Determine the work a hiker must do on a 15.8 kg backpack to carry it up a hill of height h = 13.5 m. The hill is not an even slope but rather an irregular curve as in the figure.Determine also the work done by gravity on the backpack
Can't find the work done by gravity
To determine the work a hiker must do on a backpack to carry it up a hill, we need to use the formula for work:
Work = Force * Distance * Cosine of the angle between the force and displacement.
In this case, the force we need to overcome to carry the backpack uphill is the force of gravity acting on the backpack. The work done by gravity on the backpack will be negative since it opposes the motion.
First, let's calculate the work done by the hiker. Assuming the backpack is lifted vertically, the angle between the force and displacement is 0 degrees. Hence, the equation simplifies to:
Work_hiker = Force_hiker * Distance * Cos(0) = Force_hiker * Distance
The force the hiker needs to overcome is the weight of the backpack, which is given by:
Force_hiker = Mass * Gravity
Plugging in the values:
Mass = 15.8 kg
Gravity = 9.8 m/s^2
Force_hiker = 15.8 kg * 9.8 m/s^2 = 154.84 N (Newtons)
Now, we can calculate the work done by the hiker:
Work_hiker = Force_hiker * Distance
The distance traveled is given as h = 13.5 m.
Work_hiker = 154.84 N * 13.5 m = 2092.74 Joules (J)
To determine the work done by gravity on the backpack, we use the same formula but with a negative sign:
Work_gravity = -Force_gravity * Distance * Cos(0) = -Force_gravity * Distance
The force of gravity acting on the backpack is:
Force_gravity = Mass * Gravity = 15.8 kg * 9.8 m/s^2 = 154.84 N (Newtons)
Work_gravity = -Force_gravity * Distance
Work_gravity = -154.84 N * 13.5 m = -2092.74 Joules (J)
So, the work done by the hiker is 2092.74 Joules (J), and the work done by gravity is -2092.74 Joules (J).