Chapter 2: Problem 30

We have studied four different laws authored by Sir Isaac Newton. For each of the following, indicate which law is best for the task described. a) Calculating the net force on a car as it slows down. b) Calculating the force exerted on a satellite by the Earth. c) Showing the mathematical relationship between mass and weight. d) Explaining the direction that a rubber stopper takes after the string that was keeping it moving in a circle overhead is cut. e) Explaining why a gun recoils when it is fired. f) Explaining why a wing on an airplane is lifted upward as it moves through the air.

Short Answer

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Question: Match the scenario with the appropriate Newton's law: a) A car slowing down b) The force on a satellite by the Earth c) The relationship between mass and weight d) The direction of a rubber stopper after the string is cut e) The recoil of a gun when fired f) The lift of an airplane wing as it moves through the air Answer: a) Newton's Second Law (F = ma) b) Newton's Law of Universal Gravitation (F = G * (m1 * m2) / r^2) c) Newton's Second Law (F = ma) with acceleration due to gravity (W = m * g) d) Newton's First Law (Law of Inertia) e) Newton's Third Law (action and reaction forces) f) Newton's Third Law and principle of lift due to pressure difference

Step by step solution

a) Calculating the net force on a car as it slows down.

In this case, we need to use Newton's Second Law of motion (F = ma) because it describes the relationship between force, mass, and acceleration. Slowing down means the car is decelerating, and we can use this law to calculate the net force acting on the car.

b) Calculating the force exerted on a satellite by the Earth.

In this scenario, we need to use Newton's Law of Universal Gravitation (F = G * (m1 * m2) / r^2), as it describes the force exerted by two masses (m1 and m2) on each other, separated by a certain distance (r). In this case, m1 would be the mass of the Earth and m2 would be the mass of the satellite.

c) Showing the mathematical relationship between mass and weight.

To show the relationship between mass and weight, we need to use Newton's Second Law (F = ma) with the acceleration due to gravity, g. Weight (W) is the force acting on an object due to gravity and can be calculated as W = m * g, where m is the mass of the object, and g (approximately 9.81 m/s^2) is the acceleration due to gravity.

d) Explaining the direction that a rubber stopper takes after the string that was keeping it moving in a circle overhead is cut.

In this situation, we need to use Newton's First Law of motion (Law of Inertia). The law states that an object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and direction unless acted upon by an external force. When the string is cut, the rubber stopper will continue moving in a straight line tangent to the circle it was moving in initially, due to its inertia.

e) Explaining why a gun recoils when it is fired.

To explain the recoil of a gun when it is fired, we need to use Newton's Third Law of motion, which states that for every action, there is an equal and opposite reaction. As the gun fires a bullet forward, the gun experiences an equal and opposite force that pushes it backward, which is the recoil.

f) Explaining why a wing on an airplane is lifted upward as it moves through the air.

Understanding why a wing is lifted upward as it moves through the air involves considering Newton's Third Law and the principle of lift due to the pressure difference on the top and bottom surfaces of the wing. As air moves over the top surface of the wing, it accelerates, creating a lower pressure area. Meanwhile, the pressure on the bottom surface is higher, creating a net upward force, which is the lift.

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Short Answer

Step by step solution

a) Calculating the net force on a car as it slows down.

b) Calculating the force exerted on a satellite by the Earth.

c) Showing the mathematical relationship between mass and weight.

d) Explaining the direction that a rubber stopper takes after the string that was keeping it moving in a circle overhead is cut.

e) Explaining why a gun recoils when it is fired.

f) Explaining why a wing on an airplane is lifted upward as it moves through the air.

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