Understanding Force and Calculation
Force is an external influence that can change the velocity or motion of an object. It can also be defined as the product of mass and acceleration. In this scenario, we have a 1280-kg car pulling a 350-kg trailer. The car exerts a horizontal force of 3.6 x 10³N against the ground in order to accelerate. We need to calculate the force that the car exerts on the trailer.
Mathematically, force F = mass * acceleration. Let's denote the mass of the car as m₁ (1280 kg) and the mass of the trailer as m₂ (350 kg). The coefficient of friction for the trailer is given as 0.15.
The force exerted by the car on the trailer can be calculated using the formula:
F = (m₁ + m₂)a + Ff
Where:
Ff = μm₂g (frictional force)
a = acceleration
By substituting the values:
3.6 x 10³N = (1280 + 350)a + 0.15 * 350 * 9.81
Solving the above equation, we can calculate 'a' as 1.89 m/sec².
The total force exerted on the trailer will be:
Fₙ = m₂a + μm₂g
Fₙ = 350 * 1.89 + (0.15 * 350 * 9.81)
Fₙ = 1176N
Therefore, the car will exert a force of 1176N on the trailer during acceleration.
Conclusion
In conclusion, the force exerted by a 1280-kg car on a 350-kg trailer can be calculated using the principles of force, mass, and acceleration. By taking into account the coefficient of friction and the external force applied by the car, we can determine the exact force exerted on the trailer during acceleration.
What is the formula for calculating force? How is force related to mass and acceleration?
The formula for calculating force is F = m * a, where F is the force, m is the mass of the object, and a is the acceleration. Force is directly proportional to mass and acceleration, meaning that an increase in either mass or acceleration will result in a greater force being exerted on an object.