- #1
Combinatorics
- 36
- 5
- Homework Statement
- A mass $$m=12 kg$$ is placed on a cube, as shown in the attached figure. The cube is made of a breakable material, that breaks when a force larger than $$F_{max}=150N$$ is exerted on it.
Someone pulls the cube upwards with an acceleration of $$a \, \frac{meter}{sec^2}$$. What is the maximal acceleration possible for which the cube edges will not break? ($$\theta = \frac{\pi}{6} $$)
- Relevant Equations
- Newton's laws,
g=9.8 m/s^2
Using Newton's second law,
$$
cos\left( \frac{\pi}{6} \right) m(a+g) = 150 \Leftrightarrow a = \frac{\frac{2\times 150 }{\sqrt{3}}-mg}{m} =4.633.
$$
Unfortunately, the possible answers are
A. 1.025, B. 0.625, C. 3.75, D. 2.75, E. 1.75, F. 0.
What am I getting wrong? Isn't the force exerted on the inclined part of the cube equal to $cos\left( \frac{\pi}{6} \right) m(a+g) $?
Thanks
$$
cos\left( \frac{\pi}{6} \right) m(a+g) = 150 \Leftrightarrow a = \frac{\frac{2\times 150 }{\sqrt{3}}-mg}{m} =4.633.
$$
Unfortunately, the possible answers are
A. 1.025, B. 0.625, C. 3.75, D. 2.75, E. 1.75, F. 0.
What am I getting wrong? Isn't the force exerted on the inclined part of the cube equal to $cos\left( \frac{\pi}{6} \right) m(a+g) $?
Thanks
Attachments
Last edited: