You are asked to measure the density of a cube that has a side of 10 centimeters, and weighs 1 kg nominally. The tools you have are a ruler with the smallest reading at 1 mm, and a scale with a precision down to 0.1 g. Both tools are calibrated. Please estimate the final error on the density of the object that you measure.
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Answer:
To estimate the final error on the density of the cube, we can consider the errors introduced by both the measurement of its volume and its weight.
1. Volume Measurement:
- The side length of the cube is given as 10 centimeters, and your ruler can measure to 1 mm accuracy.
- So, the error in measuring the side length is ±0.05 cm (half of the smallest measurement unit).
- To calculate volume, you need to cube the side length: Volume = (10 cm)^3 = 1000 cm^3.
- Using the error propagation rule, the relative error in volume is ±0.05 cm / 10 cm = ±0.005.
2. Weight Measurement:
- The weight is given as 1 kg nominally, which is equivalent to 1000 g.
- Your scale has a precision down to 0.1 g.
- So, the error in measuring the weight is ±0.1 g / 1000 g = ±0.0001 (0.01%) relative error.
Now, to calculate the final error in density, you need to consider both errors in volume and weight:
Density = Weight / Volume
Relative Error in Density = (Relative Error in Weight) + (Relative Error in Volume)
Relative Error in Density = (0.0001) + (0.005) = 0.0051 or 0.51%
So, the final estimated error on the density of the cube is approximately ±0.0051 g/cm^3 or ±0.51%.
Final answer:
The density of the cube is calculated using its mass and volume, with potential errors from the measurements of these quantities leading to a total estimated density error of approximately ±3.01%.
Explanation:
The density of an object is given by the formula density = mass/volume. In this case, the mass of the cube is given as 1 kg (or 1000 g for consistency with the scale's precision), and the volume of the cube can be calculated from the given side length using the formula for the volume of a cube, volume = side³, which equals 1000 cm³.
However, there are measurement errors associated with both the ruler and scale. The ruler can measure to the nearest mm (or 0.1 cm), so the error is ±0.1 cm on each measurement of the cube's sides, leading to a volume error of about ±3%. The scale can measure to the nearest 0.1 g, which gives a mass error of about ±0.01%. The total error in the density, obtained by summing these errors, is therefore approximately ±3.01%.
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Related Questions
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Peregrine falcons frequently grab prey birds from the air, as BI0 in Example 9.10. Sometimes they strike at high enough speeds that the force of the impact disables prey birds. A 480 g per- egrine falcon high in the sky spies a 240 g pigeon some dis- tance below. The falcon slows to a near stop, then goes into ve-called a stoop-and picks up speed as she falls. The n reaches a vertical speed of 45 m/s before striking the pigeon, which we can assume is stationary. The falcon strikes the pigeon and grabs it in her talons. The collision between the falco birds lasts 0.015 s. a. What is the final speed of the falcon and pigeon? b. What is the average force on the pigeon during the impact?
Which a vector quantity: speed or velocity?
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Answers
delta v = change in velocity = velocity final - velocity initial.
= -22m/s - +18m/s = -40m/s.
mdeltav = (0.40kg)(-40m/s) = -16kgm/s or -16Ns.
Final answer:
Impulse corresponds to the change in momentum. Given a soccer ball weighing 0.40kg moving first at 18m/s north and then hit in the opposite direction at 22m/s, the impulse delivered to the ball by the player is approximately 16 kg.m/s in the opposite direction of the initial movement.
Explanation:
In the field of physics, impulse is defined as the change in momentum of an object upon interaction with an external force and is calculated by multiplying the force applied to the object by the time interval (duration) the force was acting. When a soccer player strikes the ball, he or she applies a force that changes the soccer ball's momentum.
Considering your question about the soccer ball, the initial momentum of the ball can be calculated by multiplying its mass (0.40 kg) by its velocity (18 m/s), giving 7.2 kg.m/s north. When the player hits the ball, it moves in the opposite direction (south) with a velocity of 22 m/s. Thus, the final momentum of the ball is 0.40 kg x -22 m/s = -8.8 kg.m/s.
Impulse is the change in momentum, so it's the final momentum minus the initial momentum, which equates to -8.8 kg.m/s - 7.2 kg.m/s= -16 kg.m/s south or +16 kg.m/s north, depending on the coordinate system you choose (north could be either positive or negative). Since the direction reversed, this is why we have a negative sign.
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b. elevation increases.
c. acceleration decreases.
d. gravity increas
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Answer:
As elevation increases, air pressure decreases, molecules spread out, and air temperature cools.
Explanation:
B. the low pressure at the bottom.
C. the low pressure in the mountain.
D. the high pressure in the mountains.
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Answer: The correct answer is the low pressure in the mountains
Explanation:
The air pressure is lower in the mountains. As we travel up into the mountains, the air inside our ears takes some time to adjust the pressure change.
This unequal pressure causes discomfort in ears while ascending and descending on the mountain. The condition of discomfort in ear is caused by the pressure difference between the outside and inside the eardrum.
Therefore, as we travel up to into the mountains, we notice discomfort in our ears. This is due to the low pressure in the mountain.
Answers
Answer:2.81 m
Explanation:
Given
speed(u)=13 m/s
dart strikes 0.23 m below
i.e. vertical distance traveled by dart is 0.23 m
considering dart motion similar to Projectile
Horizontal distance travel by dart =u\times t
what is your weight on the Sun?
Answers
If someone have weight that is force due to gravity is X than on the sun it will become 28 X.
What is force?
A force is an effect that can alter an object's motion according to physics. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to describe force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.
Mass of body is constant on any place in the universe and weight changes with acceleration due to gravity so, at sun weight will be 28 X.
If someone have weight that is force due to gravity is X than on the sun it will become 28 X.
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if the sun makes u weight 28 times more, then
111 x 28 = 3108