The mass center of the cart is at G Determine the magnitude

The mass center of the cart is at G.

Determine the magnitude of the largest force P that can be applied to the 45-kg cart, without causing one of the wheel reactions, either at A or at B, to be zero.

What is the acceleration of the cart?

30° 0.4 m 0.3 m 0.3 m 0.2 m 0.2 m . 0.08 m

Solution

>> Now, Considering all Vertical forces,

as cart will not move vertically, so, net force in vertical direction = 0

=> P*sin30 + Ra + Rb - W = 0

W = Weight of Cart = mg = 45*9.81 = 441.45 N

=> 0.5*P + Ra + Rb = 441.45 .....(1)...............

>> Now, biggest danger due to application of force is that, due to it, there might be possibility of turning of cart about A

>> In that case, Contactfrom B will break and so, Rb = 0

>> So, Ma should be zero to avoid this situation

=> Ma = - 0.08*P*sin30 + 0.4*P*cos30 - 0.3*W + 0.5*Rb = 0

Considering extreme case, Let\'s assume Rb is very negligible

So, Equation becomes

- 0.08*P*sin30 + 0.4*P*cos30 - 0.3*W = 0

=> - 0.08*P*0.5 + 0.4*P*0.866 - 0.3*441.45 = 0

=> P = 432.23 N