A truck of mass 3000 kg is harnessed to a trailer (Trailer A) of mass 1000 kg. The trailer is hooked to ANOTHER trailer (Trailer B) of mass 500 kg. The truck begins to accelerate to the right at 1 m/s2, pulling the trailers along. What is the ratio of the force the truck exerts on Trailer A to the force Trailer A exerts on Trailer B?
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To solve this problem, we need to use Newton's second law of motion, which states that the force (F) acting on an object is equal to the mass (m) of the object multiplied by its acceleration (a):
F = m * a
Let's calculate the forces exerted on Trailer A and Trailer B separately.
For Trailer A:
Mass of Trailer A (m1) = 1000 kg
Acceleration of the truck (a) = 1 m/s^2
Force exerted by the truck on Trailer A (F1) = m1 * a
F1 = 1000 kg * 1 m/s^2
F1 = 1000 N
For Trailer B:
Mass of Trailer B (m2) = 500 kg
Acceleration of the truck (a) = 1 m/s^2
Force exerted by Trailer A on Trailer B (F2) = m2 * a
F2 = 500 kg * 1 m/s^2
F2 = 500 N
Now, let's calculate the ratio of the force the truck exerts on Trailer A to the force Trailer A exerts on Trailer B:
Ratio = F1 / F2
Ratio = 1000 N / 500 N
Ratio = 2
Therefore, the ratio of the force the truck exerts on Trailer A to the force Trailer A exerts on Trailer B is 2:1.
To find the ratio of the force the truck exerts on Trailer A to the force Trailer A exerts on Trailer B, we need to consider Newton's second law of motion, which states that the force acting on a body is equal to the mass of the body multiplied by its acceleration.
1. Calculate the total mass of Trailer A and Trailer B:
- Mass of Trailer A = 1000 kg
- Mass of Trailer B = 500 kg
- Total mass of Trailer A and Trailer B = Mass of Trailer A + Mass of Trailer B = 1000 kg + 500 kg = 1500 kg
2. Calculate the force exerted by the truck on Trailer A:
- Mass of the truck = 3000 kg
- Acceleration = 1 m/s^2
- Force exerted by the truck on Trailer A = Mass of Trailer A and B * Acceleration = 1500 kg * 1 m/s^2 = 1500 N
3. Calculate the force exerted by Trailer A on Trailer B:
- Since the truck is pulling both trailers together, the force exerted by Trailer A on Trailer B is the same as the force exerted by the truck on Trailer A, which is 1500 N.
Therefore, the ratio of the force the truck exerts on Trailer A to the force Trailer A exerts on Trailer B is 1500 N : 1500 N, or simply 1:1.