A student abseils down the outside of a building using a rope. The mass of the student is 55 kg. The rope, of negligible mass, is attached to a fixed point X at the top of the building. The rope makes an angle of 15° to the building. (a) Calculate the weight W of the student. (b) Determine the tension T in the rope. (c) As the student abseils down the building the angle the rope makes with the building decreases. State whether the tension in the rope increases, decreases or stays the same. Justify your answer.

Scottish Highers Physics Forces, Energy and Power: A student abseils down the outsi

A student abseils down the outside of a building using a rope - Scottish Highers Physics - Question 2 - 2019

Question 2

A student abseils down the outside of a building using a rope. The mass of the student is 55 kg. The rope, of negligible mass, is attached to a fixed point X at th... show full transcript

Worked Solution & Example Answer:A student abseils down the outside of a building using a rope - Scottish Highers Physics - Question 2 - 2019

Step 1

Calculate the weight W of the student.

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Answer

The weight W of the student can be calculated using the formula:

$W = mg$

Where:

m is the mass of the student (55 kg)
g is the acceleration due to gravity (approximately 9.8 m/s²)

Substituting the values:

$W = 55 imes 9.8 = 539 ext{ N (approximately 540 N)}$

Step 2

Determine the tension T in the rope.

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Answer

To determine the tension T in the rope, we need to consider the components of forces acting on the student. The vertical component of the tension balances the weight:

$W = T_y$

Where:

$T_y = T imes ext{cos}(15°)$

From part (a), we know that W = 540 N:

$540 = T imes ext{cos}(15°)$

Solving for T:

T \approx 560 ext{ N}$$

Step 3

As the student abseils down the building the angle the rope makes with the building decreases. State whether the tension in the rope increases, decreases or stays the same.

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Answer

The tension in the rope decreases as the angle decreases. This is because the cosine of the angle decreases as the angle increases, leading to a decrease in the vertical component of the tension that balances the weight. As the angle of the rope decreases, the horizontal component of the force also decreases, which results in a lower value for the tension in the rope.

A student abseils down the outside of a building using a rope - Scottish Highers Physics - Question 2 - 2019

Worked Solution & Example Answer:A student abseils down the outside of a building using a rope - Scottish Highers Physics - Question 2 - 2019

Calculate the weight W of the student.

Determine the tension T in the rope.

As the student abseils down the building the angle the rope makes with the building decreases. State whether the tension in the rope increases, decreases or stays the same.

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