Reaction pair 問題

they can stand on ice=題目假設2人平衡力夠強

They push against each other
they experience forces with the same magnitude
∵this is an action-reaction pair of forces



∵ given that mass of Tom> mass of Katie
Let mass of Katie = m, then mass of Tom= km,
where k is a constant greater than one

force experienced by Tom = force experienced by Katie
by F=ma
mass of Tom ╳ acceleration of Tom = mass of Katie ╳ acceleration of Katie
km ╳ acceleration of Tom = m ╳ acceleration of Katie
acceleration of Tom = k-1 ╳ acceleration of Katie
as k>1, acceleration of Tom > acceleration of Katie


唔明請補充問題

(1) Newton's Third Law proposed that all forces must be occured in pairs. That means a force in magnitude must be equal to its pair's. It implies that the force Tom acted on Katie is exactly equal to the force acted on himself, and the two forces are also exactly in opposite directions. As a result, statement (a) is incorrect.

(2) To find out the answer of question b), we have to look the Newton's Second Law. This theory proposed that "Force(Newton-F)=Mass(Kg-m) X Acceleration(meter per second square-a). F=ma

From your question, we know that Tom has a greater mass comparing to Katie.
Then we have: M(Tom)>M(Katie)

Also, from (1), we know that the two experienced the same force in magnitude.
F(Tom)=F(Katie)

T and K stand for Tom's and Katie's respectively.
Assumed that no other force is considered in your case, ie, ice surface is perfectly smooth, then:
F(T)=m(T)xa(T)=F(K)=m(K)xa(K)
=>m(T)xa(T)=m(K)xa(K)
=>m(T)/m(K)=a(K)/a(T)
Since m(T)>m(K)
then m(T)/m(K) must be >1
then a(K)/a(T) must also be >1
we can observe that acceleration of Katie from the force is greater than Tom's.
As a result, we could conclude that statement b) is also wrong.

(3)Last, the ice surface provided us a better and simplier environment in comparing the motions of Tom and Katie from Tom's push. It is because the frictional force of ice surface is small, allowing us to neglete it. The answers of 1&2 may vary with the smoothness of the surface they are on. To find out why they can stand on it, I think standing on an ice surface may not require high capability and talent to do so, which an ordinary person could be able to stand.