How Do You Solve Tension Problems with Friction and Acceleration?

[max1995]

Homework Statement

See image attached

Homework Equations

The Attempt at a Solution

bii) T_c=m_c(a+g)

Need help on Ci what I did is

(9x9.81) -uR-6g=10a

Have no idea what to do though really

 

[Simon Bridge]

bii) Tc=mc(a+g)

... this does not follow from b(i). Please show your reasoning.

Have no idea what to do though really...

... did you read the hint?
But you should complete b before starting c.

 

[max1995]

... this does not follow from b(i). Please show your reasoning.
... did you read the hint?
But you should complete b before starting c.

for bii i just assumed the expressions would be the same, how would i go about getting an expression for Tc?

 

[Simon Bridge]

The b(i) equation defines a sign convention ... you should work out the derivation they did using a free body diagram.
Then for b(ii), you want to do the same derivation, but you have to make sure the sign convention is consistent with the first one.

 

[HalfLostAndSearching]

Hello! I would first like to commend you for making an attempt at solving this problem. Let's break it down together.

First, let's define the variables in the problem:

Tc = tension in the main cable
m = mass of the object hanging from the main cable
a = acceleration of the object
g = acceleration due to gravity
uR = coefficient of kinetic friction between the object and the main cable

Based on the given information, we can write the following equations:

1) Sum of forces in the vertical direction = Tc - mg = ma
2) Sum of forces in the horizontal direction = uR - 6g = 0 (since there is no acceleration in the horizontal direction)

Using these two equations, we can solve for Tc and a.

1) Tc = mg + ma
2) uR = 6g

Substituting the value of uR from equation 2) into equation 1), we get:

Tc = mg + 6mg = 7mg

Now, we can solve for a by substituting the value of Tc into equation 1):

Tc = ma
7mg = ma
a = 7g

Therefore, the final solution for part bii) is:

Tc = 7mg
a = 7g

I hope this helps! Let me know if you have any further questions. Keep up the good work!