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Chapter 15: Problem 3

An object thrown straight up in the air is momentarily at rest when it reaches the top of its motion. Does that mean that it is in equilibrium at that point? Explain.

Short Answer

Expert verified
No, the object is not in equilibrium because a net force due to gravity still acts on it.

Step by step solution

01

Understanding Equilibrium

Equilibrium occurs when an object is at rest or moving with constant velocity and the net force acting on it is zero. For an object in equilibrium, the sum of all forces should be balanced so that there is no acceleration.
02

Examining Motion at the Top

When the object is thrown up, it continuously slows down until it reaches the top of its trajectory at which it momentarily rests. At the top, the velocity is zero, but this does not mean that the object is in equilibrium.
03

Analyzing Forces at the Top

At the top of its motion, despite the zero velocity, the object is still under the influence of gravity. The gravitational force continues to act on the object, pulling it downward with an acceleration of 9.8 m/s虏.
04

Conclusion on Equilibrium Status

Since there is a net force (gravity) acting on the object at the top of its motion, the object is not in equilibrium. Equilibrium requires the absence of net forces, which is not the case here.

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Key Concepts

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

Understanding Forces
Forces are pushes or pulls that can cause an object to accelerate or decelerate. They are vector quantities, which means they have both magnitude and direction. Forces can act in two ways:
  • Contact forces: These require physical contact between objects, like friction or tension.
  • Non-contact forces: These act at a distance, such as gravity or magnetism.
A key principle regarding forces is Newton's First Law, stating that an object will remain at rest or move at a constant velocity unless acted upon by a net force. This is essentially describing equilibrium. When forces are balanced, there's no change in the motion of the object. However, when unbalanced, forces cause changes in velocity, leading to acceleration.
The Role of Gravity
Gravity is a non-contact force that attracts two bodies towards each other. On Earth, it gives weight to objects and affects their motion. The force of gravity is directly proportional to the mass of the object and is directed downwards towards the center of the Earth.
  • Magnitude: The strength of gravity near Earth's surface is approximately 9.8 m/s虏, meaning for every second, an object's speed increases by 9.8 meters per second if in free fall.
  • Direction: Always directed downwards, which influences objects thrown upwards or dropped.
In our scenario, despite the object being momentarily at rest at its highest point, gravity continuously acts on it. As a result, it ensures the object is not in equilibrium, since a net force, i.e., gravity, is still present.
Exploring Velocity
Velocity is a vector quantity that refers to the speed of an object in a specific direction. It is distinct from speed, which is a scalar and only measures how fast something is moving regardless of direction.
  • Instantaneous velocity: The velocity of an object at a specific moment.
  • Average velocity: Defined as the total displacement divided by the total time taken.
When an object reaches the peak of its trajectory, like a ball thrown upwards, its instantaneous velocity is zero. However, this is a brief moment, and immediately afterwards, due to the force of gravity, the object's velocity starts increasing downwards, causing it to descend.
Understanding Acceleration
Acceleration is the rate of change of velocity over time. When an object speeds up, slows down, or changes direction, it is accelerating. Acceleration can be caused by forces and is calculated as the change in velocity per unit of time.
  • Positive acceleration: When the speed of an object increases.
  • Negative acceleration (deceleration): When the speed decreases.
In our scenario, while the velocity at the top of the trajectory is zero, acceleration due to gravity is still present at 9.8 m/s虏. This acceleration is always directed downwards, meaning the object is continually accelerating even when its velocity is momentarily zero, preventing equilibrium.

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