Solve The Following Problems. Show Your Work With Your Answe

Solve The Following Problems Show Your Work With Your Answersequatio

Solve the following problems. Show your work with your answers.

Paper For Above instruction

Understanding and applying fundamental physics concepts such as velocity, acceleration, force, and weight require a thorough grasp of the relevant equations and principles. This paper addresses a variety of physics problems involving kinematic calculations, force, and momentum, illustrating the step-by-step process to find solutions while showing work for each problem.

Calculating Acceleration of a Motorcycle

Given that a motorcycle accelerates from 0 m/s to 35 m/s in 5.1 seconds, the acceleration can be calculated using the formula:

\[ a = \frac{\Delta v}{t} \]

Where \(\Delta v = v_f - v_i = 35\, \text{m/s} - 0\, \text{m/s} = 35\, \text{m/s}\) and \(t = 5.1\, \text{s}\). Substituting these values in:

\[ a = \frac{35\, \text{m/s}}{5.1\, \text{s}} \approx 6.86\, \text{m/s}^2 \]

Thus, the motorcycle's acceleration is approximately 6.86 m/s\(^2\).

Calculating Car's Acceleration Over Time

A race car speeds from 52 m/s to 155 m/s over 5 seconds. The acceleration is obtained similarly:

\[ a = \frac{v_f - v_i}{t} = \frac{155\, \text{m/s} - 52\, \text{m/s}}{5\, \text{s}} = \frac{103\, \text{m/s}}{5\, \text{s}} = 20.6\, \text{m/s}^2 \]

The car's acceleration is 20.6 m/s\(^2\).

Velocity of a Bee Flying 160 m in 23 seconds

The average velocity of the bee can be calculated as:

\[ v = \frac{d}{t} = \frac{160\, \text{m}}{23\, \text{s}} \approx 6.96\, \text{m/s} \]

The bee's velocity is approximately 6.96 m/s.

Velocity of a Car Moving 300 m in 20 s Towards the East

The average velocity is:

\[ v = \frac{d}{t} = \frac{300\, \text{m}}{20\, \text{s}} = 15\, \text{m/s} \]

Since the problem states the car is going east toward the mall, the velocity vector is 15 m/s east.

Calculating the Weight of a 6 kg Pizza

The weight of an object is the force due to gravity:

\[ W = m \times g = 6\, \text{kg} \times 9.8\, \text{m/s}^2 = 58.8\, \text{N} \]

The pizza weighs 58.8 newtons.

Time for Dog to Stop Sliding on Ice

The dog runs at 1.5 m/s and comes to a stop with acceleration -0.50 m/s\(^2\). Using the kinematic equation:

\[ v_f = v_i + a t \]

Rearranged to solve for time \(t\):

\[ t = \frac{v_f - v_i}{a} = \frac{0 - 1.5\, \text{m/s}}{-0.50\, \text{m/s}^2} = \frac{-1.5}{-0.50} = 3\, \text{s} \]

It takes the dog 3 seconds to stop.

Acceleration of a Ball Accelerating at 10 m/s\(^2\)

The problem states the acceleration directly; therefore, the acceleration is 10 m/s\(^2\).

Mass of a Ball Hit with 5 N Force

Using Newton's second law: \(F = m a\). Assume the acceleration is known or can be derived from the context; since the problem states force and acceleration is 10 m/s\(^2\), we rearrange for mass:

\[ m = \frac{F}{a} = \frac{5\, \text{N}}{10\, \text{m/s}^2} = 0.5\, \text{kg} \]

The mass of the ball is 0.5 kg.

Calculating the Train's Acceleration

The force applied to the train is \(7.0 \times 10^4\, \text{N}\), and the mass is \(1.5 \times 10^5\, \text{kg}\). Using Newton's second law:

\[ a = \frac{F}{m} = \frac{7.0 \times 10^4\, \text{N}}{1.5 \times 10^5\, \text{kg}} \approx 0.467\, \text{m/s}^2 \]

The train's acceleration is approximately 0.467 m/s\(^2\).

Momentum of an 8 kg Box Sliding at 5 m/s

Momentum \(p = m \times v\):

\[ p = 8\, \text{kg} \times 5\, \text{m/s} = 40\, \text{kg} \cdot \text{m/s} \]

The momentum is 40 kg·m/s.

Mass of a Child with Given Momentum

The momentum \(p = 120\, \text{kg·m/s}\), and the velocity \(v = 4\, \text{m/s}\). Using \(p = m v\):

\[ m = \frac{p}{v} = \frac{120\, \text{kg·m/s}}{4\, \text{m/s}} = 30\, \text{kg} \]

The child's mass is 30 kg.

Discussion on Free Fall and Weight

Free fall occurs when the only force acting on an object is gravity. In such cases, the acceleration is \(g = 9.8\, \text{m/s}^2\). All objects, regardless of mass, accelerate at the same rate during free fall, exemplified by the Apollo 15 hammer and feather experiment on the moon. Although in real-world conditions air resistance affects falling objects, these effects are negligible for objects with similar densities or in controlled environments.

Weight is the force exerted by gravity on an object, calculated as:

\[ W = m \times g \]

Weight varies with gravitational acceleration and differs on other planets. For example, on Mars (\(g \approx 3.71\, \text{m/s}^2\)), an object’s weight would be significantly less than on Earth.

Conclusion

These calculations demonstrate the importance of fundamental physics equations and principles such as velocity, acceleration, force, and momentum. They also highlight the distinctions between mass and weight, emphasizing the applications of these concepts in real-world contexts, from vehicle dynamics to biological motion and planetary science.

References

• Halliday, D., Resnick, R., & Walker, J. (2014). Fundamentals of Physics (10th ed.). Wiley.
• Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers (9th ed.). Cengage Learning.
• Knight, R. D. (2017). Physics for Scientists and Engineers: A Strategic Approach. Pearson.
• Tipler, P. A., & Mosca, G. (2008). Physics for Scientists and Engineers. W. H. Freeman.
• Giancoli, D. C. (2014). Physics for Scientists and Engineers. Pearson.
• Young, H. D., & Freedman, R. A. (2019). University Physics with Modern Physics. Pearson.
• Newton, I. (1687). Philosophiæ Naturalis Principia Mathematica.
• NASA. (2015). Apollo 15 Hammer and Feather Drop. NASA History Office.
• Shepard, R. (2012). Zero Gravity Experiments. Journal of Physics D.
• NASA. (2023). Gravity on Other Planets. NASA.gov.