I work in a Drop in math tutoring center at my university and someone came in wi
ID: 1692220 • Letter: I
Question
I work in a Drop in math tutoring center at my university and someone came in with this question. I am currently a senior in Mechanical Engineering so hopefully i am not wrong...."A horizontal rope pulls a 10 kg wood sled across frictionless snow. A 5.0 kg wood box rides on the sled. The coefficient of static friction for wood on wood is µ(s)=0.5.
What is the largest tension force for which the box doesn't slip(in N)?"
So my approach to this problem is as follows:
Since their is no friction with the 10 kg sled and the snow, the tension to start movement with the sled is 0 N.
The force of gravity of the 10 kg sled does not act on the 5 kg wood box. So we are left with the force of gravity of the 5 kg wood box acting on the 10 kg sled. µ*m*g = Tension
0.5*5kg*9.81 m/s^2 = 24.525 N This should be the answer in my mind
but the book showed this: 0.5*(5kg+10kg)*9.81 m/s^2 = 73.575 N
To me this should be the case if their was a friction force from the snow at µ=0.5. Then you would have the total mass of the sled and box acting on the snow. I think the book is incorrect with what the question is asking, so hopefully someone here can clear this up for me. Thanks..
The force of gravity of the 10 kg sled does not act on the 5 kg wood box. So we are left with the force of gravity of the 5 kg wood box acting on the 10 kg sled. µ*m*g = Tension
0.5*5kg*9.81 m/s^2 = 24.525 N This should be the answer in my mind
but the book showed this: 0.5*(5kg+10kg)*9.81 m/s^2 = 73.575 N
To me this should be the case if their was a friction force from the snow at µ=0.5. Then you would have the total mass of the sled and box acting on the snow. I think the book is incorrect with what the question is asking, so hopefully someone here can clear this up for me. Thanks..
Explanation / Answer
you are mistaken at there is no friction between 10 kg sled and snow the tension to start the movement with the sled is 0 N. Here considering horizontal rope according to newton's first law there must be a force to change the state of rest of a body. so here the force is not equal to zero and it must be mg. Whenver you keep the 5kg wooden box on sled you must consider total weight (weight of sled+weight of box) to find the tension in the rope. So the textual answer is the right answer.