A car of mass 1000 kg is on an icy driveway
inclined at an angle of 33◦.
The acceleration of gravity is 9.8 m/s^2
θ
If the incline is frictionless, what is the
acceleration of the car?
M*g = 1000 * 9.8 = 9800 N.
Fp = 9800*sin33 = 5337 N. = Force parallel to the incline.
a = Fp/M = 5337/1000 = 5.34 m/s^2.
5.34m/s^2
To calculate the acceleration of the car on the icy driveway, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
First, let's break down the forces acting on the car along the incline:
1. The force of gravity (Fg): This force can be split into two components: one acting parallel to the incline (Fg_parallel) and one acting perpendicular to the incline (Fg_perpendicular).
Fg_parallel = m * g * sin(θ)
Fg_perpendicular = m * g * cos(θ)
where m is the mass of the car (1000 kg) and θ is the angle of the incline (33°).
g is the acceleration due to gravity (9.8 m/s^2).
2. The force parallel to the incline (F_parallel): This force is responsible for accelerating the car down the incline.
F_parallel = m * a
where a is the acceleration of the car.
Since the incline is frictionless, there is no opposing force acting parallel to the incline. Therefore, the net force acting parallel to the incline is equal to F_parallel.
Setting up the equations:
Fg_parallel = F_parallel
m * g * sin(θ) = m * a
Simplifying the equation:
a = g * sin(θ)
Now, we can calculate the acceleration of the car:
a = 9.8 m/s^2 * sin(33°)
Calculating the value:
a ≈ 5.1 m/s^2
Therefore, the acceleration of the car on the icy driveway inclined at an angle of 33° is approximately 5.1 m/s^2.
To find the acceleration of the car on the icy driveway, we can use the formula for the component of the gravitational force parallel to the incline:
F_parallel = m * g * sin(θ)
Where:
- F_parallel is the parallel component of the gravitational force.
- m is the mass of the car (1000 kg).
- g is the acceleration due to gravity (9.8 m/s^2).
- θ is the angle of the incline (33 degrees).
In this case, since the incline is frictionless, the parallel component of the gravitational force is the only force acting on the car to cause acceleration. Therefore, we can set this force equal to m * a, where a is the acceleration of the car:
m * a = m * g * sin(θ)
Now, we can cancel the mass of the car on both sides of the equation:
a = g * sin(θ)
Substituting the known values into the equation, we get:
a = 9.8 m/s^2 * sin(33 degrees)
Using a calculator, we find that sin(33 degrees) is approximately 0.544, so:
a = 9.8 m/s^2 * 0.544
Calculating this, we get:
a ≈ 5.34 m/s^2
Therefore, the acceleration of the car on the icy driveway, assuming a frictionless incline, is approximately 5.34 m/s^2.