Math / Algebra

Question74. A helicopter flies over the arctic ice pack at a constant altitude, towing an airborne $129-\mathrm{kg}$ laser sensor that measures the thickness of the ice (see the drawing). The helicopter and the sensor both move only in the horizontal direction and have a horizontal acceleration of magnitude $2.84 \mathrm{~m} / \mathrm{s}^{2}$ . Ignoring air resistance, find the tension in the cable towing the sensor.

Studdy Solution

STEP 1

What is this asking? We need to find the force in the cable pulling a sensor being towed by a helicopter accelerating horizontally. Watch out! The altitude of the helicopter is irrelevant, so don't let it trick you!
We only care about the horizontal forces.

STEP 2

1. Analyze the forces
2. Calculate the tension

STEP 3

Alright, picture this: a helicopter zipping across the arctic, towing a sensor.
The sensor is just cruising along with the helicopter, right?
That means it's accelerating at the same rate as the helicopter.

STEP 4

What's making the sensor accelerate?
It's the tension in the cable!
That cable is the only thing pulling the sensor forward horizontally.
No cable, no acceleration!

STEP 5

Newton's second law tells us that force equals mass times acceleration: $F = m \cdot a$ .
Here, the force is the tension ( $T$ ) in the cable, the mass ( $m$ ) is the mass of the sensor ( $129 \text{ kg}$ ), and the acceleration ( $a$ ) is the horizontal acceleration ( $2.84 \text{ m/s}^2$ ).

STEP 6

Let's plug the values into our equation: $T = m \cdot a$ $T = 129 \text{ kg} \cdot 2.84 \text{ m/s}^2$

STEP 7

Time to crunch the numbers!
Multiplying the mass and the acceleration gives us the tension: $T = 366.36 \text{ N}$

STEP 8

The tension in the cable towing the sensor is $\mathbf{366.36 \text{ N}}$ .

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Studdy Solution

STEP 1

What is this asking? We need to find the force in the cable pulling a sensor being towed by a helicopter accelerating horizontally. Watch out! The altitude of the helicopter is irrelevant, so don't let it trick you!
We only care about the horizontal forces.

STEP 2

1. Analyze the forces
2. Calculate the tension

STEP 3

Alright, picture this: a helicopter zipping across the arctic, towing a sensor.
The sensor is just cruising along with the helicopter, right?
That means it's accelerating at the same rate as the helicopter.

STEP 4

What's making the sensor accelerate?
It's the tension in the cable!
That cable is the only thing pulling the sensor forward horizontally.
No cable, no acceleration!

STEP 5

Newton's second law tells us that force equals mass times acceleration: $F = m \cdot a$ .
Here, the force is the tension ( $T$ ) in the cable, the mass ( $m$ ) is the mass of the sensor ( $129 \text{ kg}$ ), and the acceleration ( $a$ ) is the horizontal acceleration ( $2.84 \text{ m/s}^2$ ).

STEP 6

Let's plug the values into our equation: $T = m \cdot a$ $T = 129 \text{ kg} \cdot 2.84 \text{ m/s}^2$

STEP 7

Time to crunch the numbers!
Multiplying the mass and the acceleration gives us the tension: $T = 366.36 \text{ N}$

STEP 8

The tension in the cable towing the sensor is $\mathbf{366.36 \text{ N}}$ .

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Studdy Solution

STEP 1

What is this asking? We need to find the force in the cable pulling a sensor being towed by a helicopter accelerating horizontally. Watch out! The altitude of the helicopter is irrelevant, so don't let it trick you!We only care about the horizontal forces.

STEP 2

1. Analyze the forces2. Calculate the tension

STEP 3

Alright, picture this: a helicopter zipping across the arctic, towing a sensor.The sensor is just cruising along with the helicopter, right?That means it's accelerating at the *same rate* as the helicopter.

STEP 4

What's making the sensor accelerate?It's the **tension** in the cable!That cable is the only thing pulling the sensor forward horizontally.No cable, no acceleration!

STEP 5

STEP 6

Let's plug the values into our equation: T=m⋅aT = m \cdot aT=m⋅a T=129 kg⋅2.84 m/s2T = 129 \text{ kg} \cdot 2.84 \text{ m/s}^2T=129 kg⋅2.84 m/s2

STEP 7

Time to crunch the numbers!Multiplying the **mass** and the **acceleration** gives us the **tension**: T=366.36 NT = 366.36 \text{ N}T=366.36 N

STEP 8

The tension in the cable towing the sensor is 366.36 N\mathbf{366.36 \text{ N}}366.36 N.

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? We need to find the force in the cable pulling a sensor being towed by a helicopter accelerating horizontally. Watch out! The altitude of the helicopter is irrelevant, so don't let it trick you!
We only care about the horizontal forces.

1. Analyze the forces
2. Calculate the tension

Alright, picture this: a helicopter zipping across the arctic, towing a sensor.
The sensor is just cruising along with the helicopter, right?
That means it's accelerating at the same rate as the helicopter.

What's making the sensor accelerate?
It's the tension in the cable!
That cable is the only thing pulling the sensor forward horizontally.
No cable, no acceleration!

Let's plug the values into our equation: $T = m \cdot a$ $T = 129 \text{ kg} \cdot 2.84 \text{ m/s}^2$

Time to crunch the numbers!
Multiplying the mass and the acceleration gives us the tension: $T = 366.36 \text{ N}$

The tension in the cable towing the sensor is $\mathbf{366.36 \text{ N}}$ .