Calculating Equilibrium Mass in a Pulley System

[twerkit]

Homework Statement

Find the mass necessary for equilibrium to occur in the following image. Assume that the mass and the friction of the pulleys are negligible.

Homework Equations

None directly provided for this problem.

The Attempt at a Solution

I figured for this problem I would set the sum of the net torques on the pulley equal to zero, because then the pulley is not spinning and the system is in equilibrium.

Here is my equation:

gravity = 9.8 m/s

Since torque is the cross product of the force times the perpendicular distance from the axis of rotation, I used counterclockwise torque (provided by the truck) = F*rsin(x), but since the force is already perpendicular to the axis of rotation in the image I just used F*r, where the F = 1500*9.8*sin(45). The clockwise torque on the pulley is m*g*3r

ƩT = 1500kg*9.8*sin(45)*r - m*g*3r = 0

add m*g*3r to both sides and then divide by r to obtain:

ƩT = 1500kg*9.8*sin(45) = m*g*3

solving for the mass I get 353 kg, but the answer is 178 kg.

I noticed that multipying the right side by 6 instead of 3 yields the right answer, I just don't know why or what I'm doing wrong.

 

[gneill]

How many cables support the truck's weight?

 

[twerkit]

How many cables support the truck's weight?

I don't know, the question is literally this :

"Find the mass necessary for the truck to be balanced on the slope in the figure. Assume that the mass and frictions of the pulleys are negligible."

That is all it says, no information regarding how many cables or the like is given.

 

[gneill]

I don't know, the question is literally this :

"Find the mass necessary for the truck to be balanced on the slope in the figure. Assume that the mass and frictions of the pulleys are negligible."

That is all it says, no information regarding how many cables or the like is given.

Doesn't the picture make it clear? How many cables with tension T are holding the truck?

(Think: mechanical advantage)

 

[twerkit]

Doesn't the picture make it clear? How many cables with tension T are holding the truck?

(Think: mechanical advantage)

Ah, I thought you were asking me as if you needed more information! So since two cables are supporting the truck, I divide my answer by two and get approximately 178 kg.

 

[gneill]

That looks about right. Well done.

 

[twerkit]

That looks about right. Well done.

Thank you for the eye opener :-)