What Is the Acceleration of Block C if the Rope Between A and B Is Cut?

[ewnair]

Homework Statement

3 blocks A B C are connected by strings as in attached image. The block C is descending with constant velocity. I've worked out the tension in string A B to be 7.31N. The coefficient of kinetic friction between each block and the surface is 0.36 and block a b weighs 20.3N each. I've also calculated the weight of C to be 25.3N. The last part of the question asked for the acceleration of block C if the rope between A B is cut.

Homework Equations

Link to figure

http://b.imagehost.org/view/0603/YF-05-56.jpg

The Attempt at a Solution

I figured that if the rope was cut, the resultant force would be = t in A B which is 7.31N, working out to an equation 7.31 = (25.3/9.80) * acceleration. However the answer is wrong. The question did not provide a numerical value for g so i was wondering if i shouldn't have used 9.80. Any help would be much appreciated thanks.

 

[Hootenanny]

Homework Statement

3 blocks A B C are connected by strings as in attached image. The block C is descending with constant velocity. I've worked out the tension in string A B to be 7.31N. The coefficient of kinetic friction between each block and the surface is 0.36 and block a b weighs 20.3N each. I've also calculated the weight of C to be 25.3N. The last part of the question asked for the acceleration of block C if the rope between A B is cut.

Homework Equations

Link to figure

http://b.imagehost.org/view/0603/YF-05-56.jpg

The Attempt at a Solution

I figured that if the rope was cut, the resultant force would be = t in A B which is 7.31N, working out to an equation 7.31 = (25.3/9.80) * acceleration. However the answer is wrong. The question did not provide a numerical value for g so i was wondering if i shouldn't have used 9.80. Any help would be much appreciated thanks.

If the rope between A & B was cut, wouldn't the tension in AB be necessarily zero? Wouldn't the tension between BC be more relevant to the acceleration of C?

 

[baba89]

I would like to clarify a few things before providing a response:

1. The homework statement does not mention what type of forces are acting on the blocks. Are they only considering gravitational forces or are there other forces involved? This information is important in order to accurately solve the problem.

2. The units for the weight of blocks A and B are not provided. This could also affect the accuracy of the solution.

Assuming that the only forces acting on the blocks are gravitational forces and the coefficients of kinetic friction, here is my response:

Firstly, the weight of block C should be 25.3N, not 23.5N as mentioned in the homework statement.

Secondly, the coefficient of kinetic friction should be multiplied by the normal force on each block, not by the weight of the block. In this case, the normal force on block A and B would be equal to their weight (20.3N each).

Thirdly, the acceleration of block C can be calculated using the following equation:

mC * a = FC - μk*NA - μk*NB

Where mC is the mass of block C, a is the acceleration of block C, FC is the force of tension in string AB (which is equal to 7.31N), μk is the coefficient of kinetic friction, and NA and NB are the normal forces on blocks A and B respectively.

Substituting the values, we get:

(25.3/9.80) * a = 7.31 - 0.36*20.3 - 0.36*20.3

a = 0.55 m/s^2

Therefore, the acceleration of block C would be 0.55 m/s^2 if the rope between blocks A and B is cut.

Note: The gravitational constant g is not required in this calculation. It is only used to convert units from Newtons to kilograms.