A hill is 290 m long and makes an angle of 10 degrees with the horizontal. As a 68 kg jogger runs up the hill, how much work does gravity do on the jogger?
how high did he go? height= 290*sin10
work= mass*g*height
110J
To calculate the work done by gravity on the jogger, we need to determine the vertical component of the gravitational force.
The vertical component of the gravitational force can be calculated using the formula:
F_vertical = m * g * sin(theta)
Where:
m = mass of the jogger = 68 kg
g = acceleration due to gravity = 9.8 m/s^2
theta = angle of the hill = 10 degrees
Let's calculate the vertical component of the gravitational force:
F_vertical = 68 kg * 9.8 m/s^2 * sin(10 degrees)
F_vertical ≈ 117.39 N
The work done by gravity can be calculated using the formula:
Work = force * distance * cos(theta)
Where:
force = F_vertical = 117.39 N
distance = length of the hill = 290 m
theta = angle of the hill = 10 degrees
Let's calculate the work done by gravity:
Work = 117.39 N * 290 m * cos(10 degrees)
Work ≈ 33343.89 J
Therefore, gravity does approximately 33343.89 Joules of work on the jogger as they run up the hill.
To calculate the work done by gravity on the jogger, we need to consider the vertical component of the force of gravity. The horizontal component does not contribute to the work done since it is perpendicular to the displacement of the jogger along the hill.
To find the vertical component of the force of gravity, we can use trigonometry. The force of gravity (mg) can be broken down into two components: one parallel to the hill (mg sinθ) and one perpendicular to the hill (mg cosθ), where θ is the angle the hill makes with the horizontal.
In this case, the angle (θ) is given as 10 degrees. The mass of the jogger (m) is given as 68 kg.
Step 1: Calculate the vertical component of the force of gravity:
Vertical component (mg sinθ) = (68 kg) × (9.8 m/s²) × sin(10°) ≈ 117.82 N
Step 2: Calculate the work done by gravity on the jogger:
Work done by gravity = Force × Displacement × cos(θ)
The displacement (s) along the hill is given as 290 m. Since the jogger is running up the hill, we assume that the displacement is in the same direction as the force of gravity.
Work done by gravity = (117.82 N) × (290 m) × cos(10°) ≈ 33728 J
Therefore, gravity does approximately 33728 Joules of work on the jogger.