Subjective Type

Figure a tin of antioxidants (m1 " 1.0 kg) on a frictionless inclined surface is connected to a tin of corned beef (m2 2.0 kg). The pulley is massless and frictionless. An upward force of magnitude F " 6.0 N acts on the corned beef tin, which has a downward acceleration of 5.5 m/s2. What are (a) the tension in the connecting cord and(b) angle b?

Solution

We have two masses connected together by a cord. A force is applied to the second mass and the system accelerates together. We apply Newton’s second law to solve the problem.

The free-body diagrams for the two masses are shown below (not to scale). We first analyze the forces on $$m_1=1.0\, kg$$. The +x direction is “downhill” (parallel to $$\vec{ T}$$). With the acceleration $$a = 5.5\, m/s^2$$ in the positive x-direction for $$m_1$$, then Newton’s second law, applied to the x-axis, becomes

$$T = m_1 g \, sin \beta =m_1 a$$

On the other hand, for $$m_2 = 2.0\, kg$$, we have
$$m_2 g - F - T = m_2 a$$

where the tension comes in as an upward force (the cord can pull, not push). The two equations can be combined to solve for $$T$$ and $$\beta $$ .

(b) We solve this part first. By combining the two equations above, we obtain
$$sin \,\beta =\dfrac {(m_1+m_2)a+F-m_2g}{m_1g}=\dfrac {(1.0\, kg 2.0\, kg)(5.5\, m/s^2)+6.0 \, N-(2.0\, kg)(9.8\, m/s^2)}{(1.0\, kg)(9.8\, m/s^2)}= 0.296$$

which gives $$\beta =17^o$$.

(a) Substituting the value for $$\beta$$ found in (a) into the first equation, we have
$$ T =m_1 (a-sin \,\beta ) (1.0\,kg) [5.5\,m/s^2 \,(9.8\,m/s^2 ) sin\, 17.2^o]=2.60\, N$$.

SIMILAR QUESTIONS

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