91Ó°ÊÓ

Impulse is a crucial concept in physics that refers to the product of force and the time over which the force acts on an object. It is given by the formula \[ J = F \times t \]where

• \(J\) is the impulse,
• \(F\) is the applied force,
• \(t\) is the time duration for which the force is applied.

Impulse is directly related to the change in momentum of an object. When the child throws a rock, she applies a force for a short duration, transferring momentum to the rock. This action allows the wagon to move in the opposite direction to counteract a force such as friction. The impulse imparted per rock causes the wagon to gain speed momentarily. To sustain motion against a constant frictional force, the child needs to continue throwing rocks at a steady rate.

Friction is a resistive force that opposes the relative motion or tendency to such motion of two surfaces in contact. In the exercise, the child in the wagon must overcome a frictional force of 3.4 N. Friction works to slow down or stop the motion altogether if not compensated for. It is calculated using the equation:\[ F_f = \mu \times N \]where

• \( F_f \) is the frictional force,
• \( \mu \) is the coefficient of friction,
• \( N \) is the normal force, the force perpendicular to the surfaces in contact.

In this scenario, the normal force is the weight of the wagon and the child's combined mass. Since the wagon is trying to move against this friction, the child needs to continuously throw rocks to compensate. By exerting an impulse through each thrown rock, the child negates the slowing effect of friction, maintaining a constant speed of the wagon.

Momentum is a measure of an object's motion and is defined as the product of its mass and velocity. It is a vector quantity, which means it has both a magnitude and a direction. The formula to calculate momentum is:\[ p = m \times v \]where

• \( p \) is momentum,
• \( m \) is mass,
• \( v \) is velocity.

In this exercise, each rock has a momentum when it is thrown given its mass \(0.65 \, \text{kg}\) and velocity \(11 \, \text{m/s}\). This momentum is significant because once a rock is released, the child and wagon system gain momentum in the opposite direction due to the conservation of momentum. This principle ensures that the total momentum of the system remains constant if no external forces are acting. However, due to the presence of friction, maintaining this balance requires the child to keep throwing rocks to keep moving ahead.

Newton's Laws of Motion form the foundational bedrock in understanding the concepts in this exercise. Primarily, Newton's Third Law, which states: "For every action, there is an equal and opposite reaction." This law is observed in the rock-throwing example, where the act of throwing a rock causes the wagon to move in the opposite direction.Newton's First Law, the law of inertia, implies that an object will remain at rest or move in a straight line at constant speed unless acted upon by a net external force, like friction. Here, the child must throw rocks continuously to overcome this external force and keep the wagon moving.Finally, Newton's Second Law explains the relationship between force, mass, and acceleration (\[ F = m \cdot a \]). When the rock is thrown and momentum changes, this law helps understand how the force applied (throwing the rock) causes acceleration in the opposite direction. Together, these laws offer a comprehensive picture of how motion and forces interact in this scenario.