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)
MA=ma
so the bigger acceleration goes to the smaller child, by a factor of 2.
a= M/m * A
You are correct that the answer can be found using the equation F = ma (Force = mass * acceleration). In this scenario, the force applied to both you and the child is the same because you are giving each other a push. The mass of the child is half of your mass, which means the acceleration of the child will be greater than yours.
To understand why the child will have greater acceleration, let's consider the equation F = ma. We have the same force acting on both you and the child, but since the mass of the child is half of yours, the child will experience twice as much acceleration. This can be mathematically represented as:
F (force) = m(child) * a(child)
F = (0.5m) * a(child)
Since the force is the same, we can set the two equations equal to each other:
F = m * a
0.5m * a(child) = m * a
Now, we can cancel out the mass (m) on both sides:
0.5 * a(child) = a
Since 0.5 is less than 1, we can conclude that a(child) is greater than a. This means that the child will have a greater acceleration than you. The factor by which the child's acceleration is greater can be calculated using the ratio of their accelerations:
Factor = a(child) / a
Factor = a / a
Factor = 1
The factor is 1, which means that the child's acceleration is exactly double your acceleration.