# Guide n° 1 of solved exercises of statics

## Solve the following exercises

Example, how to calculate forces, power, resistance and weights in pulleys and tackle. Statics problems solved and easy.

### problem #1

A body of 200 kgf is lifted by means of a potential tackle with 3 mobile pulleys. What is the value of the power?

## Solution

# Potential Rigging Problem #1

## Statement of exercise n° 1

A body of 200 kgf is lifted by means of a potential tackle with 3 mobile pulleys. What is the value of the power?

### Developing

#### Data:

P = 200 kgf

n = 3

#### Formulas:

T = | P |

^{2n} _ |

### Solution

T = | 200 kgf |

23 |

T = | 200 kgf |

8 |

Result, the power applied to the rig is:

T = 25 kgf

### problem #2

A body is supported by a potential 5-pulley tackle. If the applied power is 60 N, what is the weight of the body?

## Solution

# Potential Rigging Problem #2

## Statement of exercise n° 2

A body is supported by a potential 5-pulley tackle. If the applied power is 60 N, what is the weight of the body?

### Developing

#### Data:

T = 60N

n = 5

#### Formulas:

T = | P |

^{2n} _ |

### Solution

P = ^{2n} T

P = 2 ^{5} 60 N

P = 32 60 N

Result, the weight of the sustained body is:

P = 1920N

### Problem #3

Using a 4-pulley factorial rig, a 500-kgf body is balanced. What is the applied power?

## Solution

# Factorial rigging problem #3

## Statement of exercise n° 3

Using a 4-pulley factorial rig, a 500-kgf body is balanced. What is the applied power?

### Developing

#### Data:

P = 500 kgf

n = 4

#### Formulas:

T = | P |

2 n |

### Solution

T = | 500 kgf |

2 4 |

T = | 500 kgf |

8 |

Result, the power applied to the rig is:

T = 62.5 kgf

### Problem #4

Using a lathe with a radius of 12 cm and a crank of 60 cm, a bucket weighing 3.5 kgf, loaded with 12 liters of water, is lifted. What is the applied power?

## Solution

# Lathe Problem #4

## Statement of exercise n° 4

Using a lathe with a radius of 12 cm and a crank of 60 cm, a bucket weighing 3.5 kgf, loaded with 12 liters of water, is lifted. What is the applied power?

### Developing

#### Data:

P: weight of the bucket plus the water.

P = 3.5 kgf + 12 kgf = 15.5 kgf

d1 = 12cm = _{0.12m}

d2 _{=} 60cm = 0.60m

#### Formulas:

Equilibrium condition → M F = 0

M F = ∑(F d) = P d _{1} + T d _{2}

Equilibrium condition: The sum of the moments of the forces must be zero: Newton’s first law (equilibrium)

#### Scheme:

Free body diagram of a lathe

### Solution

0 = P d _{1} + T d _{2}

-P d _{1} = T d _{2}

T = | -P d _{1} |

d2 _{_} |

T = | -15.5kgf 0.12m |

0.6m |

Result, the power applied to the lathe is:

T = -3.1 kgm

T is negative because it rotates clockwise.

### Problem #5

In a potential rig with 4 moving pulleys, a force of 30 N is applied to keep the system in equilibrium, it is desired to know the value of the resistance.

## Solution

# Potential Rigging Problem #5

## Statement of exercise n° 5

In a potential rig with 4 moving pulleys, a force of 30 N is applied to keep the system in equilibrium, it is desired to know the value of the resistance.

### Developing

#### Data:

T = 30N

n = 4

#### Formulas:

T = | P |

^{2n} _ |

### Solution

T = | P |

^{2n} _ |

T 2 ^{n} = P

P = 30 N 2 ^{4}

Result, the value of the resistance in the rig is:

P = 480N

### Problem #6

A body is lifted with a winch with a radius of 30 cm, to which 30 N is applied. What will be the weight of the body if the crank is 90 cm?

## Solution

# Lathe Problem #6

## Statement of exercise n° 6

A body is lifted with a winch with a radius of 30 cm, to which 30 N is applied. What will be the weight of the body if the crank is 90 cm?

### Developing

#### Data:

T = 30N

d1 = _{30cm} = 0.30m

d2 _{=} 90cm = 0.90m

#### Formulas:

Equilibrium condition → M F = 0

M F = ∑(F d) = P d _{1} + T d _{2}

Equilibrium condition: The sum of the moments of the forces must be zero: Newton’s first law (equilibrium)

#### Scheme:

### Solution

0 = P d _{1} + T d _{2}

-P d _{1} = T d _{2}

-P = | T d _{2} |

d1 _{_} |

-P = | -30N 0.9m |

0.3m |

T is negative because it rotates clockwise.

Result, the weight of the lifted body is:

P = 90N

### Problem #7

At the ends of a rope, which is on a fixed pulley, two loads of 5 kgf and 7 kgf have been placed. If the radius of the pulley is 12 cm, what is the moment that turns the pulley?

## Solution

# Fixed Pulley Problem #7

## Statement of exercise No. 7

At the ends of a rope, which is on a fixed pulley, two loads of 5 kgf and 7 kgf have been placed. If the radius of the pulley is 12 cm, what is the moment that turns the pulley?

### Developing

#### Data:

F1 = 5 _{kgf}

F2 = 7 _{kgf}

d = 12cm = 0.12m

#### Formulas:

M F = ∑(F d) = F _{1} d _{1} + F _{2} d _{2}

#### Scheme:

### Solution

But d1 _{=} d2 _{=} 0.12m

M F = F _{1} d + F _{2} d = (F _{1} + F _{2} ) d

One of the forces must be given a negative direction, normally the one that rotates clockwise, in this case any of them.

M F = (-5kgf + 7kgf) 0.12m

MF = 2 kgf 0.12 m

Result, the moment that makes the pulley rotate is:

MF = 0.24 kgm

### Problem #8

Calculate the weight of a body suspended from the rope of a lathe with a radius of 18 cm and a crank 45 cm long, balanced by a force of 60 kgf.

## Solution

# Lathe Problem #8

## Statement of exercise n° 8

Calculate the weight of a body suspended from the rope of a lathe with a radius of 18 cm and a crank 45 cm long, balanced by a force of 60 kgf.

### Developing

#### Data:

T = 60 kgf

d1 = 18cm = _{0.18m}

d2 _{=} 45cm = 0.45m

#### Formulas:

Equilibrium condition → M F = 0

M F = ∑(F d) = P d _{1} + T d _{2}

Equilibrium condition: The sum of the moments of the forces must be zero: Newton’s first law (equilibrium)

#### Scheme:

Free body diagram of a lathe

### Solution

0 = P d _{1} + T d _{2}

-P d _{1} = T d _{2}

P = | -T d _{2} |

d1 _{_} |

P = | -(-60kgf) 0.45m |

0.18m |

T is negative because it rotates clockwise.

Result, the weight of a suspended body is:

P = 150 kgf

### Problem #9

What will be the length of the crank of a lathe that, to balance a weight of 150 kgf, it is necessary to apply a force of 40 kgf? The radius of the cylinder is 20 cm.

## Solution

# Lathe Problem #9

## Statement of exercise n° 9

What will be the length of the crank of a lathe that, to balance a weight of 150 kgf, it is necessary to apply a force of 40 kgf? The radius of the cylinder is 20 cm.

### Developing

#### Data:

P = 150 kgf

T = 40 kgf

d1 = _{20cm} = 0.20m

#### Formulas:

Equilibrium condition → M F = 0

M F = ∑(F d) = P d _{1} + T d _{2}

#### Scheme:

Free body diagram of a lathe

### Solution

0 = P d _{1} + T d _{2}

-P d _{1} = T d _{2}

d2 = _{_} |
-P d _{1} |

T |

T is negative because it rotates clockwise.

d2 = _{_} |
-150kgf 0.20m |

-40kgf |

Result, the length of the lathe handle should be:

d2 _{=} 0.75m

### Problem #10

A body is lifted with a winch of radius 20 cm, to which 40 kgf is applied. What will be the weight of the body if the crank is 80 cm?

## Solution

# Lathe Problem #10

## Statement of exercise n° 10

A body is lifted with a winch of radius 20 cm, to which 40 kgf is applied. What will be the weight of the body if the crank is 80 cm?

### Developing

#### Data:

T = 40 kgf

d1 = _{20cm} = 0.20m

d2 _{=} 80cm = 0.80m

#### Formulas:

Equilibrium condition → M F = 0

M F = ∑(F d) = P d _{1} + T d _{2}

#### Scheme:

### Solution

0 = P d _{1} + T d _{2}

-P d _{1} = T d _{2}

-P = | T d _{2} |

d1 _{_} |

-P = | -40kgf 0.8m |

0.2m |

T is negative because it rotates clockwise.

Result, the weight of the lifted body is:

W = 160 kgm