A(n) 1100 kg car is parked on a 4� incline.
The acceleration of gravity is 9.8 m/s2 .
Find the force of friction keeping the car
from sliding down the incline.
Answer in units of N
Well, it seems like this car is going to have a gravitational "slip and slide" party down that incline! To keep it grounded, we need to calculate the force of friction.
To find this out, we need to use some good old physics. We know that the force of friction opposes motion, so it'll be directed up the incline. The formula to calculate the force of friction is:
Force of friction = Mass of the car × Acceleration due to gravity × sine of the angle of the incline.
Plugging in the given values:
Mass of the car = 1100 kg
Acceleration due to gravity = 9.8 m/s^2
Angle of the incline = 4 degrees (But remember to convert this to radians!)
After converting the angle to radians (4 degrees × π/180), we can use the formula to find the force of friction. Let's do the math and see what we get:
Force of friction = 1100 kg × 9.8 m/s^2 × sin(4 degrees × π/180)
And that, my friend, will give you the force of friction keeping the car from sliding down the incline. Make sure you have your calculator on hand - math can be as slippery as that car!
To find the force of friction keeping the car from sliding down the incline, we can start by calculating the gravitational force acting on the car.
Step 1: Calculate the gravitational force:
The gravitational force is given by the formula:
Force = mass x acceleration due to gravity
Given:
Mass (m) = 1100 kg
Acceleration due to gravity (g) = 9.8 m/s^2
Force = 1100 kg x 9.8 m/s^2
Force = 10780 N
Step 2: Calculate the component of the gravitational force acting down the incline:
The component of the gravitational force acting down the incline can be calculated using the formula:
Force along the incline = Force x sin(theta)
Given:
Incline angle (theta) = 4 degrees
Force = 10780 N
Force along the incline = 10780 N x sin(4 degrees)
Force along the incline ≈ 751.9 N (rounded to three decimal places)
Step 3: Calculate the force of friction:
The force of friction is equal in magnitude and opposite in direction to the force along the incline since it's keeping the car from sliding down.
Therefore, the force of friction keeping the car from sliding down the incline is approximately 751.9 N.
To find the force of friction keeping the car from sliding down the incline, we first need to understand the forces acting on the car.
In this case, the two main forces are the force of gravity and the force of friction.
The force of gravity, also known as the weight of the car, can be calculated using the formula:
Weight = Mass * Acceleration due to gravity
Weight = 1100 kg * 9.8 m/s^2
Weight = 10780 N
Next, we need to find the component of the weight that acts parallel to the incline. To do this, we multiply the weight by the sine of the angle of the incline:
Weight parallel to the incline = Weight * sin(angle)
Angle = 4 degrees (as given)
Weight parallel to the incline = 10780 N * sin(4 degrees)
Weight parallel to the incline = 746.6 N
Finally, the force of friction can be determined as the force that opposes the car from sliding down the incline. The force of friction can be calculated using the formula:
Force of friction = μ * Normal force
Here, μ represents the coefficient of friction and the Normal force is the perpendicular force acting on the car.
Since the car is parked, there is no vertical acceleration, and hence, the Normal force is equal to the weight of the car.
Normal force = Weight
Normal force = 10780 N
Assuming the coefficient of friction is µ, the force of friction can then be calculated as:
Force of friction = µ * 10780 N
Please provide the coefficient of friction (µ) to calculate the exact force of friction that keeps the car from sliding down the incline.
mg x sin(beta)
1100(9.8)sin(4)
=751.97