A constant force is applied to an object, causing the object to accelerate at 10 m/s². What will the acceleration be if

d. The force is halved and the object's mass is doubled?

Question

A constant force is applied to an object, causing the object to accelerate at 10 m/s². What will the acceleration be if

d. The force is halved and the object's mass is doubled?

Accepted Answer

Hey, everyone in this problem, a uniform net force accelerates a car at 8.2 m per second squared. We're asked to calculate the resulting acceleration If the uniform net force is reduced to 3/5 of the initial value and is now applied to a truck with 1.5 times the car's mass. The answer choices were given are a 4. m/s squared B 12.1 m per second squared, C 20.5 m per second squared N D 3.28 m per second squared. Now we're given information about force and acceleration as well as mass. So let's recall Newton's second law that relates to all three of these values. And Newton's second law tells us that the sum of the forces is equal to the mass multiplied by the acceleration. So starting with this initial situation where we have a net force that accelerates a car at 8.2 m/s. So we're gonna have F net that net force, this is going to be equal to the mass. And in this case, it's the mass of the car multiplied by The acceleration which is 8.2 m/s squared. Alright, so this is the initial situation. Now, what we're asked to do is calculate the resulting acceleration If the net force is reduced to 3/5 of its value. And we're also giving information about the mass. So let's start F R we're gonna call this the resulting force and this is going to be equal to the mass of the truck because it goes from being a car to being a truck times the acceleration. And we're going to call this A R, the resulting acceleration. Now, we don't know any of these values fr M truck are, but we do know a relationship between them and this original net force. So This resulting force is 3/ of the net force. Okay. So what that tells us is we can replace F R with 3/5 multiplied by F net. And we're also told that the mass of the truck is 1.5 times the mass of the car. So we can replace m truck with 1.5 multiplied by M. Car and that's still multiplied by A R, the resulting acceleration and A R, this resulting acceleration is what we're looking for. Now, we have this F net in here. We know what F net is equal to, okay. We have it equal to the mass of the car times 8.2. So let's replace that. We get 3/5 times the mass of the car Multiplied by 8.2 m/s squared. And this is equal to 1.5, multiplied by the mass of the car multiplied by A are the acceleration that we're looking for. Now, this M car, the mass of the car, we don't know that we're not given that value. However, you'll notice now that it's in the term on the left and the term on the right. So we can divide the whole equation by that mass and those are going to cancel it. Now, what you'll notice is that we have this A R value and everything else is numbers. So we can actually calculate A R. So even though we were only given information about the acceleration in the relationship between the forces and the masses were able to get this value that we were looking for. And so the acceleration A R that we're looking for is going to be equal to 3/5 multiplied by 8.2 m per second squared, divided by 1.5. And this gives us a value of 3.2, 8 meters per second squared. That is that acceleration that we were looking for the resulting acceleration when the net force and mass are changed, we go back up to our answer choices and compare what we get. And we see that we found answer choice D is the correct choice. 3.28 m per second squared. Thanks everyone for watching. I hope this video helped see you in the next one.

A constant force is applied to an object, causing the object to accelerate at 10 m/s². What will the acceleration be if d. The force is halved and the object's mass is doubled?

Verified Solution

Key Concepts

Newton's Second Law of Motion

Force and Mass Relationship

Acceleration Calculation