Momentum and Collisions Alıştırma Soruları — Armed Services Vocational Aptitude Battery (ASVAB)

Soru 1Soru →

A cargo crate has a weight of $4,900 \text{ N}$ on Earth (where $g = 9.8 \text{ m/s}^2$ ). It is sliding across a frictionless floor at a velocity of $12 \text{ m/s}$ when it hits a padded wall. If the crate comes to a complete stop in $0.6 \text{ s}$ , what is the average impact force exerted on the crate during this collision?

98,000 \text{ N}

10,000 \text{ N}

3,600 \text{ N}

25 \text{ N}

Cevabı ve açıklamayı göster

Cevap: $10,000 \text{ N}$

Cevap

The average impact force is

10,000 \text{ N}

.

To find the average impact force, we use the impulse-momentum theorem (

F\Delta t = m\Delta v

) or Newton's second law (

F = ma

). First, we must convert the weight to mass by dividing by the acceleration due to gravity:

4,900 \text{ N} / 9.8 \text{ m/s}^2 = 500 \text{ kg}

. Next, we calculate the acceleration by dividing the change in velocity by the impact time:

12 \text{ m/s} / 0.6 \text{ s} = 20 \text{ m/s}^2

. Multiplying the mass by the acceleration gives the force:

500 \text{ kg} \times 20 \text{ m/s}^2 = 10,000 \text{ N}

.

Adım Adım Çözüm

1

Calculate the mass of the crate from its weight.

m = \frac{W}{g} = \frac{4,900 \text{ N}}{9.8 \text{ m/s}^2} = 500 \text{ kg}

Newton's laws and momentum calculations require mass, not weight.

2

Calculate the crate's change in velocity.

\Delta v = 12 \text{ m/s} - 0 \text{ m/s} = 12 \text{ m/s}

The crate comes to a complete stop, so the total change in velocity is its initial velocity.

3

Calculate the crate's acceleration (or deceleration) during the impact.

a = \frac{\Delta v}{\Delta t} = \frac{12 \text{ m/s}}{0.6 \text{ s}} = 20 \text{ m/s}^2

Acceleration is the change in velocity divided by the time it takes to change.

4

Calculate the average impact force using Newton's Second Law.

F = m \times a = 500 \text{ kg} \times 20 \text{ m/s}^2 = 10,000 \text{ N}

Force equals mass times acceleration. (Alternatively, impulse

F\Delta t = \Delta p

yields the same result:

F = \frac{500 \times 12}{0.6} = 10,000 \text{ N}

).

Anahtar Kavram

The impulse-momentum theorem and the distinction between mass and weight.

Soru 2Soru →

A $2,000 \text{ kg}$ pickup truck is coasting along a level road at a velocity of $15 \text{ m/s}$ . What is the magnitude of the truck's momentum?

Cevabı ve açıklamayı göster

Cevap: 30000

Cevap

30000

Momentum is directly proportional to both mass and velocity. By multiplying the

2,000 \text{ kg}

mass by the

15 \text{ m/s}

velocity, we determine the total momentum is

30,000 \text{ kg} \cdot \text{m/s}

.

Adım Adım Çözüm

1

Identify the known variables from the text.

Mass (

m

) is

2,000 \text{ kg}

and velocity (

v

) is

15 \text{ m/s}

.

Momentum calculation requires both the mass and the velocity of the object.

2

Apply the formula for momentum.

p = m \times v

The linear momentum of an object is defined as the product of its mass and its velocity.

3

Calculate the final value.

p = 2,000 \times 15 = 30,000

Multiplying the mass by the velocity yields the total magnitude of momentum.

Anahtar Kavram

Momentum is the product of an object's mass and its velocity (

p = mv

).

Soru 3Soru →

A $4,000 \text{ kg}$ empty railcar is rolling along a straight, level track at a velocity of $6 \text{ m/s}$ . It collides and automatically couples with a stationary loaded railcar that has a mass of $8,000 \text{ kg}$ . Assuming no external friction is acting on the railcars, what is the final velocity of the two coupled railcars immediately after the impact?

2 \text{ m/s}

3 \text{ m/s}

6 \text{ m/s}

19.6 \text{ m/s}

Cevabı ve açıklamayı göster

Cevap: $2 \text{ m/s}$

Cevap

The final velocity is

2 \text{ m/s}

.

By the law of conservation of momentum, the total momentum before the collision equals the total momentum after. The initial momentum is

4,000 \text{ kg} \times 6 \text{ m/s} = 24,000 \text{ kg}\cdot\text{m/s}

. After the railcars couple, the new total mass is

12,000 \text{ kg}

. Dividing the total momentum by the total mass gives a final velocity of

2 \text{ m/s}

.

Adım Adım Çözüm

1

Calculate the total initial momentum of the system.

p_{initial} = 4,000 \text{ kg} \times 6 \text{ m/s} = 24,000 \text{ kg}\cdot\text{m/s}

Because momentum is conserved in the collision, finding the total momentum before impact is required.

2

Determine the total mass of the coupled railcars.

m_{total} = 4,000 \text{ kg} + 8,000 \text{ kg} = 12,000 \text{ kg}

In an inelastic collision where objects couple together, they move as a single combined mass after impact.

3

Calculate the final velocity using the conserved momentum and total mass.

v_{final} = \frac{24,000 \text{ kg}\cdot\text{m/s}}{12,000 \text{ kg}} = 2 \text{ m/s}

Dividing the total conserved momentum by the new total mass isolates the final velocity of the combined system.

Anahtar Kavram

Conservation of Momentum in Inelastic Collisions

Soru 4Soru →

Momentum is defined as the product of an object's mass and its velocity ( $p = mv$ ). Arrange the following vehicles in order of their total momentum, from the lowest to the highest.

Öğeleri doğru sıraya koymak için sürükleyin

Cevabı ve açıklamayı göster

Cevap

The correct sequence from lowest to highest momentum is: motorcycle, bus, car, and finally the truck.

The correct sequence is found by multiplying each vehicle's mass by its velocity and then ordering the products from smallest to largest: motorcycle (

10,000

), bus (

25,000

), car (

30,000

), and truck (

36,000

).

Adım Adım Çözüm

1

Recall the formula for calculating momentum.

p = m \times v

Momentum requires multiplying the mass of the object by its velocity.

2

Calculate the momentum for the motorcycle.

400 \text{ kg} \times 25 \text{ m/s} = 10,000 \text{ kg}\cdot\text{m/s}

This establishes the total momentum for the first vehicle.

3

Calculate the momentum for the bus.

5,000 \text{ kg} \times 5 \text{ m/s} = 25,000 \text{ kg}\cdot\text{m/s}

This establishes the total momentum for the second vehicle.

4

Calculate the momentum for the car.

1,500 \text{ kg} \times 20 \text{ m/s} = 30,000 \text{ kg}\cdot\text{m/s}

This establishes the total momentum for the third vehicle.

5

Calculate the momentum for the truck.

3,000 \text{ kg} \times 12 \text{ m/s} = 36,000 \text{ kg}\cdot\text{m/s}

This establishes the total momentum for the fourth vehicle.

6

Order the resulting values from lowest to highest.

10,000 < 25,000 < 30,000 < 36,000

The question requires arranging the vehicles in ascending order based on their momentum.

Anahtar Kavram

The total momentum of a moving object is directly proportional to both its mass and its velocity.

Tahmini Süre:1m 0s

Soru 5Soru →

A sledgehammer head with a weight of $19.6 \text{ N}$ on Earth strikes a metal spike with a downward velocity of $4 \text{ m/s}$ . The impact brings the hammer head to a complete stop in $20 \text{ ms}$ (milliseconds). What is the average impact force exerted on the spike? (Assume $g = 9.8 \text{ m/s}^2$ )

0.4 \text{ N}

3,920 \text{ N}

400 \text{ N}

0.16 \text{ N}

Cevabı ve açıklamayı göster

Cevap: $400 \text{ N}$

Cevap

The correct answer is

400 \text{ N}

.

The force is found by first converting weight to mass (

19.6 / 9.8 = 2 \text{ kg}

) and time to seconds (

20 \text{ ms} = 0.02 \text{ s}

). The change in momentum is

2 \text{ kg} \times 4 \text{ m/s} = 8 \text{ kg} \cdot \text{m/s}

. Dividing this change by the impact duration (

0.02 \text{ s}

) gives an average impact force of

400 \text{ N}

.

Adım Adım Çözüm

1

Calculate the mass of the sledgehammer head.

m = \frac{W}{g} = \frac{19.6 \text{ N}}{9.8 \text{ m/s}^2} = 2 \text{ kg}

Momentum equations require mass, not weight.

2

Convert the impact time to standard SI units (seconds).

t = 20 \text{ ms} = 0.02 \text{ s}

Standard units must be used to calculate force in Newtons.

3

Calculate the change in momentum (impulse).

\Delta p = m \times \Delta v = 2 \text{ kg} \times 4 \text{ m/s} = 8 \text{ kg} \cdot \text{m/s}

Impulse is equal to the change in momentum.

4

Calculate the average impact force.

F = \frac{\Delta p}{\Delta t} = \frac{8 \text{ kg} \cdot \text{m/s}}{0.02 \text{ s}} = 400 \text{ N}

Force is the rate of change of momentum.

Anahtar Kavram

Impulse and Momentum

Soru 6Soru →

A test sled has a weight of $2,940 \text{ N}$ (where $g = 9.8 \text{ m/s}^2$ ). During a braking test, a friction track applies a constant drag force of $588 \text{ N}$ . If it takes exactly $10 \text{ seconds}$ for the sled to come to a complete halt, what was its initial velocity?

1.96 \text{ m/s}

2 \text{ m/s}

19.6 \text{ m/s}

50 \text{ m/s}

Cevabı ve açıklamayı göster

Cevap: $19.6 \text{ m/s}$

Cevap

19.6 \text{ m/s}

The correct answer applies the impulse-momentum theorem. First, the mass is found by dividing the weight by gravity (

2,940 \text{ N} / 9.8 \text{ m/s}^2 = 300 \text{ kg}

). Then, the impulse is calculated as the braking force multiplied by time (

588 \text{ N} \times 10 \text{ s} = 5,880 \text{ N}\cdot\text{s}

). Because impulse equals the change in momentum (

m \times \Delta v

), dividing the impulse by the mass yields the sled's initial velocity (

5,880 \text{ N}\cdot\text{s} / 300 \text{ kg} = 19.6 \text{ m/s}

).

Adım Adım Çözüm

1

Calculate the mass of the sled from its given weight.

m = 2,940 \text{ N} / 9.8 \text{ m/s}^2 = 300 \text{ kg}

Momentum and kinematic equations require mass (in kg), not weight (in N).

2

Calculate the total impulse applied by the friction track.

\text{Impulse} = F \times t = 588 \text{ N} \times 10 \text{ s} = 5,880 \text{ N}\cdot\text{s}

Impulse is defined as the product of the average force and the time duration over which it acts.

3

Relate the impulse to the change in velocity.

5,880 = 300 \times \Delta v

, which solves to

\Delta v = 19.6 \text{ m/s}

.

The impulse-momentum theorem states that impulse equals the change in momentum (

\Delta p = m \times \Delta v

). Since the sled stops, the change in velocity equals its initial velocity.

Anahtar Kavram

Impulse and Momentum Conservation

Alternatif Yöntem

You can also solve this using Newton's Second Law and basic kinematics. First, find the deceleration:

a = F / m = 588 / 300 = 1.96 \text{ m/s}^2

. Then, use the kinematic equation

v_f = v_i - a \times t

. Since

v_f = 0

,

v_i = a \times t = 1.96 \times 10 = 19.6 \text{ m/s}

.

Tahmini Süre:1m 30s

Soru 7Soru →

A carpenter uses a $5\text{ kg}$ pneumatic nail gun. The gun fires a $50\text{ gram}$ nail forward with a velocity of $100\text{ m/s}$ . Based on the conservation of momentum, if the gun is unrestrained, what is its backward recoil speed?

0.1\text{ m/s}

1\text{ m/s}

100\text{ m/s}

1,000\text{ m/s}

Cevabı ve açıklamayı göster

Cevap: $1\text{ m/s}$

Cevap

The nail gun will have a backward recoil speed of

1\text{ m/s}

.

According to the law of conservation of momentum, the forward momentum of the nail must be perfectly balanced by the backward momentum of the nail gun. First, convert the nail's mass to standard units (

50\text{ g} = 0.05\text{ kg}

). The nail's momentum is

0.05\text{ kg} \times 100\text{ m/s} = 5\text{ kg}\cdot\text{m/s}

. Because the gun's mass is

5\text{ kg}

, dividing the total momentum (

5

) by its mass (

5

) gives a recoil speed of

1\text{ m/s}

.

Adım Adım Çözüm

1

Convert the nail's mass from grams to kilograms to ensure consistent standard units.

50\text{ grams} = 0.05\text{ kg}

.

Momentum equations require matching mass units on both sides, typically kilograms.

2

Calculate the forward momentum of the nail.

p_{nail} = m \times v = 0.05\text{ kg} \times 100\text{ m/s} = 5\text{ kg}\cdot\text{m/s}

.

Momentum is the product of mass and velocity.

3

Apply the principle of conservation of momentum.

Initial momentum is zero, so

p_{gun} = p_{nail}

. The gun's backward momentum must be

5\text{ kg}\cdot\text{m/s}

.

In a closed system with no external forces, the total momentum before and after firing must remain equal.

4

Calculate the backward recoil speed of the nail gun.

v_{gun} = \frac{p_{gun}}{m_{gun}} = \frac{5\text{ kg}\cdot\text{m/s}}{5\text{ kg}} = 1\text{ m/s}

.

Rearranging the momentum formula (

p = mv

) solves for the unknown velocity.

Anahtar Kavram

Conservation of Momentum (Recoil)

Momentum and Collisions

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