Have you ever wondered how much force a 1-ton truck needs to accelerate? This article will help you discover that through an interesting and easy-to-understand physics problem, applying the basic principles of Newton’s laws.
Problem Summary
A truck with a mass of m = 1 ton starts moving and reaches a speed of 18 km/h after 10 seconds. The resistance force from the road acting on the truck is 500N. The question is: Calculate the driving force of the truck’s engine.
Problem Analysis and Solution Approach
To solve this problem, we will apply Newton’s second law of motion. This law states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to the mass of the object. In other words, for the truck to move and accelerate, the driving force from the engine must be greater than the resistance force.
We need to determine:
- Acceleration of the truck: Based on the initial velocity (0 km/h), the velocity after 10 seconds (18 km/h), and the acceleration time (10s).
- Net force acting on the truck: This net force is the sum of the engine’s driving force and the road’s resistance force.
- Engine’s driving force: Use Newton’s second law to calculate.
Detailed Solution
Step 1: Convert Units and Calculate Acceleration
- Convert velocity units: The velocity needs to be converted from km/h to m/s to be consistent with SI units in physics. 18 km/h = 18 * (1000 m / 3600 s) = 5 m/s
- Calculate acceleration (a): Acceleration is the change in velocity over time. Since the truck starts from rest, the initial velocity is 0 m/s. Acceleration ( a = frac{v – v_0}{t} = frac{5 m/s – 0 m/s}{10 s} = 0.5 m/s^2 )
Step 2: Apply Newton’s Second Law
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Convert mass units: The truck’s mass is given as 1 ton, which needs to be converted to kg: 1 ton = 1000 kg
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Apply Newton’s Second Law (F = ma): Where:
- F is the net force acting on the truck (N)
- m is the mass of the truck (kg)
- a is the acceleration of the truck (m/s²)
The net force F here is the difference between the engine’s driving force (Fpđ) and the resistance force (Fc). We assume the positive direction is the direction of the truck’s movement, so the driving force is in the positive direction and the resistance force is in the opposite direction.
The formula becomes: ( F = F_{pđ} – F_c = ma )
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Calculate the driving force (Fpđ): From the above formula, we deduce: ( F_{pđ} = ma + Fc ) Substituting the values: ( F{pđ} = (1000 kg * 0.5 m/s^2) + 500 N ) ( F_{pđ} = 500 N + 500 N = 1000 N )
Diagram showing forces acting on the 1-ton truck
Conclusion
Therefore, the driving force of the engine of a 1-ton truck in this case is 1000N. This means that the truck’s engine needs to generate a driving force of 1000 Newton to accelerate to a speed of 18km/h in 10 seconds, when the resistance force from the environment is 500N. This problem illustrates the basic relationship between force, mass, and acceleration, which are important factors in the operation and design of trucks and other vehicles.
