One dimensional problem

In summary, the first problem involves finding the force needed to keep a 2kg body moving on a horizontal surface at a constant velocity of 4 m/sec. The correct force is 4 Newton, but the book answer is 2 Newton, which is most likely a typo. The second problem involves finding the velocity of sound based on the time it takes for a splash to be heard after a stone is dropped into a well. The correct velocity is 341 m/sec, but the book answer is 280 m/sec, which may be due to incorrect numbers provided in the problem.
  • #1
Amith2006
427
2
Sir,
Please say whether these 2 problems are right.
1) A body of mass 2kg moving on a horizontal surface with an initial velocity of 4 m/sec comes to rest after 2 seconds. If one wants to keep this moving on the same surface with same velocity, what is the force that is needed to be applied?
I solved it in the following way:
Acceleration = (0 – 4)/2
= -2m/sec^2
Retarding force = mass x retardation
= 2 x 2
= 4 Newton
So if a force equal to the retarding force is applied, the body will move with a constant velocity of 4 m/sec^2. But the book answer is 2 Newton. What is your opinion Sir?

2) A splash is heard 4.28 seconds after a stone is dropped into a well 78.4 meters deep. What is the velocity of sound?
I solved it in the following way:
Time taken by the stone to reach the well = [2H/g]^1/2
(Here H is depth of well & g = 9.8 m/sec^2)
= 4 seconds
Time taken by sound to reach the observer = 4.28 – 4
= 0.28 seconds
Velocity of sound = 78.4/0.28
= 280 m/sec
But the book answer is 341 m/sec. What is your opinion?I think the book answer is wrong.
 
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  • #2
for the first problem i also get an acceleration of 2 m/s^2
since sum F = 0, then it should follow that F = m*a = 4 N
The book must have a typo

for the second problem it also looks like you solved the problem correctly.
While speed typically does travel around 340 m/s at standard atmospheric conditions, the answer does come out to 280 m/s with the numbers they have given you. What text is this anyways?
 
  • #3
The calculation and reasoning for both problems seem to be correct. In the first problem, the retarding force should indeed be equal to the mass x acceleration, which in this case is 4 Newtons. In the second problem, the calculation for the velocity of sound also seems to be correct. The book may have made a mistake in their calculation or may have used a different value for the acceleration due to gravity. As a scientist, it is important to always double check calculations and sources to ensure accuracy. If you are confident in your calculations, then your answers are most likely correct.
 

1. What is a one dimensional problem?

A one dimensional problem is a mathematical or scientific problem that involves only one independent variable or dimension. This means that the problem can be represented on a single number line or axis.

2. What are some examples of one dimensional problems?

Some examples of one dimensional problems include linear motion, simple harmonic motion, and problems involving one variable such as temperature, pressure, or time.

3. How do you solve a one dimensional problem?

To solve a one dimensional problem, you need to identify the independent variable, set up an appropriate equation or model, and then use mathematical techniques to find the solution. This may involve graphing, algebraic manipulation, or differential equations.

4. What are the limitations of one dimensional problems?

One dimensional problems have several limitations, including the inability to fully capture the complexity of real-life situations that often involve multiple variables. They also may not accurately represent the behavior of systems that are inherently multidimensional.

5. How are one dimensional problems used in scientific research?

One dimensional problems are commonly used in scientific research as simplified models that help to understand more complex systems. They are also used to make predictions and test hypotheses, and can provide valuable insights and solutions in a wide range of scientific fields.

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