Net Force Of 2000N On A 1000kg Rocket — How Long

1 A Net Force Of 2000n Act On A Rocket Of Mass 1000 Kg How Long Mus

Analyze and solve physics problems involving net force, momentum, impulse, work, and power, including calculations related to rockets, collisions, projectile motion, and work-energy principles. Explain the concepts clearly with appropriate formulas and step-by-step reasoning.

Paper For Above instruction

Physics encompasses a vast array of principles that describe how objects move and interact forces. This paper explores several fundamental physics problems—ranging from the application of Newton's second law to the conservation of momentum and the work-energy theorem—highlighting their practical calculations and implications.

The first problem involves determining the duration for which a net force must be applied to a rocket to accelerate it from one velocity to another. Using Newton's second law (F = m * a), the acceleration can be deduced, and with kinematic equations, the time required can be calculated.

Specifically, with a net force of 2000 N acting on a 1000 kg rocket, the acceleration (a) is given by a = F/m = 2000 N / 1000 kg = 2 m/s². The change in velocity (Δv) is from 10.0 m/s to 200.0 m/s, so Δv = 190 m/s. Using the equation of motion v = u + at, where u is initial velocity, the time (t) to achieve this acceleration is t = Δv / a = 190 m/s / 2 m/s² = 95 seconds.

The second scenario involves the conservation of momentum in a collision between two marbles. Marble A, with a mass of 5 g (0.005 kg), initially moves at 20.0 cm/s (0.2 m/s). Marble B, with a mass of 10 g (0.01 kg), moves at 10.0 cm/s (0.1 m/s). To calculate the momenta before collision, we multiply mass by velocity for each marble. Evidence of elastic or inelastic collision can be studied by applying the conservation of momentum and comparing velocities afterward.

Before collision, momentum of marble A is p_A = m_A v_A = 0.005 kg 0.2 m/s = 0.001 kg·m/s, and marble B is p_B = 0.01 kg 0.1 m/s = 0.001 kg·m/s. Post-collision, with marble A's velocity decreasing to 8.0 cm/s (0.08 m/s), the momentum of marble A is p_A' = 0.005 kg 0.08 m/s = 0.0004 kg·m/s. Applying conservation of momentum, the momentum of marble B after collision is p_B' = p_A + p_B - p_A' = 0.001 + 0.001 - 0.0004 = 0.0016 kg·m/s. Therefore, the velocity of marble B after collision is v_B' = p_B' / m_B = 0.0016 kg·m/s / 0.01 kg = 0.16 m/s, or 16.0 cm/s, moving in the same direction.

The third problem involves an impulse-momentum approach to projectile motion, calculating the velocity of a wooden block after a bullet passes through it. Since the bullet's initial momentum is m_bullet v_bullet = 0.035 kg 475 m/s ≈ 16.625 kg·m/s, and after passing through, its velocity is 275 m/s, its momentum afterward is 0.035 kg * 275 m/s ≈ 9.625 kg·m/s. The change in momentum of the bullet is then about 16.625 - 9.625 = 7 kg·m/s, which equals the impulse imparted to the wooden block. Using the impulse-momentum theorem (Impulse = change in momentum), the velocity of the block after the bullet exits is calculated as v_block = Impulse / mass of the block = 7 kg·m/s / 2.5 kg ≈ 2.8 m/s.

In the case of recoil velocity, a projectile of mass m leaves a launcher with velocity v, imparting an opposite recoil velocity v_recoil to the launcher that can be calculated by conservation of momentum: m_projectile v = m_launcher v_recoil. Substituting values: 40 kg 800 m/s = 2000 kg v_recoil, yields v_recoil = (40 kg * 800 m/s) / 2000 kg = 16 m/s in the opposite direction.

Regarding rocket fuel expulsion, the conservation of momentum states that the mass of fuel expelled times its exhaust velocity equals the change in momentum of the rocket. Given the initial velocity of 7.5 m/s, fuel mass of 50 g (0.05 kg), and exhaust velocity of 600 m/s, the rocket's mass can be determined by the relation: m_rocket v_rocket = m_fuel v_exhaust. Rearranged to solve for m_rocket, considering initial momentum, yields that the total mass of the rocket is approximately 1.95 kg.

Further, analyzing impulse and velocity change, an object of 2 kg moving at 4 m/s feels an impulse which changes its velocity. The impulse, given by the area under the force-time graph, results in a different final velocity depending on the magnitude and duration of the force applied.

To address work done when climbing stairs, the fundamental principle is that work equals the force times the displacement in the direction of the force, which for lifting objects is related to gravitational potential energy (m g h). Doubling the height increases the work done by a factor of three if the weight remains constant, due to the proportionality of potential energy to height.

Similarly, when the weight of a box increases (triples), the work done to carry it up also triples, reflecting the increased gravitational potential energy needed.

Double power implies either doubling the work done or halving the time taken to perform the same amount of work. Thus, to increase power, the carrying time decreases proportionally, mathematically expressed as Power = Work / Time.

In cases of running stairs with a box, work done can be calculated by the change in potential energy (m g h), since kinetic energy variations during ascent are typically minimal or secondary. Power, being work over time, further measures the rate of energy transfer. Comparing Tommy and Timmy, even though they perform the same work, Timmy's higher power output is evident because he completes the task faster.

Finally, in pushing an object along a frictionless surface, energy conservation principles allow calculation of work done (which equals the force times distance), final velocity derived from kinetic energy, and power as work divided by time. For Liki, applying these principles illustrates the relationship between work, energy, and power in simple mechanical systems.

References

  • Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers. Cengage Learning.
  • Halliday, D., Resnick, R., & Walker, J. (2014). Fundamentals of Physics. John Wiley & Sons.
  • Tipler, P. A., & Mosca, G. (2008). Physics for Scientists and Engineers. W. H. Freeman.
  • Knight, R. D. (2017). Physics for Scientists and Engineers: A Strategic Approach. Pearson.
  • Young, H. D., & Freedman, R. A. (2019). University Physics with Modern Physics. Pearson.
  • Walker, J. (2015). Physics. Pearson Education.
  • Feynman, R. P. (2010). The Feynman Lectures on Physics. Basic Books.
  • Galili, I., & Hazan, A. (2014). Conceptual and quantitative understanding of physics principles. The Physics Teacher, 52(4), 216-221.
  • Hewitt, P. G. (2014). Conceptual Physics. Pearson.
  • Resnick, H., Halliday, D., & Walker, J. (2014). Fundamentals of Physics. Wiley.

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