This problem can be solved by applying Newton's Second Law of Motion, which states that the force acting on an object is equal to the product of its mass and acceleration (\(F = ma\)). We are given the force and the mass, and we need to find the acceleration.
Correct Option: B) 5 m/s²
To find the average force exerted on the target, we need to use Newton's second law of motion, which relates force to the rate of change of momentum. First, we'll calculate the change in momentum of the bullet, and then divide it by the time taken to bring it to rest.
Since the standard unit for mass in physics calculations is kilograms, convert grams to kilograms.
\[ m = 20 \text{ g} = 20 \times 10^{-3} \text{ kg} = 0.02 \text{ kg} \]The change in momentum (\(\Delta p\)) is given by the final momentum minus the initial momentum.
\[ \Delta p = m \cdot v - m \cdot u \]\[ \Delta p = (0.02 \text{ kg}) \cdot (0 \text{ m/s}) - (0.02 \text{ kg}) \cdot (500 \text{ m/s}) \]\[ \Delta p = 0 - 10 \text{ kg} \cdot \text{m/s} \]\[ \Delta p = -10 \text{ kg} \cdot \text{m/s} \]According to Newton's second law, the average force (\(F_{\text{avg}}\)) is the rate of change of momentum.
\[ F_{\text{avg}} = \frac{\Delta p}{\Delta t} \]\[ F_{\text{avg}} = \frac{-10 \text{ kg} \cdot \text{m/s}}{0.01 \text{ s}} \]\[ F_{\text{avg}} = -1000 \text{ N} \]The negative sign indicates that the force is in the opposite direction to the initial motion of the bullet, which is expected as it's a retarding force. The magnitude of the force is \(1000 \text{ N}\).D) The calculated average force is \(1000 \text{ N}\).
Newton's Second Law of Motion establishes a fundamental relationship between force, mass, and acceleration. Understanding this relationship helps identify what quantity the law primarily measures.
B) Force
Newton's Second Law of Motion, \(F = ma\), directly relates the net force acting on an object to its mass and the acceleration it experiences. It provides a precise way to quantify or measure the force.
To solve this problem, we need to understand the relationship between kinetic energy, momentum, mass, and velocity. We will use the standard formulas for kinetic energy and momentum and then see how kinetic energy changes when momentum is doubled.
Correct Option: A) Four times
This question asks for the change in momentum when a force acts on a body for a certain time. This concept is directly related to Newton's Second Law of Motion and the definition of impulse.
B) Ft is the correct answer. The change in momentum is equal to the impulse, which is the product of the force applied and the time for which it acts.
The question asks about the fundamental principle behind a rocket's operation. We need to recall the basic physics laws governing motion and interactions, particularly those involving propulsion through expulsion of mass.
B) Conservation of momentum. A rocket works on the principle of conservation of momentum. The rocket expels exhaust gases at high velocity in one direction, and in doing so, experiences a thrust (force) in the opposite direction. The momentum gained by the exhaust gases is equal in magnitude and opposite in direction to the momentum gained by the rocket, thus conserving the total momentum of the system (rocket + exhaust gases).