you and a child are on skates and you give each other a push. if the mass of the child is half your mass, who has the greater acceleration? by what factor?
i know it is the child but im not sure about the factor. im pretty sure the answer has something to do with F=ma (Force=mass*acceleration)
You are correct that the answer to this question involves the concept of force, mass, and acceleration. To determine who has the greater acceleration, we can apply Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. Mathematically, this law can be expressed as F = ma, where F is the net force, m is the mass of the object, and a is the acceleration.
In this scenario, let's assume that you both start with the same initial velocity and are pushed by the same force. Given that the mass of the child is half of your mass, we can represent your mass as M, and the child's mass as 0.5M.
Now, let's consider the forces acting on each of you. According to Newton's third law, if you push the child with a certain force, the child pushes back on you with an equal but opposite force. Since the child's mass is half of your mass, their force will have the same magnitude but opposite direction. So, the net force acting on you will be zero, as the forces cancel each other out.
However, the child experiences a net force but with the same magnitude. Therefore, applying Newton's second law, we can write equations for both of you:
For you: F = M * 0 (net force) -> a = 0 (acceleration)
For the child: F = 0.5M * a -> a = F / 0.5M = 2F / M
Comparing the two accelerations, we can see that the child's acceleration is greater by a factor of 2. So, the child has twice the acceleration as you do.