Convert The Quantity Given To The Requested Units

Convert The Quantity Given To Be In The Units Requested1an Objec

Convert the quantity given to be in the units requested.

1. An object weighs 3000 N. What is the object's mass? _______kg

2. An object weighs 2700 lb. What is the object's weight in N? _______N

3. An object weighs 3500 N. What is the object's weight in lb? _______lb

4. The mass of a certain elephant is 2,667 kg. (a) Find the elephant's weight in newtons. _______N (b) Find its weight in pounds. _______lb

5. A jet aircraft with a mass of 4,275 kg has an engine that exerts a force (thrust) equal to 59,400 N. (a) What is the jet's acceleration? (Give the magnitude.) ________ (b) What is the jet's speed after it accelerates for 9 s? (Assume it starts from rest.) ________ (c) How far does the jet travel during the 9 s? ________

6. A motorcycle and rider have a total mass equal to 335 kg. The rider applies the brakes, causing the motorcycle to accelerate at a rate of −4 m/s². What is the net force on the motorcycle? ________

7. In an experiment performed in a space station, a force of 62 N causes an object to have an acceleration equal to 2 m/s². What is the object's mass? ________

8. On aircraft carriers, catapults are used to accelerate jet aircraft to flight speeds in a short distance. One such catapult takes a 17,800-kg jet from 0 to 67 m/s in 2.7 s. (Assume the catapult acts in the positive horizontal direction.) (a) What is the acceleration of the jet in m/s²? ________ (b) What is the acceleration of the jet in g's? ________ (c) How far does the jet travel while it is accelerating? ________ (d) How large is the force that the catapult must exert on the jet? __________

9. An airplane is built to withstand a maximum acceleration of 7 g. If its mass is 1,210 kg, what size force would cause this acceleration? _________

10. Under certain conditions, the human body can safely withstand an acceleration of 10 g. (a) What net force would have to act on someone with mass of 75 kg to cause this acceleration? _________ (b) First, find the weight of such a person in pounds. Second, convert the answer obtained in part (a) into pounds. Weight of person ________ Net force from part (a) ________

11. A race car rounds a curve at 55 m/s. The radius of the curve is 434 m, and the car's mass is 685 kg. (Assume the car's speed remains constant. Take the radially inward direction to be positive.) (a) What is the car's (centripetal) acceleration? ________ (b) What is it in g's? ________ (c) What is the centripetal force acting on the car? ________

12. A hang glider and its pilot have a total mass equal to 128 kg. While executing a 360° turn, the glider moves in a circle with a 9 m radius. The glider's speed is 13 m/s. (Assume the glider turns along the horizontal plane.) (a) What is the net force on the hang glider? __________ (b) What is the acceleration? ____________

13. As a spacecraft approaches a planet, the rocket engines on it are fired (turned on) to slow it down so it will go into orbit around the planet. The spacecraft's mass is 1,925 kg and the thrust (force) of the rocket engines is 345 N. If its speed must be decreased by 1,134 m/s, how long (in minutes) must the engines be fired? (Ignore the change in the mass as the fuel is burned.) ___________

14. As a baseball is being caught, its speed goes from 27 to 0 m/s in about 0.008 s. Its mass is 0.145 kg. (Take the direction the baseball is thrown to be positive.) (a) What is the baseball's acceleration in m/s²? (Indicate the direction with the sign of your answer.) _________ What is the baseball's acceleration in g's? (Indicate the direction with the sign of your answer.) _________ (b) What is the size of the force acting on it? ___________

15. As a rocket ascends, its acceleration increases even though the net force on it stays constant. Why? (Choose the correct explanation)

16. A person is riding on a train while watching a GPS display. Both "speed" and "heading" readings are not changing. What can the person conclude about the net force acting on the train? ________

17. A car starts at position x=0, with an initial velocity of 4.7 m/s and an acceleration of 0 m/s². What is its position after 6.5 seconds? ________

18. A car has an initial position of x=0 m, an initial velocity of 0 m/s, and a constant acceleration of 2.6 m/s². What is its position after 4.2 seconds? ________

19. A car has an initial position of x=0 m, an initial velocity of 0 m/s, and a constant acceleration of 4.1 m/s². What is its velocity after 5.7 seconds? ________

Paper For Above instruction

This comprehensive exploration addresses fundamental principles of physics related to units conversion, kinematics, and dynamics, providing detailed solutions and explanations for each problem statement to foster understanding of forces, motion, and related concepts.

Introduction

Converting quantities between different units and understanding the relationships between force, mass, acceleration, and velocity are essential skills in physics. These skills enable accurate problem-solving and application in real-world contexts, such as engineering, transportation, and space exploration. This paper systematically approaches each problem, demonstrating how to convert units, compute forces and accelerations, and interpret physical phenomena.

Problem 1-3: Conversions between Newtons, Pounds, and Kilograms

The relationship between weight, force, and mass is rooted in Newton's second law, F = ma, where force is measured in Newtons (N), and mass in kilograms (kg). The weight of an object in Newtons can be calculated from its mass by considering gravitational acceleration (approximately 9.81 m/s²). Conversely, converting weight from pounds to Newtons involves recognizing that 1 lb ≈ 4.44822 N. For instance, a weight of 3000 N corresponds to a mass of approximately 306 kg (3000 N / 9.81 m/s²), illustrating the inverse process.

Conversion from pounds to Newtons involves multiplying by the conversion factor 4.44822 (since 1 lb ≈ 4.44822 N). For example, 2700 lb in Newtons equals 2700 × 4.44822 ≈ 12,021 N, which highlights the importance of accurate unit conversion for engineering calculations.

Problem 4: Elephant’s Weight in Newtons and Pounds

The weight of the elephant is computed using its mass: Weight = mass × gravitational acceleration, giving 2667 kg × 9.81 m/s² ≈ 26,173 N. Converting this to pounds: 26,173 N / 4.44822 ≈ 5882 lb. These calculations demonstrate the dual perspectives of weight measurement essential in biological and engineering fields.

Problem 5-10: Dynamics and Kinematics of Vehicles and Humans

Applying Newton's second law (F = m×a), the acceleration of the jet is calculated from the thrust divided by mass: 59,400 N / 4275 kg ≈ 13.91 m/s². The velocity after 9 seconds, starting from rest, follows v = at: 13.91 m/s² × 9 s ≈ 125.19 m/s. The distance traveled is found using s = 0.5×a×t²: 0.5×13.91×81 ≈ 564.2 meters.

For the motorcycle, the net force is F = m×a: 335 kg × (-4 m/s²) = -1340 N, indicating deceleration in the negative direction. In space simulations, mass determination from force and acceleration uses rearranged Newton’s law: m = F / a.

Calculations for the jet's acceleration and force during catapult launch employ similar principles, converting forces to g's where 1 g ≈ 9.81 m/s², providing insights into high-speed aircraft launch mechanisms. The maximum force causing the maximum acceleration of aircraft involves multiplying the mass by the maximum acceleration (7 g × 9.81 m/s² = 68.67 m/s², then force = mass × acceleration).

Problem 11-14: Motion on Curves, Turns, and Impacts

For the race car, the centripetal acceleration a_c = v² / r = (55)² / 434 ≈ 6.98 m/s², and in g's, a_c / 9.81 ≈ 0.711 g. The centripetal force is then F_c = m×a_c: 685 kg × 6.98 m/s² ≈ 4785 N.

In the case of the hang glider, the net force during a turn is F = m×a: first, find the acceleration from a = v² / r; then multiply by mass for force. Similarly, the deceleration of the spacecraft involves dividing the change in velocity by the time in seconds to find duration of thrust application.

Problem 15-19: Kinematics and Motion Equations

The acceleration of a baseball during catching is a = Δv / Δt = (0 - 27) / 0.008 ≈ -3375 m/s²; in g's, this is approximately -344 g. The force is then F = m×a: 0.145 kg × -3375 ≈ -489 N.

Explaining why rocket acceleration increases with constant net force involves understanding that as mass decreases due to fuel consumption, the same force results in a larger acceleration, following Newton's second law.

The problem with the train's constant velocity and no change in heading indicates that net force is zero, demonstrating a state of dynamic equilibrium. The kinematic equations for position and velocity over time are fulfilled, confirming constant velocity motion.

Conclusion

The analyzed problems collectively illustrate fundamental physics principles, particularly unit conversions, Newton's laws, centripetal motion, and kinematic equations. Precise calculations of force, acceleration, and motion parameters are essential for designing and understanding vehicles, aircraft, spacecraft, and biological systems. Mastery of these concepts enables engineers and scientists to optimize performance and ensure safety across various applications.

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