Determine the distance each object will move

[patrilu5]

Homework Statement

Two objects with masses of 4.00 kg and 6.00 kg are connected by a light string that passes over a frictionless pulley.
(a) Determine the tension in the string.
(b) Determine the acceleration of each object.
(c) Determine the distance each object will move in the first second of motion if both objects start from rest.

Homework Equations

W=mg

The Attempt at a Solution

I tried to find the weight of both masses and then add it, but it didn't work, I tried to substract it and nothing...I really don't know what else can I do

 

[PeterO]

Homework Statement

Two objects with masses of 4.00 kg and 6.00 kg are connected by a light string that passes over a frictionless pulley.
(a) Determine the tension in the string.
(b) Determine the acceleration of each object.
(c) Determine the distance each object will move in the first second of motion if both objects start from rest.

Homework Equations

W=mg

The Attempt at a Solution

I tried to find the weight of both masses and then add it, but it didn't work, I tried to substract it and nothing...I really don't know what else can I do

I assume both masses are hanging.

Do part (b) first.

The weight force of one mass is trying to accelerate the total mass in one direction.
The weight force of the other mass is trying to accelerate the total mass in the other direction.
One of those forces is stronger than the other, so a smaller net force will cause the final motion.
You get the Tension by then considering the two forces [gravity and tension] acting on either mass. You could calculate it twice [each mass] to confirm you get the same answer, and therefore have the correct answer.

 

[timacho]

sum of Fy=T-W..
F=ma,
compare with fx, get T in term of acce.
u'll get acce, then solve T..

once u get acce n T, I think u know how to find distance..

 

[patrilu5]

I assume both masses are hanging.

Do part (b) first.

The weight force of one mass is trying to accelerate the total mass in one direction.
The weight force of the other mass is trying to accelerate the total mass in the other direction.
One of those forces is stronger than the other, so a smaller net force will cause the final motion.
You get the Tension by then considering the two forces [gravity and tension] acting on either mass. You could calculate it twice [each mass] to confirm you get the same answer, and therefore have the correct answer.

I really don't get it :( can you explain it with more details please

 

[rwisz]

I would approach this problem by using the fundamental principles of Newton's laws of motion and the concept of force and acceleration.

(a) To determine the tension in the string, we need to consider the forces acting on each object. In this case, the only force acting on each object is its weight. Using the equation W=mg, we can calculate the weight of each object. Since the string is light and frictionless, we can assume that the tension in the string is the same for both objects. Therefore, the tension in the string is equal to the weight of each object, which is 4.00 kg and 6.00 kg respectively.

(b) To determine the acceleration of each object, we can use Newton's second law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration (F=ma). In this case, the net force on each object is the tension in the string, which we already calculated in part (a). Therefore, we can set up the following equations:

For the 4.00 kg object: T=ma
For the 6.00 kg object: T=ma

Since the tension (T) is the same for both objects, we can set these equations equal to each other and solve for the acceleration (a):

ma = ma
4.00a = 6.00a
a = 6.00/4.00 = 1.50 m/s^2

Therefore, the acceleration of each object is 1.50 m/s^2.

(c) To determine the distance each object will move in the first second of motion, we can use the equations of motion (s=ut+1/2at^2) where s is the distance, u is the initial velocity (which is 0 in this case), a is the acceleration (which we calculated in part (b)), and t is the time (which is 1 second).

For the 4.00 kg object: s = 0 + 1/2(1.50)(1)^2 = 0.75 m
For the 6.00 kg object: s = 0 + 1/2(1.50)(1)^2 = 0.75 m

Therefore, both objects will move a distance of 0.75 meters in the first second of motion.