Problem 4 - Astronomy Journey to the Cosmic Frontier

Question

Two forces, oppositely directed, act on a body. The force acting toward the right is twice as strong as the force acting toward the left. Describe the motion of the body.

Step-by-Step Solution

Answer

The body will accelerate and move towards the right.

Step 1: Understand the Forces

There are two forces acting on a body. Denote the force acting towards the left as \(F_L\) and the force acting towards the right as \(F_R\). We know that \(F_R = 2F_L\).

Step 2: Determine the Net Force

Since the forces are acting in opposite directions, the net force \(F_{net}\) is calculated by subtracting the smaller force (\(F_L\)) from the larger force (\(F_R\)). Thus, \(F_{net} = F_R - F_L = 2F_L - F_L = F_L\).

Step 3: Analyze the Direction of Motion

The net force \(F_{net} = F_L\) is directed towards the right because it is positive when we consider the rightward force as positive. This means the body will move toward the right.

Step 4: Describe the Motion

Since there is a net force acting on the body towards the right, the body will accelerate in that direction, following Newton's second law of motion. Therefore, the body will move continuously towards the right with increasing velocity, assuming no other resistive forces are acting.

Key Concepts

Net Force

In physics, the net force is crucial in determining how an object moves. Net force is the total force acting on an object when all the individual forces are combined. It represents the 'sum effect' of multiple forces.
In the exercise, we have two opposing forces. If we denote the leftward force as \(F_L\) and the rightward force as \(F_R\), where \(F_R = 2F_L\), this means that the force moving the object to the right is stronger.

• To find the net force, we subtract the leftward force from the rightward force.
• So, the net force \(F_{net} = F_R - F_L = F_L\).

The net force determines not just if the object will move but also in which direction it will move. Here, since the net force is equal to \(F_L\), the body experiences a net force to the right.

Direction of Motion

The direction of motion of an object is influenced by the direction of the net force acting upon it.
The exercise details that the net force is directed towards the right. This is because the force to the right \(F_R\) is twice as strong as the opposing leftward force \(F_L\). When we determine net force to be \(F_L\) to the right, it means the stronger force dictates the direction.

• Positive net force usually indicates motion in the positive force direction.
• In this case, rightward is deemed positive, so the motion goes right as well.

Newton's laws suggest that when a net force acts on an object, it must accelerate in the same direction as the net force. Thus, direction of motion completely aligns with net force direction unless another force interferes, such as friction.

Acceleration

Acceleration is a change in the velocity of an object due to a net force acting on it. According to Newton's second law of motion, acceleration happens in the direction of the applied net force.
In our problem, as the net force is directed toward the right, the object will accelerate in that direction. The relationship between net force and acceleration can be represented as:\[F_{net} = m imes a\]where \(m\) is the mass of the object and \(a\) is the acceleration.

• Since \(F_{net} = F_L\), the object will experience an acceleration forward to the right.
• Assuming no other forces, like friction, are acting, acceleration implies increasing speed.

Thus, the body keeps speeding up in the rightward direction as long as the net force continues to act, perfectly illustrating the principle of Newton's second law.