There are some questions preceding the following situation. I will also try to a
ID: 2027073 • Letter: T
Question
There are some questions preceding the following situation. I will also try to answer some of the questions with what I feel could be right. Please help?A student pushes two boxes, one in front of the other. Box A has mass 75 kg, while box B has mass 25 kg. Fortunately for the student, the boxes are mounted on tiny rollers and slide with negligible friction. The student exerts a 200 N horizontal force on box A.
1. Without doing any calculations, state whether the acceleration of block A is greater than, less than, or equal to that of block B. How do you know? - I think that the acceleration of block A is less than that of Block B since Block A weighs more.
2. Using any method you want, find the acceleration of the blocks. (Hint: It’s possible to do this quickly.) - Do I do this simply using F=ma ? 200N=75kg*a?
Box B contains kitchen stuff, including some poorly packed glassware that might break if the force pushing on the side of the box approaches 200 newtons.
Recall that the student pushes on box A with a force of 200 newtons. Is that force “transmitted” to box B? In other words, is the glassware in the box in danger of breaking? Don’t do any calculations; answer intuitively, and explain your thinking.
- I think that the force is transmitted to cause box B to move, but because it is indirect, the glassware doesn't break. I'm very unsure though.
D. Find a way to calculate FA on B exactly, and do it. (Hint: Way back in part A, you found the acceleration of both blocks.) - Not sure
E. Which approach to multi-body problems would you use: (i) Lumping the boxes together and thinking of them as a single big mass, or (ii) Thinking separately about box A and box B? Or would you use some of each approach?
G. Try to come up with an intuitive way of understanding why FA on B is less than 200 newtons, not equal to 200 newtons – a way that makes sense to you personally. -This is what I thought, but how would I explain this?
Explanation / Answer
1. they have the same acceleration. This may sound funny, because in real life, the heavy box would slow down faster due to friction, as the lighter box keeps moving at a fast pace, but ideally, without friction, they will act as one COMBINED unit and moving together with one acceleration. If this bothers you, understand that the 200 N push isn't pushing the smaller block B. The only thing pushing that block is the force of block A touching it. Therefore, there is no reason to assume block b will will go flying off really fast.
2. Yes, use F=ma, but use the combined mass to treat them as one combined unit.
200 N = ( 75 kg + 25 kg )a, therefore a = 2 m/s2 FOR BOTH!
C) Box b will NOT break. Remember, box b has less mass, therefore it needs LESS force to get moving. The 200 N was only touching box A, and it was heavier. Box b will be pushed with LESS force in order to have the SAME acceleration as box A.
D) Ok, well, the ONLY force acting on block B is the wall of block A touching it. AND we know the acceleration of each block, so we use F=ma on just the small block alone
F = ( 25 kg )( 2 m/s2 ) therefore F = 50 N
By the way, to prove that this mathematically works, check this out:
On box A, there are 2 forces, the 200 N, and the equal and opposite force that was used to push box b. We already know box b is pushed forward 50N, so there is an equal and opposite force pushing BACK on box A with 50 N. So, F = ma, and F is the SUM of all forces,
200 N - 50 N is the total force = 150 N.
150 N = ( 75 kg ).
Solve for acceleration, and guess what you get? It proves that all of our math obeys all 3 of newtons laws.
E) As you can see, I did both. I FIRST lumped them together to get the acceleration of all objects, then I treat each individually to find individual pieces.
G) I kinda already answered this in c) and d)