a 3000 pound car is parked on a hill at an angle of elevation of 16 degrees. how much force must the brakes exert to keep the car from rolling down the hill?
Wc=3000Lbs*0.454kg/Lb * 9.8N/kg=13,348N
= Wt. of car.
Fp = 13348*sin16 = 3679 N. = Force parallel to the hill.
Fe - Fp = m*a
Fe - 3679 = m*0 = 0.
Fe = 3679 N. = Force exerted by brakes.
To determine the force required to keep the car from rolling down the hill, we need to consider the weight of the car acting downhill and the friction force acting uphill.
The weight of the car acting downhill is given by the equation:
Weight = Mass x Acceleration due to gravity,
where the mass of the car can be calculated using the formula:
Mass = Weight / Acceleration due to gravity.
In this case, the weight of the car is given as 3000 pounds. However, we need to convert it to mass in order to use the equation. The approximate value for the acceleration due to gravity is 32.2 ft/s^2.
1 pound (lb) ≈ 0.454 kg,
1 kg ≈ 9.81 m/s^2 ≈ 32.2 ft/s^2.
So, the mass of the car is:
Mass = 3000 lb * 0.454 kg/lb = 1362 kg.
Now, we can calculate the weight of the car:
Weight = Mass x Acceleration due to gravity = 1362 kg * 9.81 m/s^2 ≈ 13362.42 N.
Next, we need to find the friction force acting uphill. The friction force can be calculated using the equation:
Friction Force = coefficient of friction * Normal Force.
The normal force can be calculated as:
Normal Force = Weight * cos(angle of elevation).
Since we know the angle of elevation is 16 degrees, the normal force becomes:
Normal Force = Weight * cos(16 degrees).
Now, we can calculate the normal force:
Normal Force = 13362.42 N * cos(16 degrees).
Using a calculator, we find the normal force is approximately 12782.51 N.
Finally, we can calculate the friction force required to keep the car from rolling down the hill:
Friction Force = coefficient of friction * Normal Force.
Since we are interested in finding the force, we need to rearrange the equation:
Force = Friction Force = coefficient of friction * Normal Force.
Given that the force required to keep the car from rolling down the hill is equal to the friction force, we need the coefficient of friction. This value depends on the surfaces of the car tires and the slope of the hill. Without this information, we cannot provide an exact value for the required force.
To calculate the force required to keep the car from rolling down the hill, we need to consider the gravitational force acting on the car and the component of the force that tries to roll the car downhill.
Let's break down the situation step by step:
1. Determine the weight of the car: Given that the car weighs 3000 pounds, we know that its weight is 3000 lbs.
2. Calculate the component of the weight that acts parallel to the hill: The weight can be divided into two components: one that acts perpendicular to the hill and one that acts parallel to the hill. The component parallel to the hill is given by the formula:
Component parallel = weight * sin(angle of elevation)
In this case, the angle of elevation is 16 degrees.
Component parallel = 3000 lbs * sin(16°)
3. Calculate the force required to keep the car stationary: The force required to keep the car stationary is equal to the component of the weight parallel to the hill. This force counteracts the tendency of the car to roll down the hill.
Since the car is not accelerating, we know that the force required to keep it stationary is equal to the force of friction between the brakes and the car.
Therefore, the force required to keep the car from rolling down the hill is equal to the component of the weight parallel to the hill, which we calculated in step 2.
I'll calculate it for you now:
Component parallel = 3000 lbs * sin(16°)
≈ 814.42 lbs
So, the brakes must exert a force of approximately 814.42 pounds to keep the car from rolling down the hill.