TBR C1 Easy question about mass and acceleration but I'm confused!!!

[DeMoNdOgDFM]

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In TBR Physics Chapter 1 Question 17, the answer states that mass of the cart and acceleration is not related. However, don't we get an inverse relationship between mass and acceleration from F=ma? That's what I thought at least...I understand the whole "if you throw a bowling ball and a feather from the top of a cliff they will strike the ground at the same time" thing but i'm confused after reading this question why mass and acceleration aren't related when F=ma shows an inverse relationship...
Help?

EDIT: After relooking at the question, is this the reason why? F=ma but because all the carts of different masses have the same initial velocity, the only way that could happen would be to push the bigger carts with more force in order for them to all have the same initial velocity, which in this case, would allow the acceleration to be constant throughout all the carts???

 

[BerkReviewTeach]

In TBR Physics Chapter 1 Question 17, the answer states that mass of the cart and acceleration is not related. However, don't we get an inverse relationship between mass and acceleration from F=ma? That's what I thought at least...I understand the whole "if you throw a bowling ball and a feather from the top of a cliff they will strike the ground at the same time" thing but i'm confused after reading this question why mass and acceleration aren't related when F=ma shows an inverse relationship...
Help?

F_net = ma is correct, but what you need to consider is that there is an m in the F_net term.

Ignoring friction, we get:

F_net = ma . . where . . ma = mgsin(theta)​

The result is that m cancels from both sides of the equation.

ma = mgsin(theta)​

So:

a = gsin(theta)​

Conceptually this means that a heavier cart experiences a stronger gravitational force pulling it down than a lighter cart, but the perentage increase of that force is equal to the percentage increase in the mass, so there is no net change in the acceleration.

 

[DeMoNdOgDFM]

Thanks for the help. I understand your reasoning, but want to make sure this is what you mean:

Are you treating the track like an incline plane? Which would have the cart on an angle and the force pushing the cart up the track is equal to mgsin(theta)? I want to make sure that's where you are getting that term from.

Thanks again.

 

[BerkReviewTeach]

Thanks for the help. I understand your reasoning, but want to make sure this is what you mean:

Are you treating the track like an incline plane? Which would have the cart on an angle and the force pushing the cart up the track is equal to mgsin(theta)? I want to make sure that's where you are getting that term from.

Thanks again.

Consider the cart on the inclined track at any point in time. All carts in Experiment 3 are pushed up the track with the same initial speed, but once they are released from that pushing force, the only forces acting on the cart are the Normal force (from the track) and gravity. The normal force is equal to mgcos(theta), which cancels out that portion of the gravitational force. The result is that the net force acting on the cart during the entire path (up the track until it comes to rest and then down the track) is mgsin(theta). So at any point when the carts are free of the pushing force, the net force they feel is mgsin(theta).

 

[chem4ever]

In TBR Physics Chapter 1 Question 17, the answer states that mass of the cart and acceleration is not related. However, don't we get an inverse relationship between mass and acceleration from F=ma? That's what I thought at least...I understand the whole "if you throw a bowling ball and a feather from the top of a cliff they will strike the ground at the same time" thing but i'm confused after reading this question why mass and acceleration aren't related when F=ma shows an inverse relationship...
Help?

EDIT: After relooking at the question, is this the reason why? F=ma but because all the carts of different masses have the same initial velocity, the only way that could happen would be to push the bigger carts with more force in order for them to all have the same initial velocity, which in this case, would allow the acceleration to be constant throughout all the carts???

BerkReviewTeach said it perfectly but I just want to say in slightly different words for you.

Conceptually: You are right that if you apply the SAME force to two objects, then the acceleration would be inversely related. Which is why if you push two carts with the same force, the heavier one will not accelerate as much as the lighter one.

However, when dealing with gravity, the force due to gravity comes from the masses of the objects. The larger the mass, the more force it feels from gravity. So a heavier object will have a greater force than a lighter object. This greater force will allow the heavier object to have the same acceleration as the lighter object.

Mathematically: F(gravitation) = Gm1m(earth)/r^2 = m1a
m1 cancels and you get Gm(earth)/r^2 = a