Inclined Planes Alıştırma Soruları — Armed Services Vocational Aptitude Battery (ASVAB) — Sayfa 2

Soru 21Soru →

A depot worker must slide a $1200\text{ lb}$ steel safe up a straight ramp to a storage platform that is $3\text{ feet}$ above the main floor. The worker uses a mechanical winch that can pull with a maximum force of $240\text{ lbs}$ . Assuming a frictionless surface, what is the minimum ramp length required to move the safe?

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Cevap: 15

Cevap

15

The mechanical advantage required to move a

1200\text{ lb}

load using only

240\text{ lbs}

of force is

1200 / 240 = 5

. Because the Ideal Mechanical Advantage of an inclined plane is its length divided by its height, a ramp with an IMA of

5

lifting a load

3\text{ feet}

vertically must be

5 \times 3 = 15\text{ feet}

long.

Adım Adım Çözüm

1

Calculate the required Ideal Mechanical Advantage (IMA).

IMA = 5

The mechanical advantage is the ratio of the load force to the maximum effort force (

1200 / 240 = 5

).

2

Set up the equation for the mechanical advantage of an inclined plane.

5 = Length / 3

For an inclined plane, IMA is equal to the length of the slope divided by the vertical height.

3

Solve for the ramp length.

Length = 15 feet

Multiplying the IMA by the height (

5 \times 3

) gives the minimum required ramp length to achieve that mechanical advantage.

Anahtar Kavram

Ideal Mechanical Advantage (IMA) of an Inclined Plane

Soru 22Soru →

A combat engineer squad needs to push a $60\text{ kg}$ supply crate up a smooth, frictionless ramp onto a platform. The platform is $2\text{ meters}$ above the ground, and the ramp is $6\text{ meters}$ long. Assuming the acceleration due to gravity is $10\text{ m/s}^2$ , what is the ideal effort force required to push the crate up the ramp?

20\text{ N}

200\text{ N}

600\text{ N}

1200\text{ N}

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Cevap: $200\text{ N}$

Cevap

The required effort force is

200\text{ N}

.

The ideal mechanical advantage (IMA) of an inclined plane is calculated by dividing its length by its height (6 m / 2 m = 3). The crate's weight is its mass multiplied by gravity (60 kg × 10 m/s² = 600 N). The effort force required is the weight divided by the IMA (600 N / 3 = 200 N).

Adım Adım Çözüm

1

Calculate the weight (gravitational force) of the crate.

Weight = 60\text{ kg} \times 10\text{ m/s}^2 = 600\text{ N}

Effort force must oppose the weight (force of gravity) pulling the object down, not just the mass.

2

Calculate the ideal mechanical advantage (IMA) of the ramp.

IMA = \frac{6\text{ m}}{2\text{ m}} = 3

IMA compares the length of the ramp (distance the effort is applied) to the vertical height the load is lifted.

3

Calculate the effort force.

Effort = \frac{600\text{ N}}{3} = 200\text{ N}

The inclined plane reduces the required force by a factor equal to its mechanical advantage.

Anahtar Kavram

Ideal Mechanical Advantage of Inclined Planes

Soru 23Soru →

Arrange the following inclined planes in order from the LEAST ideal mechanical advantage (IMA) to the GREATEST ideal mechanical advantage.

Öğeleri doğru sıraya koymak için sürükleyin

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Cevap

The correct order from least to greatest mechanical advantage is: the 10-foot ramp (IMA=2), the 12-foot ramp (IMA=4), the 15-foot ramp (IMA=5), and the 16-foot ramp (IMA=8).

The ideal mechanical advantage (IMA) of an inclined plane is calculated by dividing the length of the slope by its vertical height. A longer slope relative to its height yields a higher mechanical advantage, meaning less effort force is required. Ordering the ramps by their calculated IMA values gives 2 (least), 4, 5, and 8 (greatest).

Adım Adım Çözüm

1

Recall the formula for the ideal mechanical advantage (IMA) of an inclined plane.

\text{IMA} = \frac{\text{Length of Incline}}{\text{Vertical Height}}

The mechanical advantage quantifies how much the inclined plane multiplies the input force or reduces the required effort.

2

Calculate the IMA for each given ramp.

10-foot ramp:

10 \div 5 = 2

. 12-foot ramp:

12 \div 3 = 4

. 16-foot ramp:

16 \div 2 = 8

. 15-foot ramp:

15 \div 3 = 5

.

Calculating the individual values allows for direct comparison.

3

Order the calculated values from least to greatest.

The values in ascending order are 2, 4, 5, and 8.

The question specifically asks for the arrangement starting from the lowest mechanical advantage to the highest.

Anahtar Kavram

The ideal mechanical advantage of a ramp is determined by the ratio of its length to its vertical height.

Soru 24Soru →

A theater stage crew needs to roll a heavy $400$ -pound lighting rig up to a stage platform that is $5$ feet high. They can build either a steep ramp that is $10$ feet long or a gentle ramp that is $20$ feet long. Assuming the ramp surfaces and wheels are perfectly frictionless, which of the following statements correctly compares the two ramp options?

The

20

-foot ramp reduces both the required effort force and the total work done by half compared to the

10

-foot ramp.

The

10

-foot ramp requires less total work than the

20

-foot ramp because the lighting rig is moved across a shorter total distance.

The

20

-foot ramp requires half the effort force of the

10

-foot ramp, but the total work done remains exactly the same for both.

The

20

-foot ramp requires less effort force because placing the rig on a shallower angle effectively reduces the mass of the rig.

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Cevap: The $20$ -foot ramp requires half the effort force of the $10$ -foot ramp, but the total work done remains exactly the same for both.

Cevap

The

20

-foot ramp requires half the effort force of the

10

-foot ramp, but the total work done remains exactly the same for both.

The Ideal Mechanical Advantage (IMA) of an inclined plane is its length divided by its height. The

20

-foot ramp has an IMA of

4

(

20/5

), requiring

100

lbs of effort force. The

10

-foot ramp has an IMA of

2

(

10/5

), requiring

200

lbs of effort force. Therefore, the longer ramp requires half the effort force. However, because simple machines do not change the total amount of work done (

\text{Work} = \text{Force} \times \text{Distance}

), both ramps require

2000

ft-lbs of total work to lift the rig

5

feet vertically.

Adım Adım Çözüm

1

Calculate the Ideal Mechanical Advantage (IMA) for both ramps using the formula

IMA = \text{Length} / \text{Height}

.

Steep ramp IMA =

10 / 5 = 2

. Gentle ramp IMA =

20 / 5 = 4

.

IMA determines how much the inclined plane multiplies the input force.

2

Determine the required effort force for each ramp using the formula

\text{Effort} = \text{Load} / IMA

.

Steep ramp effort =

400 / 2 = 200

lbs. Gentle ramp effort =

400 / 4 = 100

lbs.

This mathematical relationship shows that the

20

-foot ramp requires exactly half the effort force of the

10

-foot ramp.

3

Calculate the total work done for both scenarios using

\text{Work} = \text{Force} \times \text{Distance}

(along the ramp).

Work for steep ramp =

200 \text{ lbs} \times 10 \text{ ft} = 2000 \text{ ft-lbs}

. Work for gentle ramp =

100 \text{ lbs} \times 20 \text{ ft} = 2000 \text{ ft-lbs}

.

This confirms the principle of conservation of energy: while simple machines alter the force required, they do not change the total work done against gravity.

Anahtar Kavram

Ideal Mechanical Advantage and the Work-Force Tradeoff

Soru 25Soru →

A contractor uses a $15\text{-foot}$ ramp and a motorized winch to load a $600\text{-lb}$ generator. If the winch can pull with a maximum steady force of $120\text{ lbs}$ , what is the maximum vertical height, in feet, that the ramp can reach assuming a frictionless surface?

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Cevap: 3

Cevap

The maximum vertical height the ramp can reach is 3 feet.

An inclined plane multiplies the applied effort force by spreading the required work over a longer distance. First, determine the Mechanical Advantage needed by dividing the load (

600\text{ lbs}

) by the available effort force (

120\text{ lbs}

), which gives an IMA of

5

. This means the ramp must be

5

times longer than it is high. Given a ramp length of

15\text{ feet}

, divide this length by the IMA of

5

to find the maximum vertical height, which is

3\text{ feet}

.

Adım Adım Çözüm

1

Determine the required Ideal Mechanical Advantage (IMA).

\text{IMA} = \frac{600}{120} = 5

The IMA represents how many times the machine multiplies the effort force. It is found by dividing the load force by the effort force.

2

Use the inclined plane IMA formula to set up an equation for the height.

5 = \frac{15}{\text{Height}}

For an inclined plane, the

\text{IMA}

is also equal to the ratio of the

\text{Ramp Length}

to the

\text{Vertical Height}

.

3

Solve the equation for the vertical height.

\text{Height} = \frac{15}{5} = 3

Rearrange the equation to isolate the height, dividing the ramp length by the required IMA.

Anahtar Kavram

Ideal Mechanical Advantage (IMA) of an inclined plane and determining vertical height from force ratios.

Inclined Planes

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