Ch 07: Newton's Third Law

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 07: Newton's Third Law

Problem 29b

Chapter 7, Problem 29b

An 85 kg cheerleader stands on a scale that reads in kg. What does the scale read if the 85 kg cheerleader lifts the 50 kg cheerleader upward with an acceleration of 2.0 m/s²?

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Identify the forces acting on the 85 kg cheerleader. The scale measures the normal force exerted by the ground on the cheerleader. This force will change if the cheerleader exerts an additional force to lift the 50 kg cheerleader.

Calculate the force required to lift the 50 kg cheerleader with an upward acceleration of 2.0 m/s². Use Newton's second law:

F = m a

, where

m

is the mass of the 50 kg cheerleader and

a

is the acceleration.

Add the gravitational force acting on the 50 kg cheerleader to the force calculated in the previous step. The total force exerted by the 85 kg cheerleader is the sum of the force required to lift the 50 kg cheerleader and the weight of the 50 kg cheerleader:

F = m a + m g

, where

g

is the acceleration due to gravity (9.8 m/s²).

Determine the total force acting on the 85 kg cheerleader. This includes the gravitational force acting on the 85 kg cheerleader and the additional force exerted to lift the 50 kg cheerleader. The total force is:

F = m g + F

_lift, where

F

_lift is the force calculated in the previous step.

The scale reading corresponds to the normal force exerted by the ground on the 85 kg cheerleader. This is equal to the total force acting on the 85 kg cheerleader. Substitute the values into the equation to find the scale reading.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Newton's Second Law of Motion

Newton's Second Law states that the force acting on an object is equal to the mass of that object multiplied by its acceleration (F = ma). This principle is crucial for understanding how forces interact when an object is in motion, particularly when calculating the net force acting on the cheerleaders in this scenario.

Weight and Normal Force

Weight is the force exerted by gravity on an object, calculated as the product of mass and gravitational acceleration (W = mg). The normal force is the support force exerted by a surface, which in this case is the scale. When the cheerleader lifts another cheerleader, the normal force changes based on the net force acting on the system.

Net Force and Acceleration

The net force is the total force acting on an object after all the forces are combined. In this scenario, the net force will determine the acceleration of the 50 kg cheerleader being lifted. By applying Newton's Second Law, we can calculate how the scale reading changes when the cheerleader accelerates the other cheerleader upward.

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