Moving blocks on an incline - relative motion

In summary: However, the given answer of 52.5m/s2 may be correct if the acceleration of block A is actually 80m/s2 instead of 80mm/s2. This would make the calculation for the acceleration of block B: aB = 80m/s2 + 120mm/s2 = 52.5m/s2. So, it seems like the professor may have made a mistake in the units used for the acceleration of block A.
  • #1
JJBladester
Gold Member
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2

Homework Statement


Block A starts moving downward to the left at a constant acceleration = 80mm/s2. At the same time block B moves along block A to the right at an acceleration of 120mm/s2 relative to block A.

a) Determine the acceleration of block B. Answer: aB=52.5m/s2
b) Determine the velocity of B at t = 3.0 seconds. Answer: vB=157.5m/s2

relative%20motion%20blocks.png


Note: I think the professor didn't convert between mm's and m's when he obtained the answers. Looks like he wrote the answers in meters by accident.

Homework Equations



aB/A = acceleration of B with respect to A
aB = acceleration of B (w.r.t. fixed origin)
aA = acceleration of A (w.r.t. fixed origin)

v(t) = v0 + at

The Attempt at a Solution


[tex]\left|a_{A}\right|=80mm/s^{2}=.08m/s^{2}[/tex]
[tex]a_{A_{x}}=-a_{A}cos(\theta)\approx-.0274m/s^{2}\hat{i}[/tex]
[tex]a_{A_{y}}=-a_{A}sin(\theta)\approx-.0752m/s^{2}\hat{j}[/tex]

[tex]a_{B/A}=.12m/s^{2}\hat{i}+0\hat{j}[/tex]

[tex]a_{B}=a_{A}+a_{B/A}=(-.0274+.12)\hat{i}+(-.0752+0)\hat{j}[/tex]
[tex]\left|a_{B}\right|=\sqrt{(-.0274+.12)^{2}+(-.0752+0)^{2}}\approx.119m/s^{2}[/tex]

My answer of .119m/s2 is not the correct answer of 52.5m/ss. Where did I go wrong?

I know the answer to the second part (b) of the question is a simple application of v(t) = v0 + at.
 
Last edited:
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  • #2
JJBladester said:

Homework Statement


Block A starts moving downward to the left at a constant acceleration = 80mm/s2. At the same time block B moves along block A to the right at an acceleration of 120mm/s2 relative to block A.

a) Determine the acceleration of block B. Answer: aB=52.5m/s2
b) Determine the velocity of B at t = 3.0 seconds. Answer: vB=157.5m/s2

[...snip...]

[tex]\left|a_{B}\right|=\sqrt{(-.0274+.12)^{2}+(-.0752+0)^{2}}\approx.119m/s^{2}[/tex]

My answer of .119m/s2 is not the correct answer of 52.5m/ss. Where did I go wrong?
Given the way the problem statement was written above, I think your answer is correct.
 
Last edited:

1. How does the angle of the incline affect the motion of the blocks?

The angle of the incline determines the force of gravity acting on the blocks and therefore affects their acceleration and speed.

2. What factors influence the friction between the blocks and the incline?

The type of surface, the mass of the blocks, and the angle of the incline can all affect the friction between the blocks and the incline.

3. How does the motion of the blocks change if the incline is made steeper?

If the incline is made steeper, the force of gravity acting on the blocks will increase, causing them to accelerate and move faster down the incline.

4. Can the blocks move up the incline without an external force?

No, the blocks will not be able to move up the incline without an external force acting on them. The force of gravity will cause them to move down the incline.

5. How does the mass of the blocks affect their motion on the incline?

The mass of the blocks affects their inertia, which in turn affects their acceleration and speed on the incline. Heavier blocks will require more force to move up the incline compared to lighter blocks.

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