Finding acceleration of block with block on top, connected by rope

In summary, the two equations of motion are:2kg body: a = -9.8m/s^2 * 0.161kg body: a = 9.8m/s^2 * 0.16
  • #1
sentimentaltrooper
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1
Homework Statement
A rope pulls on the lower block in the figure with a tension force of 20 N. The coefficient of kinetic friction between the lower block and the surface is 0.16. The coefficient of kinetic friction between the lower block and the upper block is also 0.16. The pulley has no appreciable mass or friction. What is the acceleration of the 2.0 kg block?
Relevant Equations
F=ma
a=F/m
block.jpg

I have already concluded that the way to solve this problem is through
(20 N - (3 kg * 9.8 m/s^2 * 0.16) - (2*(1 kg * 9.8 m/s^2 * 0.16))) / 3 kg

I have several questions:
  • Why do we multiply the second set of parentheses by 2? Why do we count the friction between the 1 kg box and the 2 kg box twice?
  • Also, the fact that the frictions are both 0.16 does not allow me to differentiate between the calculations. The first set of parentheses with 3 * 9.8 * 0.16 is multiplied by 0.16 because that is the friction between the lower block and the surface correct?
Thank you
 
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  • #2
This problem seems "wicked" (at least to me) but can be solved relatively easily with repetitive applications of Newton's 2nd law in the horizontal and vertical direction. Both of your questions will be answered if you correctly and repeatedly apply Newton's 2nd law and combine correctly the resulting equations.
 
  • #3
sentimentaltrooper said:
Why do we count the friction between the 1 kg box and the 2 kg box twice?
One way to think of it is that the relative motion of the two surfaces is double that of the relative motion of the lower block and the ground. So for a given frictional force, twice as much work is done there for each unit of distance by which the 20N force advances.
 
  • #4
I thank you for your responses and I apologize for this but for some reason I still cannot understand why it is double, or twice as much work.
 
  • #5
sentimentaltrooper said:
I thank you for your responses and I apologize for this but for some reason I still cannot understand why it is double, or twice as much work.
If the applied 20N force advances distance x, the lower block moves x relative to the ground. If the the frictional force there is ##F_L## then the work done is ##xF_L##. At the same time, the upper block moves x the other way, so the surfaces of the two blocks in contact move 2x wrt each other. If the frictional force there is ##F_U## then the work done against that is ##2xF_U##.
 
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  • #6
haruspex said:
If the applied 20N force advances distance x, the lower block moves x relative to the ground. If the the frictional force there is ##F_L## then the work done is ##xF_L##. At the same time, the upper block moves x the other way, so the surfaces of the two blocks in contact move 2x wrt each other. If the frictional force there is ##F_U## then the work done against that is ##2xF_U##.
Thank you so much for this.
 
  • #7
Say 2kg body has acceleration ##a##, 1 kg body has acceleration ##-a## due to binding by rope. We can make two equations of motion for the two bodies and get ##a## from them.
 
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1. What is the formula for finding acceleration in this scenario?

The formula for finding acceleration in this scenario is a = (m1-m2)g / (m1+m2), where m1 is the mass of the block on the bottom, m2 is the mass of the block on top, and g is the acceleration due to gravity.

2. How does the tension in the rope affect the acceleration of the blocks?

The tension in the rope does not affect the acceleration of the blocks. It only affects the force acting on each block, but the acceleration remains the same.

3. Can the acceleration in this scenario be negative?

Yes, the acceleration can be negative if the blocks are moving in the opposite direction of the force of gravity. This would indicate that the blocks are slowing down.

4. How does the mass of the blocks affect the acceleration?

The mass of the blocks affects the acceleration by increasing the force of gravity acting on the blocks. The larger the mass, the greater the force of gravity, and therefore the greater the acceleration.

5. What is the relationship between the acceleration and the angle of the rope?

The angle of the rope does not affect the acceleration in this scenario. As long as the rope remains taut, the acceleration will remain constant regardless of the angle.

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