World-class sprinters can accelerate out of the starting blocks with an acceleration that is nearly horizontal and has magnitude 1515 m/s2. How much horizontal force must a 55 55-kg sprinter exert on the starting blocks to produce this acceleration? Which body exerts the force that propels the sprinter: the blocks or the sprinter herself?

Ch 04: Newton's Laws of Motion

Young & Freedman Calc - University Physics 14th Edition

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Young & Freedman Calc 14th Edition

Ch 04: Newton's Laws of Motion

Problem 21

Chapter 4, Problem 21

World-class sprinters can accelerate out of the starting blocks with an acceleration that is nearly horizontal and has magnitude $15$ m/s². How much horizontal force must a $55$ -kg sprinter exert on the starting blocks to produce this acceleration? Which body exerts the force that propels the sprinter: the blocks or the sprinter herself?

Verified step by step guidance

Step 1: Begin by identifying the relationship between force, mass, and acceleration using Newton's Second Law of Motion, which is expressed as

F = m a

. Here,

F

is the force,

m

is the mass, and

a

is the acceleration.

Step 2: Substitute the given values into the formula. The mass of the sprinter is

55

kg, and the acceleration is

15

m/s². The equation becomes

F = 55 \times 15

Step 3: Perform the multiplication to calculate the force. This will give the horizontal force exerted by the sprinter on the starting blocks.

Step 4: Address the second part of the question: The force that propels the sprinter forward is exerted by the starting blocks. According to Newton's Third Law of Motion, for every action, there is an equal and opposite reaction. The sprinter pushes against the blocks, and the blocks push back with an equal and opposite force, propelling the sprinter forward.

Step 5: Conclude by emphasizing the importance of understanding Newton's laws in analyzing motion and forces. The sprinter's ability to accelerate depends on the reaction force provided by the blocks, which is a direct consequence of the sprinter's action force.

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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 the sprinter's mass and the desired acceleration relate to the force she must exert on the starting blocks.

Friction and Force Interaction

Friction is the force that opposes the relative motion of two surfaces in contact. In this scenario, the sprinter exerts a force against the blocks, and the friction between her shoes and the blocks allows her to accelerate. The interaction between these forces determines how effectively she can push off the blocks.

Action and Reaction Forces

According to Newton's Third Law, for every action, there is an equal and opposite reaction. When the sprinter pushes against the starting blocks, she exerts a force on them, and in response, the blocks exert an equal force back on her. This reaction force is what propels her forward.

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Textbook Question

At the surface of Jupiter's moon Io, the acceleration due to gravity is $g equals 1.81$ m/s². A watermelon weighs $44.0$ N at the surface of the earth. What is the watermelon's mass on the earth's surface?

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Textbook Question

A ball is hanging from a long string that is tied to the ceiling of a train car traveling eastward on horizontal tracks. An observer inside the train car sees the ball hang motionless. Draw a clearly labeled free-body diagram for the ball if the train is speeding up uniformly. Is the net force on the ball zero in either case? Explain.

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Textbook Question

At the surface of Jupiter's moon Io, the acceleration due to gravity is $g = 1.81$ m/s². A watermelon weighs $44.0$ N at the surface of the earth. What would be its mass and weight on the surface of Io?

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Textbook Question

Crates $A$ and $B$ sit at rest side by side on a frictionless horizontal surface. They have masses $m_{A}$ and $m_{B}$ , respectively. When a horizontal force $F$ is applied to crate $A$ , the two crates move off to the right. Draw clearly labeled free-body diagrams for crate $A$ and for crate $B$ . Indicate which pairs of forces, if any, are third-law action–reaction pairs.

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