91Ó°ÊÓ

In physics, the net force is the sum of all the forces acting on an object. In our exercise, the net force includes both horizontal and vertical components. To find the net force acting on the passenger, we use the Pythagorean theorem. Given two perpendicular forces, the formula for the net force (\text{Net Force}) is: \ \text{Net Force} = \ \ \text{Net Force} = \ \sqrt(F_h^2 + F_v^2) \ where:\ \(F_h = 210\ N\) (horizontal force) \ \(F_v = 500\ N\) (vertical force). \ Substituting the values, we get: \ \ \text{Net Force} = \ \sqrt((210)^2 + (500)^2) = \ \sqrt(44100 + 250000) = \ \sqrt(294100) \ \ Net Force \approx 542.36\ N. \ By calculating this, we find that the net force acting on the passenger is approximately 542.36 N. This value helps in understanding the total influence on the passenger due to various forces in motion.

Centripetal force is a crucial concept when dealing with circular motion. It is the force that keeps an object moving in a circular path, directed towards the center of rotation. In our exercise, the horizontal component of the force (\text{F_h = 210 N}) provides the necessary centripetal force (\text{F_c}). \ To recall, the formula for centripetal force is: \ \ F_c = m \ \frac(v^2)(r) \ where: \ \(m\) = 51.0 kg (mass of the passenger), and \ \(r\) = 470 m (radius of the circle). \ Substituting the values into the formula, we get: \ \ \ 210 = \frac(51.0 \ \times v^2)(470). \ Solving this equation provides further insight on circular motion parameters, mainly the speed of the car which is derived thereafter. Understanding centripetal force helps us connect the force with the motion and velocity of the car.

Newton's second law states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. It can be expressed as: \ \ F = ma \ where: \ \(F\) = net force (N) \ \(m\) = mass (kg) \ \(a\) = acceleration (m/s^2). \ For circular motion, the centripetal acceleration is given by the equation: \ \ a = \ \frac(v^2)(r). \ Applying this in our context, we can further isolate the speed (\text{v}) of the railway car. Replacing the needed variables into the centripetal force equation, \ F_c = m \ \frac(v^2)(r) \ allows us to solve for speed (\text{v}). Rearranging terms, we get: \ \ v^2 = \ \frac(210 \ \times 470)(51.0) \ \ Solving, we find: \ v^2 = 1935.29 \ v \ \approx 43.99\ m/s. \ Thus, Newton's second law provides a comprehensive framework to understand forces, acceleration, and their impact on motion. This law is essential for analyzing and solving many physics problems related to motion.