a 3262 kg car starts from rest at the top of a 5m long driveway that is sloped at 20 degrees with the horizontal. If an average friction force of 612N impedes the motion, fing the speed of the car at the bottom of the driveway.
Do this with energy:
KEtop + PEtop =KEbottom+PEbottom + frictionwork
0+mgh = 1/2 m v^2 +0 + 612*5
h= 5sin20
solve for v
To find the speed of the car at the bottom of the driveway, we need to first calculate the net force acting on the car.
Step 1: Calculate the gravitational force on the car.
The gravitational force can be calculated using the equation: Fg = m * g, where m is the mass of the car and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Fg = 3262 kg * 9.8 m/s^2
Step 2: Calculate the component of the gravitational force along the slope.
Since the driveway is sloped at an angle of 20 degrees with the horizontal, we need to find the component of the gravitational force acting along the slope. This can be calculated using the equation: Fgs = Fg * sin(θ), where θ is the angle of inclination.
Fgs = Fg * sin(20 degrees)
Step 3: Calculate the friction force acting on the car.
Given that the average friction force is 612 N, we know that the friction force acts opposite to the motion of the car.
Step 4: Calculate the net force.
The net force acting on the car is the vector sum of the gravitational force along the slope and the friction force. Since the car is moving downward, the net force can be calculated as:
Net force = Fgs - friction force
Step 5: Apply Newton's second law.
Newton's second law of motion states that the acceleration of an object is equal to the net force acting on it divided by its mass. In this case, we need to calculate the acceleration of the car:
Acceleration = Net force / mass
a = (Fgs - friction force) / 3262 kg
Step 6: Apply the kinematic equation.
Using the kinematic equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity (which is 0 because the car starts from rest), a is the acceleration, and s is the distance traveled along the slope (which is 5 m in this case).
Rearranging the equation, we get:
v = sqrt(0 + 2as)
Substituting the known values, we get:
v = sqrt(2 * a * 5)
Finally, substitute the previously calculated value for a into this equation to find the final velocity, v.