A curve in a road is banked. There is a car on the curve. What is the component of its weight parallel to the incline? The acceleration of gravity is 9.8 m/s 2 . Answer in units of N
Mass of Car: 1.5Mg
coefficient of friction: 0.17
theta: 25 degrees
Hardly anyone uses Megagrams for mass.
Mass of Car: 1500 kg
Weight = M*g = 14,700 N
Component parallel to incline
= 14,700 sin25
= 621 N
The coefficient of friction does not affect the answer, but does determine if the tires slip, and affects the acceleration.
To find the component of the car's weight parallel to the incline, we need to consider the forces acting on the car. Here's how you can calculate it:
1. Determine the weight of the car:
The weight of an object is calculated by multiplying its mass by the acceleration due to gravity. In this case, the mass of the car is given as 1.5Mg, where Mg represents the weight of the car in newtons. Since 1 Mg is equal to 1000 kg × 9.8 m/s^2, we can calculate the weight of the car as follows:
Weight = 1.5Mg × 9.8 m/s^2
2. Determine the angle of incline:
The problem states that the road is banked, and the angle of incline is given as theta = 25 degrees. This angle will help us determine the components of the weight later.
3. Resolve the weight force into components:
The weight of the car can be resolved into two components: one perpendicular to the incline, and the other parallel to the incline. The component perpendicular to the incline will be balanced by the normal force of the road, leaving only the parallel component relevant to this question.
To calculate the parallel component, we need to find the sine of the angle between the weight vector and the incline, which is given by theta. So the parallel component will be:
Weight parallel = Weight × sin(theta)
4. Calculate the final answer:
Plug in the values and calculate the component of weight parallel to the incline:
Weight parallel = (1.5Mg × 9.8 m/s^2) × sin(25)
The resulting value will give you the component of the car's weight parallel to the incline in newtons.