Answer to Question #242401 in Classical Mechanics for zarss

Question

Figure 3 shows a 200 N block that sits on a frictionless incline at an angle 30°. This

box is connected by a relatively massless string, over a frictionless pulley, and finally

connected to a second block.

(a) Identify all the forces acting on the block and draw them separately.

(b) If the system is in equilibrium, determine the:

(i) weight of the second block.

(ii) normal force exerted on the first block.

Answer 1

$\text{(a) forces acting on the block:}$

$\vec N \text{ - Normal Force}$

$\vec P =200N \text{ Gravity Force}$

$\vec T\text{- Tension Force}$

$(b)\text{When all the forces acting on the object are balanced,}$

$\text {then the object is in a state of equilibrium.}$

$\text{or } \vec F=0\text{ where }\vec F\text{ resultant force}$

$(i) \vec F= 0$

$\text{projection of forces on an axis }Y$

$T-m_2g = 0$

$N -P\cos\alpha=0$

$\text{projection of forces on an axis }X$

$T -P\sin\alpha = 0$

$m_2 = \frac{P\sin\alpha}{g}=\frac{P\sin30\degree}{9.8}=10.2 kg$

$(ii) N -P\cos\alpha=0$

$N =P\cos\alpha = 200*\cos30\degree= 173.21N$