A car of mass 1060 kg is on an icy driveway
inclined at an angle of 39◦
.
The acceleration of gravity is 9.8 m/s
2
.
θ
If the incline is frictionless, what is the
acceleration of the car?
Answer in units of m/s
2
6.167
To determine the acceleration of the car on the icy driveway, we need to break down the force components acting on the car along the incline.
First, we need to find the force due to gravity acting down the incline. The force due to gravity can be found using the formula:
Force_gravity = mass * acceleration_gravity
where mass is the mass of the car and acceleration_gravity is the acceleration due to gravity (9.8 m/s^2).
Force_gravity = 1060 kg * 9.8 m/s^2
Force_gravity = 10388 N
Next, we need to find the component of the force of gravity that acts along the incline. This can be found using the formula:
Force_along_incline = Force_gravity * sin(θ)
where θ is the angle of the incline (39 degrees) and sin(θ) is the sine of the angle.
Force_along_incline = 10388 N * sin(39°)
Force_along_incline = 6413 N
Since the incline is frictionless, the only force acting to accelerate the car along the incline is the force along the incline. Therefore, using Newton's second law of motion (F = mass * acceleration), we can equate the force along the incline to the product of the mass and the acceleration:
Force_along_incline = mass * acceleration
6413 N = 1060 kg * acceleration
To find the acceleration, we can rearrange the equation:
acceleration = Force_along_incline / mass
acceleration = 6413 N / 1060 kg
acceleration ≈ 6.05 m/s^2
So, the acceleration of the car on the icy driveway is approximately 6.05 m/s^2.