A mobile phone is at rest on a table top. And the phone’s owner flicks the phone with their fingers, which applies a 0.01-newton force to the phone. The phone is accelerated at a rate of 0.1 meters per second squared in the direction of the flick. What is the mass of the phone?
Alright, let’s start by underlining all of the important bits of the question so we don’t miss any information out. So we’ve got a mobile phone. Initially, it’s at rest on a table top. The phone’s owner then flicks the phone with their fingers, which applies is 0.01-newton force to the phone. The phone, due to this flick, is accelerated at a rate of 0.1 meters per second squared in the direction of the flick. We need to find the mass of the phone.
So, okay, so here we’ve got a diagram of our banana phone. Quick disclaimer: other phone manufacturers are available. And we can see the owner’s hand on the left ready to flick the phone. And there it goes. The owner of the phone has flicked it, probably hurting their finger in the process. But the important thing is that the flick has applied a 0.01-newton force to the phone. We also know that the phone accelerates at 0.1 meters per second squared. And we need to find out the mass of the phone.
So we need to find a relationship between the mass of the phone, the acceleration of the phone, and the force applied to the phone. The relationship we’re looking for is known as Newton’s second law of motion. Newton’s second law states that the force on an object, 𝐹, is equal to the mass of the object, 𝑚, multiplied by its acceleration, 𝑎. And these are exactly the three quantities that we’ve been working with so far.
So in order to find the mass of the phone, we need to rearrange this equation first. We can do this by dividing both sides of the equation by the acceleration. The acceleration cancels on the right-hand side. And so we’re left with 𝐹 divided by 𝑎 is equal to 𝑚. The force divided by the acceleration is equal to the mass. So let’s plug in all the values we’ve been given. But before we do this, let’s quickly discuss the standard units of the quantities in the equation 𝐹 over 𝑎 is equal to 𝑚.
Well we’ve got a force here. That has a standard unit of newtons. The standard unit of acceleration is meters per second squared. And for mass, it’s kilograms. That means that if our value of force is in newtons and the acceleration is in meters per second squared, then the mass that we’ll get out of this equation is gonna be in kilograms. And that is perfectly fine. So let’s get on with doing that.
The mass of the phone, therefore, is equal to the force, 0.01 newtons, divided by the acceleration, 0.1 meters per second squared. Evaluating this, we find that the fraction simplifies to 0.1. And now we’ve gotta remember to put in the units. We’re working out a mass. And we’ve just said earlier that the unit is going to be kilograms. And so our final answer is that the mass of the phone is 0.1 kilograms.