HELP WITH AP PHYSICS- 5 min drill Multiple choice easy?

[girlphysics]

EXACTLY the same way you solved for t1, with the difference that the distance traveled is the full height h, now, instead of h/2. Think about it: it's an exactly equivalent situation in both cases. You have a ball that starts at rest from some height, and then it gets dropped, and you want to know how long it will take to fall a certain distance.



We think that the problem is asking for t2/t1 rather than t1/t2 (which is what you wrote), simply because the former makes more sense given the answer choices (which are all less than 1).

thank you! Now can you help me with number 2? I am not sure how to start it.

 

[cepheid]

thank you! Now can you help me with number 2? I am not sure how to start it.

To know how far the block will go, you need to know its acceleration. Then you can just use the kinematics equations like before.

To find the acceleration, you can use Newton's Second Law, which says that

a = F/m

where a is the acceleration of the body, F is the NET force acting on it, and m is the mass of the body.

The NET force is the sum of all forces acting on the body. You can do this summing separately for the horizontal and vertical directions (i.e. you can apply Newton's 2nd law separately for each direction).

The key to finding the net force is to draw a free body diagram. It's called that because it includes only the object in question and the forces acting on it (nothing from the surroundings). A free body diagram for the block is therefore an inventory of all the forces that are acting on it.

Newton's 2nd law for the y (vertical) direction will give you the normal force. Hint: what is the acceleration in the vertical direction?

Once you know the normal force, you know the frictional force. And since the friction force is the only force that acts in the horizontal direction, that completes the force inventory for that direction. So now you know the net horizontal force and hence the horizontal acceleration.

 

[girlphysics]

To know how far the block will go, you need to know its acceleration. Then you can just use the kinematics equations like before.

To find the acceleration, you can use Newton's Second Law, which says that

a = F/m

where a is the acceleration of the body, F is the NET force acting on it, and m is the mass of the body.

The NET force is the sum of all forces acting on the body. You can do this summing separately for the horizontal and vertical directions (i.e. you can apply Newton's 2nd law separately for each direction).

The key to finding the net force is to draw a free body diagram. It's called that because it includes only the object in question and the forces acting on it (nothing from the surroundings). A free body diagram for the block is therefore an inventory of all the forces that are acting on it.

Newton's 2nd law for the y (vertical) direction will give you the normal force. Hint: what is the acceleration in the vertical direction?

Once you know the normal force, you know the frictional force. And since the friction force is the only force that acts in the horizontal direction, that completes the force inventory for that direction. So now you know the net horizontal force and hence the horizontal acceleration.

ahh thank you! My last query is about the ball dropping from 2m and bouncing to about the same height. The force of the floor on the ball should just be mg right? I think I have to find the impulse, the change in momentum or whatever, but I think I need the chage in velocity. I am not sure what to do.

 

[cepheid]

ahh thank you! My last query is about the ball dropping from 2m and bouncing to about the same height. The force of the floor on the ball should just be mg right? I think I have to find the impulse, the change in momentum or whatever, but I think I need the chage in velocity. I am not sure what to do.

The impulse-momentum theorem says that:

impulse = change in momentum

The impulse is equal to the average force on the object multiplied by the time interval over which the force acts. So:

FΔt = Δp = mΔv

where p is momentum, and assuming the mass doesn't change, the change in momentum is just equal to the mass times the change in velocity.

So you're right. In order to solve for F, you DO need to know the change in velocity Δv. To get that, you need to use another physics principle (a very important one) which is the conversation of energy. Think about it: the ball starts out a height h with gravitational potential energy mgh. The ball falls to height h = 0, which means its potential energy goes to 0. The conservation of energy says that all of that initial potential energy is converted into kinetic energy. That means you know the kinetic energy at the moment of impact, which means you know the speed at the moment of impact.

On the way back up, the reverse is true. Whatever initial kinetic energy the ball has just after the impact is entirely converted back into gravitational potential energy as the ball reaches its maximum height. Now, the fact that the ball reaches almost the same height as before tells you that the ball has almost the same amount of kinetic energy after the impact as it did just before the impact. In other words, the collision is almost perfectly elastic (no kinetic energy is lost). If you assume a perfectly elastic collision, then the kinetic energy before is the same as the kinetic energy after. This means that the speed "v" before is the same as the speed "v" after.

Now, remember that momentum is a vector. So it's not enough to consider speed. We have to consider velocity. Before the collision, the velocity was -v (downward). After the collision, it had changed to +v (upward). They have the same magnitude (speed) but opposite directions. Therefore Δv = v_after - v_before = v - (-v) = 2v.

You need to use the conservation of energy to compute what "v" actually is. I can't help you any further today because I have to go to sleep.

EDIT: By the way, looking at #3, I'm pretty sure you DO need calculus to solve it.

 

[girlphysics]

The impulse-momentum theorem says that:

impulse = change in momentum

The impulse is equal to the average force on the object multiplied by the time interval over which the force acts. So:

FΔt = Δp = mΔv

where p is momentum, and assuming the mass doesn't change, the change in momentum is just equal to the mass times the change in velocity.

So you're right. In order to solve for F, you DO need to know the change in velocity Δv. To get that, you need to use another physics principle (a very important one) which is the conversation of energy. Think about it: the ball starts out a height h with gravitational potential energy mgh. The ball falls to height h = 0, which means its potential energy goes to 0. The conservation of energy says that all of that initial potential energy is converted into kinetic energy. That means you know the kinetic energy at the moment of impact, which means you know the speed at the moment of impact.

On the way back up, the reverse is true. Whatever initial kinetic energy the ball has just after the impact is entirely converted back into gravitational potential energy as the ball reaches its maximum height. Now, the fact that the ball reaches almost the same height as before tells you that the ball has almost the same amount of kinetic energy after the impact as it did just before the impact. In other words, the collision is almost perfectly elastic (no kinetic energy is lost). If you assume a perfectly elastic collision, then the kinetic energy before is the same as the kinetic energy after. This means that the speed "v" before is the same as the speed "v" after.

Now, remember that momentum is a vector. So it's not enough to consider speed. We have to consider velocity. Before the collision, the velocity was -v (downward). After the collision, it had changed to +v (upward). They have the same magnitude (speed) but opposite directions. Therefore Δv = v_after - v_before = v - (-v) = 2v.

You need to use the conservation of energy to compute what "v" actually is. I can't help you any further today because I have to go to sleep.

EDIT: By the way, looking at #3, I'm pretty sure you DO need calculus to solve it.

Thank you for your help. I handed this in yesterday, Are you allowed to tell me what you would have chosen as the correct answers? I am still trying to fully understand these questions, and I ended up guessing. 2.A 3.B 4.D 5.E