a tractor is towing a large trailer on a horizontal road at a constant speed of 15 km/h. The mass of the trailer is 1,3 t and the mass of the load is 5 t. A wind is blowing from behind the trailer with an affective force of 320 N. The tractive resistance of the trailer and load is 270 N/t on this road. Calculate the force exerted by the towbar of the tractor.
To calculate the force exerted by the towbar of the tractor, we need to determine the net force acting on the trailer and load.
The gravitational force acting on the trailer and load is given by:
Gravitational force = (mass of the trailer + mass of the load) * acceleration due to gravity
= (1.3 t + 5 t) * 9.8 m/s^2 (converting tons to kg)
= 6.3 t * 9.8 m/s^2 * 1000 kg/t (converting tons to kg)
= 61,740 N
The tractive resistance force acting on the trailer and load is given by:
Tractive resistance force = (tractive resistance per ton) * (mass of the trailer + mass of the load)
= 270 N/t * (1.3 t + 5 t)
= 270 N/t * 6.3 t
= 1,701 N
The net force acting on the trailer and load is the sum of the tractive resistance force and the force exerted by the wind:
Net force = Tractive resistance force + Force exerted by the wind
= 1,701 N + 320 N
= 2,021 N
Since the tractor is towing the trailer and load at a constant speed, the net force must be zero. Therefore, the force exerted by the towbar of the tractor is equal in magnitude and opposite in direction to the net force. So, the force exerted by the towbar of the tractor is 2,021 N, directed opposite to the motion of the trailer and load.
To calculate the force exerted by the towbar of the tractor, we need to consider the forces acting on the trailer.
Given:
Speed of the tractor, v = 15 km/h = 15,000 m/3600 s = 4.17 m/s
Mass of the trailer, m_t = 1.3 t = 1.3 * 1000 kg = 1300 kg
Mass of the load, m_l = 5 t = 5 * 1000 kg = 5000 kg
Tractive resistance, R = 270 N/t
First, let's calculate the total resistance of the trailer and load:
Total resistance, T = R * (m_t + m_l)
= 270 N/t * (1300 kg + 5000 kg)
= 270 N/kg * 6300 kg
= 1,701,000 N
Next, let's calculate the force due to the wind:
Force due to wind, F_wind = 320 N (given)
Now, we can calculate the force exerted by the towbar:
Force exerted by the towbar, F_towbar = T - F_wind
= 1,701,000 N - 320 N
= 1,700,680 N
Therefore, the force exerted by the towbar of the tractor is 1,700,680 N.