around and falls. 3) Rising time = falling time

…is thrown horizontally…

1) viy=0 m/s

2) ay=-9.8 m/s2

3) vx is given, and constant

4) Time is the same for both x and y motion

…is thrown at an angle of…

• This is the big one—ballistic motion.1) Separate motion into x and y components.2) Calculate time in the air by the vy component

3) Motion in the x direction is constant.

4) Highest point is halfway through the flight5) Rising and falling times are equal if the height

is the same.

0 5 10 15 20 25 30 350

5

10

15

20

25

30

35

Time (s)

Spee

d (m

/s)