Questions: No Parque Estadual do Guartelá, em Tibagi, no Paraná, está localizado o cânion do Rio lapó, o sexto maior cânion do planeta, em extensão. Um alpinista de massa 80 kg, transportando uma mochila de 20 kg Considerando que a aceleração da gravidade é igual a 10 m / s^2, assinale a alternativa que apresenta, corretamente, o trabalho τ realizado pelo alpinista para subir essa montanha.

Solution Steps

The total mass of the alpinist and the backpack is the sum of their individual masses. The alpinist has a mass of 80 kg, and the backpack has a mass of 20 kg.

\[ \text{Total mass} = 80 \, \text{kg} + 20 \, \text{kg} = 100 \, \text{kg} \]

The gravitational force acting on the alpinist and the backpack is given by the product of the total mass and the acceleration due to gravity. The acceleration due to gravity is \(10 \, \text{m/s}^2\).

\[ F = m \cdot g = 100 \, \text{kg} \times 10 \, \text{m/s}^2 = 1000 \, \text{N} \]

The work done (\(\tau\)) by the alpinist in climbing the mountain is the product of the gravitational force and the height of the mountain. The height of the mountain is 400 m.

\[ \tau = F \cdot h = 1000 \, \text{N} \times 400 \, \text{m} = 400,000 \, \text{J} \]

Final Answer