How to find synthesis of data in physics - ACT Science

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Question

Laura is performing an experiment with a 5kg weight tied to a 3m rope tied to the ceiling as shown:

Laura drops the weight and allows it to swing freely. She measures how long it takes for the weight to return to it's original position (assume no forces outside of gravity are acting upon the pendulum). This is also called one oscillation.

Experiment 1:

Laura created the following table for her first measurement of the pendulum's oscillations.

Experiment 2:

Laura performed the experiment again, this time using a 6kg weight.

Experiment 3:

Laura performed the experiment again, this time using a 3kg weight and a 5m rope.

If Laura recreated experiment 1 using a 10kg weight, how long would 2 oscillations last?

Answer

As shown by comparing experiment 1 and 2, the actual mass of the weight has no effect upon how long each oscillation is.

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Question

Laura is performing an experiment with a 5kg weight tied to a 3m rope tied to the ceiling as shown:

Laura drops the weight and allows it to swing freely. She measures how long it takes for the weight to return to it's original position (assume no forces outside of gravity are acting upon the pendulum). This is also called one oscillation.

Experiment 1:

Laura created the following table for her first measurement of the pendulum's oscillations.

Experiment 2:

Laura performed the experiment again, this time using a 6kg weight.

Experiment 3:

Laura performed the experiment again, this time using a 3kg weight and a 5m rope.

How long would 4 oscillations be, using the 3m rope and the 6kg weight?

Answer

Based on experiment 2, each oscillation is approximately 3.474 seconds long. 4 oscillations would therefore last approximately 13.896 seconds

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Question

Laura is performing an experiment with a 5kg weight tied to a 3m rope tied to the ceiling as shown:

Laura drops the weight and allows it to swing freely. She measures how long it takes for the weight to return to it's original position (assume no forces outside of gravity are acting upon the pendulum). This is also called one oscillation.

Experiment 1:

Laura created the following table for her first measurement of the pendulum's oscillations.

Experiment 2:

Laura performed the experiment again, this time using a 6kg weight.

Experiment 3:

Laura performed the experiment again, this time using a 3kg weight and a 5m rope.

Which of the following statements is a valid conclusion?

Answer

In the experiment, the only variable that affects the amount of time of each oscillation is the length of the rope.

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Question

Laura is performing an experiment with a 5kg weight tied to a 3m rope tied to the ceiling as shown:

Laura drops the weight and allows it to swing freely. She measures how long it takes for the weight to return to its original position (assume no forces outside of gravity are acting upon the pendulum). This is also called one oscillation.

Experiment 1:

Laura created the following table for her first measurement of the pendulum's oscillations.

Experiment 2:

Laura performed the experiment again, this time using a 6kg weight.

Experiment 3:

Laura performed the experiment again, this time using a 3kg weight and a 5m rope.

If Laura stopped experiment 3 after 10 seconds, how many oscillations would the pendulum have gone through?

Answer

Since each oscillation lasts 4.486 seconds,

${\frac{10\ seconds}{4.486\ seconds}}{}$

gives us the answer of 2.23 oscillations.

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Question

Laura is performing an experiment with a 5kg weight tied to a 3m rope tied to the ceiling as shown:

Laura drops the weight and allows it to swing freely. She measures how long it takes for the weight to return to it's original position (assume no forces outside of gravity are acting upon the pendulum). This is also called one oscillation.

Experiment 1:

Laura created the following table for her first measurement of the pendulum's oscillations.

Experiment 2:

Laura performed the experiment again, this time using a 6kg weight.

Experiment 3:

Laura performed the experiment again, this time using a 3kg weight and a 5m rope.

How much longer does each oscillation in experiment 3 take in comparison to experiment 1?

Answer

To compare how much longer each oscillation in experiment 3 is, simply subtract the two values.

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Question

Laura is performing an experiment with a 5kg weight tied to a 3m rope tied to the ceiling as shown:

Laura drops the weight and allows it to swing freely. She measures how long it takes for the weight to return to it's original position (assume no forces outside of gravity are acting upon the pendulum). This is also called one oscillation.

Experiment 1:

Laura created the following table for her first measurement of the pendulum's oscillations.

Experiment 2:

Laura performed the experiment again, this time using a 6kg weight.

Experiment 3:

Laura performed the experiment again, this time using a 3kg weight and a 5m rope.

If Laura recreated experiment 3 using a 5m rope and a 20kg weight, how long would 2 oscillations last?

Answer

As shown by comparing experiments 1 and 2, the mass of the weight has no effect upon the time of each oscillation.

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Question

Laura is performing an experiment with a 5kg weight tied to a 3m rope tied to the ceiling as shown:

Laura drops the weight and allows it to swing freely. She measures how long it takes for the weight to return to it's original position (assume no forces outside of gravity are acting upon the pendulum). This is also called one oscillation.

Experiment 1:

Laura created the following table for her first measurement of the pendulum's oscillations.

Experiment 2:

Laura performed the experiment again, this time using a 6kg weight.

Experiment 3:

Laura performed the experiment again, this time using a 3kg weight and a 5m rope.

Which of the following could be an equation for the length of time of one oscillation in experiment 1? (L represents the length of the rope)

Answer

By plugging in the values from experiment one, the correct answer can be found. $Time=2\pi\sqrt{\frac{L}{9.81}}$

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Question

Laura is performing an experiment with a 5kg weight tied to a 3m rope tied to the ceiling as shown:

Laura drops the weight and allows it to swing freely. She measures how long it takes for the weight to return to it's original position (assume no forces outside of gravity are acting upon the pendulum). This is also called one oscillation.

Experiment 1:

Laura created the following table for her first measurement of the pendulum's oscillations.

Experiment 2:

Laura performed the experiment again, this time using a 6kg weight.

Experiment 3:

Laura performed the experiment again, this time using a 3kg weight and a 5m rope.

Laura wants to run a new experiment that has a shorter length of time per oscillation than in experiment 1. Which one of the following would be a good choice for length of rope?

Answer

The shorter the length of rope, the less time each oscillation takes.

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Question

Laura is performing an experiment with a 5kg weight tied to a 3m rope tied to the ceiling as shown:

Laura drops the weight and allows it to swing freely. She measures how long it takes for the weight to return to it's original position (assume no forces outside of gravity are acting upon the pendulum). This is also called one oscillation.

Experiment 1:

Laura created the following table for her first measurement of the pendulum's oscillations.

Experiment 2:

Laura performed the experiment again, this time using a 6kg weight.

Experiment 3:

Laura performed the experiment again, this time using a 3kg weight and a 5m rope.

If Laura recreates experiment 2 using a 300kg weight, how long would each oscillation last?

Answer

The weight of the object has no effect upon the time of oscillation.

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Question

Laura is performing an experiment with a 5kg weight tied to a 3m rope tied to the ceiling as shown:

Laura drops the weight and allows it to swing freely. She measures how long it takes for the weight to return to it's original position (assume no forces outside of gravity are acting upon the pendulum). This is also called one oscillation.

Experiment 1:

Laura created the following table for her first measurement of the pendulum's oscillations.

Experiment 2:

Laura performed the experiment again, this time using a 6kg weight.

Experiment 3:

Laura performed the experiment again, this time using a 3kg weight and a 5m rope.

In experiment 3, how long would 2.5 oscillations last?

Answer

Each oscillation lasts 4.486 seconds; therefore, 2.5 oscillations would last 11.215 seconds.

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Question

Laura is performing an experiment with a 5kg weight tied to a 3m rope tied to the ceiling as shown:

Laura drops the weight and allows it to swing freely. She measures how long it takes for the weight to return to it's original position (assume no forces outside of gravity are acting upon the pendulum). This is also called one oscillation.

Experiment 1:

Laura created the following table for her first measurement of the pendulum's oscillations.

Experiment 2:

Laura performed the experiment again, this time using a 6kg weight.

Experiment 3:

Laura performed the experiment again, this time using a 3kg weight and a 5m rope.

If Laura created a new experiment (experiment 4) and used a 3kg mass and a 6m rope, how long would one oscillation likely be?

Answer

A 6m rope would provide results close to the 5m rope results in experiment 3, but would be slightly bigger. 10 seconds is too long. The other incorrect answers are too small. 4.914 seems most likely.

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Question

Mary is performing an experiment involving the electromagnetic spectrum. She observes several different types of waves and records their wavelength, frequency, and speed.

A new type of radiation is discovered on the electromagnetic spectrum that has a higher frequency than gamma rays. What would its speed most likely be?

Answer

Notice that all of the waves, regardless of their frequencies move at the same speed: $\small 299,792,458 \frac{m}{s}$ . The newly discovered wave would also move at $\small 299,792,458 \frac{m}{s}$ .

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Question

Mary is performing an experiment involving the electromagnetic spectrum. She observes several different types of waves and records their wavelength, frequency, and speed.

Which of the following would be a valid conclusion for this experiment?

Answer

All of the waves move with the same speed; therefore, there is no relationship.

Another valid conclusion would be that wavelength and frequency are inversely proportional. As frequency increases, wavelength decreases.

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Question

Mary is performing an experiment involving the electromagnetic spectrum. She observes several different types of waves and records their wavelength, frequency, and speed.

A new type of radiation is discovered with wavelength measurements between those of microwaves and infrared radiation. What is the most likely value of its frequency?

Answer

If the new radiation has a wavelength between the wavelengths of microwaves and infrared waves, then it must have a frequency between the frequencies of microwaves and infrared waves as well. Following the trends in the table, we can set up the flowing inequalities.

$Wavelength:\ 10^{-2}>?>10^{-5}$

$Frequency:\ 10^8<?<10^{12}$

$10^{10}$ is the only answer choice that satisfies the inequality for frequency.

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Question

Mary is performing an experiment involving the electromagnetic spectrum. She observes several different types of waves and records their wavelength, frequency, and speed.

A soccer field is approximately long. Which wave has a wavelength closest to the length of a soccer field?

Answer

Radio waves have a wavelength of $\small 10^3m$ , which is the closest to the soccer field's length of $\small 10^2m$ . All of the other waves have wavelengths that are much smaller, due to the negative exponents.

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Question

Mary is performing an experiment involving the electromagnetic spectrum. She observes several different types of waves and records their wavelength, frequency, and speed.

A water molecule is approximately $\small 10^{-10}m$ in diameter. Which wave has a wavelength closest to this length?

Answer

X-rays have a wavelength of $\small 10^{-10}m$ , which is exactly the same size as the water molecule mentioned in the problem.

Radio waves and microwaves have wavelengths that are larger than the diameter of the water molecule, and gamma rays have a wavelength that is smaller.

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Question

Mary is performing an experiment involving the electromagnetic spectrum. She observes several different types of waves and records their wavelength, frequency, and speed.

With which of the following variables is wavelength inversely proportional?

Answer

The trends in the table, from top to bottom, are a decrease in wavelength, an increase in frequency, and no change in speed. Based on these trends, we can see that as wavelength decreases, frequency increases. This type of trend describes an inverse proportionality.

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Question

Mary is performing an experiment involving the electromagnetic spectrum. She observes several different types of waves and records their wavelength, frequency, and speed.

FM radio waves are at the higher end of the radio wave frequency spectrum. Which of the following could be possible value for the frequency of an FM radio wave?

Answer

If FM radio waves are at the higher end of radio wave frequency, then they are closer to microwaves. The only possible answer choice between the frequency of radio waves and the frequency of microwaves is $\small 7*10^6Hz$ .

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Question

Mary is performing an experiment involving the electromagnetic spectrum. She observes several different types of waves and records their wavelength, frequency, and speed.

The Earth's atmosphere prevents certain wavelengths on the electromagnetic spectrum from reaching the Earth's surface. If anything smaller than $\small 10^{-9}m$ is blocked, then which of the following rays would not reach the Earth's surface?

Answer

The question states that any wavelengths less than $\small 10^{-9}m$ are blocked and do not reach the surface.

The only answer choice with a wavelength smaller than $\small 10^{-9}m$ is gamma rays, which have a length of $\small 10^{-12}m$ .

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Question

Mary is performing an experiment involving the electromagnetic spectrum. She observes several different types of waves and records their wavelength, frequency, and speed.

The Earth's atmosphere allows types of radiation to enter the atmosphere, and blocks others. It allows in wavelengths from $\small 10^{-8}m$ to $\small 10^{-5}m$ , but creates some distortion. Which type of radiation would not potentially be affected by the distortion?

Answer

X-rays are the only answer with a wave length that does not fall within the range of distortion. Regardless of whether or not they are BLOCKED by the atmosphere, they are not DISTORTED by the given parameters.

$10^{-10}<10^{-8}<\text{distorted}<10^{-5}$

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How to find synthesis of data in physics - ACT Science

As shown by comparing experiment 1 and 2, the actual mass of the weight has no effect upon how long each oscillation is.

Based on experiment 2, each oscillation is approximately 3.474 seconds long. 4 oscillations would therefore last approximately 13.896 seconds

In the experiment, the only variable that affects the amount of time of each oscillation is the length of the rope.

Since each oscillation lasts 4.486 seconds, gives us the answer of 2.23 oscillations.

To compare how much longer each oscillation in experiment 3 is, simply subtract the two values.

As shown by comparing experiments 1 and 2, the mass of the weight has no effect upon the time of each oscillation.

By plugging in the values from experiment one, the correct answer can be found.

The shorter the length of rope, the less time each oscillation takes.

The weight of the object has no effect upon the time of oscillation.

Each oscillation lasts 4.486 seconds; therefore, 2.5 oscillations would last 11.215 seconds.

A 6m rope would provide results close to the 5m rope results in experiment 3, but would be slightly bigger. 10 seconds is too long. The other incorrect answers are too small. 4.914 seems most likely.

Notice that all of the waves, regardless of their frequencies move at the same speed: . The newly discovered wave would also move at .

Mary is performing an experiment involving the electromagnetic spectrum. She observes several different types of waves and records their wavelength, frequency, and speed. Which of the following would be a valid conclusion for this experiment?

All of the waves move with the same speed; therefore, there is no relationship. Another valid conclusion would be that wavelength and frequency are inversely proportional. As frequency increases, wavelength decreases.

Mary is performing an experiment involving the electromagnetic spectrum. She observes several different types of waves and records their wavelength, frequency, and speed. A soccer field is approximately long. Which wave has a wavelength closest to the length of a soccer field?

Radio waves have a wavelength of , which is the closest to the soccer field's length of . All of the other waves have wavelengths that are much smaller, due to the negative exponents.

Mary is performing an experiment involving the electromagnetic spectrum. She observes several different types of waves and records their wavelength, frequency, and speed. A water molecule is approximately in diameter. Which wave has a wavelength closest to this length?

X-rays have a wavelength of , which is exactly the same size as the water molecule mentioned in the problem. Radio waves and microwaves have wavelengths that are larger than the diameter of the water molecule, and gamma rays have a wavelength that is smaller.

Mary is performing an experiment involving the electromagnetic spectrum. She observes several different types of waves and records their wavelength, frequency, and speed. With which of the following variables is wavelength inversely proportional?

The trends in the table, from top to bottom, are a decrease in wavelength, an increase in frequency, and no change in speed. Based on these trends, we can see that as wavelength decreases, frequency increases. This type of trend describes an inverse proportionality.

If FM radio waves are at the higher end of radio wave frequency, then they are closer to microwaves. The only possible answer choice between the frequency of radio waves and the frequency of microwaves is .

The question states that any wavelengths less than are blocked and do not reach the surface. The only answer choice with a wavelength smaller than is gamma rays, which have a length of .

X-rays are the only answer with a wave length that does not fall within the range of distortion. Regardless of whether or not they are BLOCKED by the atmosphere, they are not DISTORTED by the given parameters.

Since each oscillation lasts 4.486 seconds,

${\frac{10\ seconds}{4.486\ seconds}}{}$

gives us the answer of 2.23 oscillations.

By plugging in the values from experiment one, the correct answer can be found. $Time=2\pi\sqrt{\frac{L}{9.81}}$

Notice that all of the waves, regardless of their frequencies move at the same speed: $\small 299,792,458 \frac{m}{s}$ . The newly discovered wave would also move at $\small 299,792,458 \frac{m}{s}$ .

Mary is performing an experiment involving the electromagnetic spectrum. She observes several different types of waves and records their wavelength, frequency, and speed.

Which of the following would be a valid conclusion for this experiment?

All of the waves move with the same speed; therefore, there is no relationship.

Another valid conclusion would be that wavelength and frequency are inversely proportional. As frequency increases, wavelength decreases.

Mary is performing an experiment involving the electromagnetic spectrum. She observes several different types of waves and records their wavelength, frequency, and speed.

A soccer field is approximately long. Which wave has a wavelength closest to the length of a soccer field?

Radio waves have a wavelength of $\small 10^3m$ , which is the closest to the soccer field's length of $\small 10^2m$ . All of the other waves have wavelengths that are much smaller, due to the negative exponents.

Mary is performing an experiment involving the electromagnetic spectrum. She observes several different types of waves and records their wavelength, frequency, and speed.

A water molecule is approximately $\small 10^{-10}m$ in diameter. Which wave has a wavelength closest to this length?

X-rays have a wavelength of $\small 10^{-10}m$ , which is exactly the same size as the water molecule mentioned in the problem.

Radio waves and microwaves have wavelengths that are larger than the diameter of the water molecule, and gamma rays have a wavelength that is smaller.

Mary is performing an experiment involving the electromagnetic spectrum. She observes several different types of waves and records their wavelength, frequency, and speed.

With which of the following variables is wavelength inversely proportional?

If FM radio waves are at the higher end of radio wave frequency, then they are closer to microwaves. The only possible answer choice between the frequency of radio waves and the frequency of microwaves is $\small 7*10^6Hz$ .

The question states that any wavelengths less than $\small 10^{-9}m$ are blocked and do not reach the surface.

The only answer choice with a wavelength smaller than $\small 10^{-9}m$ is gamma rays, which have a length of $\small 10^{-12}m$ .

X-rays are the only answer with a wave length that does not fall within the range of distortion. Regardless of whether or not they are BLOCKED by the atmosphere, they are not DISTORTED by the given parameters.

$10^{-10}<10^{-8}<\text{distorted}<10^{-5}$