# Find Tension and mass of painting equipment on scuffle board.

• MHB
• cbarker1
In summary, the scaffold has a mass of 41.0 kg and a length of 5.8 m. The painter has a mass of 78.0 kg and stands 1.0 m from the left end of the scaffold, with his painting equipment 1.6 m from the right end. The tension in the left cable is twice that in the right cable and the system can be solved to find the tensions in the cables and the mass of the painting equipment. The length for the torque of the mass of the painting can be found by subtracting the distance between the painter and the equipment (1.6 m) from the total length of the scaffold (5.8 m).
cbarker1
Gold Member
MHB
A uniform 41.0 kg scaffold of length 5.8 m is supported by two light cables, as shown below. A 78.0 kg painter stands 1.0 m from the left end of the scaffold, and his painting equipment is 1.6 m from the right end. If the tension in the left cable is twice that in the right cable, find the tensions in the cables (in N) and the mass of the equipment in kgs.

View attachment 7617

Works
Givens:

The mass of the scaffold=41.0 kg
Length of the scaffold=5.8 m
the mass of the painter= 78 kg
The length betwen left end and the painter= 1 m
The length between painting equipment and painter= 1.6 m
The Tension of the Left= twice in the right cable.
the mass of the painting equipment=?

$\Sigma F_y=0$
$-m_b*g-m_p*g-m_s*g+T_L+T_R=0$
$\Sigma\tau=0$
$-m_p*g*L_1-m_b*g*L_2+T_R*L_3+(m_s*g*(L1+L2)/2)(?)=0$

If I place the pivot for the torque on left end of the scaffold, then would the weight of the scaffold be not needed?

View attachment 7616

Last edited by a moderator:
$T$ = tension in the right cable
$P$ = mass of paint equipment

forces up = forces down

$2T + T = 78g + 41g + Pg$

about the left end, torques CW = torque CCW (yes, the scaffold weight exerts a torque)

$78g \cdot 1.0 + 41g \cdot 2.9 + Pg \cdot 4.2 = T \cdot 5.8$

solve the system of equations for $T$ and $P$

skeeter said:
$T$ = tension in the right cable
$P$ = mass of paint equipment

forces up = forces down

$2T + T = 78g + 41g + Pg$

about the left end, torques CW = torque CCW (yes, the scaffold weight exerts a torque)

$78g \cdot 1.0 + 41g \cdot 2.9 + Pg \cdot 4.2 = T \cdot 5.8$

solve the system of equations for $T$ and $P$

how to get the length for the torque of mass of the painting?

Cbarker1 said:
how to get the length for the torque of mass of the painting?

5.8 - 1.6 = 4.2

## 1. What is tension and mass in relation to a painting equipment on a scuffle board?

Tension refers to the force that is pulling on an object, while mass is the amount of matter an object contains. In this case, tension and mass are important factors in determining the stability and movement of the painting equipment on the scuffle board.

## 2. How do I find the tension of the painting equipment on the scuffle board?

The tension of the painting equipment can be found by using the formula T = mg, where T is the tension, m is the mass of the equipment, and g is the gravitational acceleration (9.8 m/s²). Simply plug in the values and solve for T.

## 3. How do I determine the mass of the painting equipment on the scuffle board?

To find the mass of the painting equipment, you can use a scale to weigh the equipment or you can calculate it by using the formula m = T/g, where m is the mass, T is the tension, and g is the gravitational acceleration. Make sure to use consistent units (such as kilograms or pounds) for accurate results.

## 4. Is the tension and mass of the painting equipment on the scuffle board important for safety?

Yes, the tension and mass of the equipment are important for safety as they can affect the stability and movement of the equipment. It is important to ensure that the tension is not too high or too low, and that the mass is evenly distributed to prevent accidents or damage to the equipment.

## 5. How can I adjust the tension and mass of the painting equipment on the scuffle board?

The tension and mass can be adjusted by adding or removing weight from the equipment or by changing the position of the equipment on the scuffle board. It may require some trial and error to find the optimal tension and mass for stability and smooth movement.

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