a 725 pound trailer is sitting on a ramp inclined at 36 degrees.
how much force is required to keep the trailer from rolling down the ramp??
To calculate the force required to keep the trailer from rolling down the ramp, we'll need to consider the gravitational force acting on the trailer and the frictional force opposing its motion.
1. Gravitational Force:
The gravitational force acting on the trailer is the weight of the trailer, which is given as 725 pounds. However, we need to convert pounds to Newtons to maintain consistent units. 1 pound is approximately equal to 4.44822 Newtons, so the weight of the trailer can be calculated as follows:
Weight = 725 pounds × 4.44822 N/pound
2. Decomposing the Weight:
The weight of the trailer can be decomposed into two components: the component acting perpendicular to the ramp's surface and the component parallel to the ramp's surface. The component parallel to the ramp is responsible for trying to roll the trailer down the ramp, while the component perpendicular to the ramp can be disregarded in this scenario.
Force parallel to the ramp = Weight × sin(θ), where θ represents the angle of inclination, which is given as 36 degrees.
3. Determining the Frictional Force:
The force required to keep the trailer from rolling down the ramp is equal to the frictional force opposing its motion. This frictional force can be calculated using the formula:
Frictional force = Force parallel to the ramp × coefficient of friction
The coefficient of friction depends on the surface of the ramp and the trailer. Let's assume a coefficient of friction of 0.5, which is common for rubber on concrete.
4. Calculation:
Now, we can calculate the force required to keep the trailer from rolling down the ramp using the above information:
Force required = Frictional force = Force parallel to the ramp × coefficient of friction
Please note that for a more precise calculation, it is always advisable to consider the specific weight of the trailer and the actual coefficient of friction between its tires and the ramp's surface.
Using the above steps, you will be able to find the force required to keep the trailer from rolling down the ramp.
Mass = 725Lbs * 0.454kg/Lb = 329.2 kg.
m*g = 329.2 * 9.8 = 3226 N. = Wt. of
trailer.
Fp = 3226*sin36 = 1896 N. = Force
parallel to the ramp.
F = Fp = 1896 N. Required.