Solving a Physics Problem Involving Two Blocks Connected by a Cord

[Edwardo_Elric]

Homework Statement

A block with mass 6.00kg resting on a horizontal surface is connected by a horizontal cord passing over a light frictionless pulley to a hanging block with mass 4.00kg. The coefficient of kinetic friction between the block and the horizontal surface is 0.50. After the blocks are released,
a.) Find the acceleration of each block
b.) The tension in the cord.

Homework Equations

The Attempt at a Solution

a.)
uk = 0.50
fk = ukN
fk = 0.50(6.00kg)(9.8m/s^2)
Summation of the mass of 6.00kg block
m1a = T - fk
m1a = T - 0.50(6.00kg)(9.8m/s^2)

Summation of the mass of 4kg block
m2a = m2g - T

so i add both the two forces:
m1a = T - 0.50(6.00kg)(9.8m/s^2)
+m2a = m2g - T
________________
(m1+m2)a = m2g - 0.50(6.00kg)(9.8m/s^2)
a = { (4.00kg)(9.8m/s^2) - 0.50(6.00kg)(9.8m/s^2) } / {6.00kg+4.00kg}
a = 0.98m/s^2

dont know how the back of the book got an answer of 0.1m/s^2

b.) m2a = m2g - T
(4.00kg)(.98m/s^2) = (4.00kg)(9.8) - T
T = 35.28N

 

[Doc Al]

Your method and answers look correct to me. (Must be a typo in the book.)

 

[m2003]

I would like to commend your attempt at solving this physics problem. However, I noticed that you have made a mistake in your calculation for the acceleration. The correct equation for the summation of forces on the 6.00kg block should be m1a = T - fk, where fk is the kinetic friction force. This means that the final equation should be (m1+m2)a = m2g - fk, where fk = 0.50(6.00kg)(9.8m/s^2) = 29.4N. This would result in an acceleration of 0.55m/s^2. This may be the reason why the back of the book got an answer of 0.1m/s^2.

For b.), your calculation for the tension is correct. I would just like to add that it is important to always check your units to ensure that they are consistent. In this case, the units for acceleration should be m/s^2, so the final answer for the tension should be T = 35.28N. Overall, your attempt at solving this problem is commendable, and it is important to always double check your calculations to ensure accuracy. Keep up the good work!