FIGURE EX5.14 shows an object's acceleration-versus-force graph. What is the object's mass?

Question

Graph showing acceleration versus force, illustrating Newton's laws for mass calculation.

Accepted Answer

Hey, everyone in this problem, a computerized scientific probe is used to measure the net force acting on an object and the resulting acceleration, the probe creates the acceleration force graph that's shown and we're asked to determine the object's mass. Now, the graph that were shown has the acceleration in meters per second squared on the Y axis, the force in newtons along the X axis. And we have a linear curve here, it starts at 00 and goes up to a maximum acceleration of three m per second squared. When the force is 150 newtons, we're given four answer choices, option, a 50 kg, option B 100 kg, option C 25 kg and option D five kg. So we need to think about the relationship between the variables we're given and the one we're trying to find. So we have the force and the acceleration given in our graph, we're trying to find the mass. So let's recall Newton's second law which tells us that the force is going to be equal to the mass multiplied by the acceleration F is equal to ma now because we have a linear curve. OK. The relationship between the force and the acceleration is linear. All we need to choose do is choose any point on this curve. OK. So we're gonna choose the final point that were shown in the graph and I'm gonna draw it in blue. So we have a force of 150 newtons, an acceleration of three m per second squared. We're gonna substitute those into our equation. So we have 150 newtons is equal to the mass M multiplied by three m per second squared. And this means that the mass M is gonna be equal to 150 newtons. OK. And we're called that we can write a Newton as a kilogram meter per second squared. And this is divided by that acceleration of three m per second squared. Now writing the Newton as kilogram meter per second squared allows us to see that that unit of meters per second squared is gonna divide it. We're gonna be left with just the unit of kilogram, which is what we want for the mass. Here, we get 150 divided by three, which is equal to 50 kg. And that is gonna be that mass we were looking for. And again, because this relationship is linear, we could have chosen any point along this curve. A we could imagine taking the point when we have the force of 100 newtons and an acceleration of two m per second squared. We'd end up with 100 divided by two, which would again give us that same mass of 50 kg. So the correct answer here is option a 50 kg. Thanks everyone for watching. I hope this video helped see you in the next one.

FIGURE EX5.14 shows an object's acceleration-versus-force graph. What is the object's mass?

Verified Solution

Key Concepts

Newton's Second Law of Motion

Force-Acceleration Graph

Slope of a Line