a tractor is towing a large trailer on a horizontal road at a constant speed of 15 km/h. The mass of the is 1,3 t and the mass of the load is 5 t. A wind is blowing from behind the trailer with an effective force of 320 N. The tractive resistance of the trailer and load is 270 N/t on this road. Calculate the work done by the tractor in 30 minutes.
To calculate the work done by the tractor, we need to determine the net force acting on the trailer and load and then multiply it by the distance travelled.
Given:
Tractor speed, v = 15 km/h
Tractor mass, m1 = 1.3 t = 1300 kg
Load mass, m2 = 5 t = 5000 kg
Wind force, F_wind = 320 N
Tractive resistance, R = 270 N/t
First, let's convert the speed from km/h to m/s:
15 km/h = (15 * 1000 m) / (60 * 60 s) = 4.1667 m/s
The net force acting on the trailer and load can be calculated as:
F_net = (m1 + m2) * a,
where a is the acceleration. Since the tractor is moving at a constant speed, the acceleration is zero, so the net force is also zero.
Next, let's calculate the tractive resistance force:
R_total = R * (m1 + m2)
= 270 N/t * (1300 kg + 5000 kg)
= 7 * 270 N
= 1890 N
We also need to consider the effective force of the wind. Since the wind is blowing from behind the trailer, it helps reduce the tractive resistance, so we subtract it from the total tractive resistance force:
F_net = R_total - F_wind
= 1890 N - 320 N
= 1570 N
The work done by the tractor is given by:
Work = F_net * d,
where d is the distance travelled.
To find the distance, we can use the formula:
Distance = speed * time,
where the time is given as 30 minutes, but we need to convert it to seconds:
30 minutes = 30 * 60 s = 1800 s
Therefore, the distance is:
Distance = 4.1667 m/s * 1800 s
= 7499.988 m
Finally, substituting the values into the work formula:
Work = F_net * distance
= 1570 N * 7499.988 m
= 11,749,983.16 J
Therefore, the work done by the tractor in 30 minutes is approximately 11,749,983.16 Joules.
To calculate the work done by the tractor in 30 minutes, we can use the equation:
Work = Force × Distance.
First, let's calculate the force required to overcome the tractive resistance of the trailer and load:
Force = Tractive resistance × Mass of the trailer and load
= 270 N/t × (1.3 t + 5 t)
= 270 N/t × 6.3 t
= 1701 N.
Next, we need to calculate the distance the tractor travels in 30 minutes. Since the tractor is moving at a constant speed of 15 km/h, we convert this speed to meters per second:
Speed = 15 km/h = (15 × 1000 m) / (60 × 60 s)
= 250 m/s.
Distance = Speed × Time
= 250 m/s × (30 × 60 s)
= 450,000 m.
Now, we can calculate the work done by the tractor:
Work = Force × Distance
= 1701 N × 450,000 m
= 765,450,000 N·m
= 765,450 J. (since 1 Joule (J) is equal to 1 N·m.)
Therefore, the work done by the tractor in 30 minutes is 765,450 Joules.