a car pulling two trailers accelerates from 10m/s to 12m/s in 10s. if the masses of the car and the trailers are respectively 2000kg, 500kg and 300kg.calculate the tension in the tow bar
a)between the car and 500kg trailor
b)between the 500kg and 300kg trailers
160n and 60n
500n and 100n
To calculate the tension in the tow bar between the car and each trailer, we need to use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration.
a) Tension between the car and the 500kg trailer:
To find the tension between the car and the 500kg trailer, we need to calculate the net force acting on the system. This force can be determined by using the formula:
Force = Mass × Acceleration
First, we need to calculate the total mass of the system, which is the sum of the car's mass and the 500kg trailer's mass:
Total Mass = Mass of Car + Mass of 500kg Trailer
Total Mass = 2000kg + 500kg
Total Mass = 2500kg
Next, we need to calculate the acceleration of the system. To find the acceleration, we can use the formula:
Acceleration = (Final Velocity - Initial Velocity) / Time
Acceleration = (12m/s - 10m/s) / 10s
Acceleration = 0.2m/s²
Now we can calculate the force acting on the system:
Force on the system = Total Mass × Acceleration
Force on the system = 2500kg × 0.2m/s²
Force on the system = 500N
Since there are no other external forces acting on the system, the force is transmitted equally through each trailer. Therefore, the tension in the tow bar between the car and the 500kg trailer is also 500N.
b) Tension between the 500kg and 300kg trailers:
Similarly, to find the tension between the 500kg and 300kg trailers, we can use the same approach. The total mass for this calculation will be the sum of the masses of the 500kg trailer and the 300kg trailer:
Total Mass = Mass of 500kg Trailer + Mass of 300kg Trailer
Total Mass = 500kg + 300kg
Total Mass = 800kg
The acceleration remains the same since it is the same system as before:
Acceleration = 0.2m/s²
Now we can calculate the force acting on the system:
Force on the system = Total Mass × Acceleration
Force on the system = 800kg × 0.2m/s²
Force on the system = 160N
Therefore, the tension in the tow bar between the 500kg and 300kg trailers is 160N.