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Chapter 3: Problem 37

Imagine you throw a ball straight up in the air. At the top of its flight, it stops and then falls again. What is the acceleration of the ball at the top of its flight?

Short Answer

Expert verified
The acceleration of the ball at the top of its flight is \( 9.8 \ \text{m/s}^2 \) downwards.

Step by step solution

01

- Understand the scenario

Visualize the situation where the ball is thrown straight up. It rises, slows down, momentarily stops at the peak, and then starts to fall back down.
02

- Identify forces acting on the ball

Throughout the ball's flight, including at the top, the only significant force acting on it is gravity. Other forces like air resistance are negligible for this problem.
03

- Define acceleration due to gravity

The acceleration caused by gravity is constant and is denoted as \( g = 9.8 \ \text{m/s}^2 \) towards the Earth's surface.
04

- Apply concept at the top of the flight

At the peak of its flight, even though the ball's velocity is zero, gravity still acts on it. Thus, the acceleration is still \( 9.8 \ \text{m/s}^2 \) downwards.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Gravitational Force
Gravitational force is the force of attraction between two masses. On Earth, this force gives us what we call 'weight.' It's always directed towards the center of the Earth. The force due to gravity is represented by the equation: \[ F = m \times g \] where \( F \) is the gravitational force, \( m \) is the mass of the object, and \( g \) is the acceleration due to gravity, which is approximately \( 9.8 \, \text{m/s}^2 \) on Earth's surface. This force is crucial in our everyday life and governs how objects move under its influence. For example, in our exercise, when the ball is thrown up, gravity works against its upward motion, eventually stopping it and pulling it back down.
Vertical Motion
Vertical motion refers to the motion of objects that are moving straight up or down. When an object is thrown vertically upwards, it will rise to a certain height, stop for a moment, and then fall back down. Let's break this down:
  • As the object rises, its speed decreases due to the downward pull of gravity.
  • At the highest point (or peak), the object stops momentarily; its velocity is zero for an instant.
  • After reaching the peak, it starts to fall back down, accelerating due to gravity.
At every point in this motion, including at the peak, the acceleration due to gravity is constant at \( 9.8 \, \text{m/s}^2 \) downwards. This means that even though the object's velocity is zero at the top, it's still under gravitational influence.
Physics Principles
Understanding the basic principles of physics can help us make sense of the world around us. Some fundamental principles that are useful in understanding vertical motion and gravitational force include:
  • Newton's First Law of Motion: An object will remain at rest or in uniform motion unless acted upon by an external force. In our case, the ball starts to fall back down due to the gravitational force.
  • Newton's Second Law of Motion: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. \[ a = \frac{F}{m} \]
  • Newton's Third Law of Motion: For every action, there is an equal and opposite reaction. When the ball is thrown up, the force exerted on it by your hand is countered by the gravitational force pulling it down.
These principles are interconnected and help us understand why and how objects move. By applying these principles, we can predict the behavior of the ball throughout its flight, from being thrown upward to falling back to the ground.

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Most popular questions from this chapter

When involved in an automobile collision, a person not wearing a seat belt will move through the car and often strike the windshield directly. Which of Newton's laws explains why the person continues forward, even though the car stopped?

Suppose you watch a car sliding on ice down a hill. As it slides, it slowly drifts to your right across the road, speeding up in that direction until it bumps into the curb. In this situation, which of the following is more likely, and why? a. The car was already traveling diagonally across the street before it hit the patch of ice. b. The road surface is rounded (or "crowned"), causing the car to be pushed across the street.

Planets with high eccentricity may be unlikely candidates for life because a. the speed varies too much. b. the period varies too much. c. the temperature varies too much. d. the orbit varies too much.

A_______model of the Solar System puts Earth at the model of the Solar System puts Earth at the center, while a ______ model of the Solar System puts the Sun at the center. a. geocentric; heliocentric b. heliocentric; geocentric c. heliocentric; Copernican d. geocentric; Ptolemaic

Galileo observed that Jupiter has moons. From this information, you may conclude that a. Jupiter is the center of the Solar System. b. Jupiter orbits the Sun. c. Jupiter orbits Earth. d. some things do not orbit Earth.
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