Determine the acceleration of a 1500 kg automobile that rolls down an incline of 30° from the horizontal if a coefficient of friction between the tires and the incline is 0.12
fricton force : mgCosTheta*mu
gravity force: mg*sinTheta
netforce=mg
mg(sinTheta-mu*CosTheta)=ma
solve fodr acceleartion a.
a=3.88
To determine the acceleration of the automobile, we need to consider the forces acting on it.
1. Calculate the force of gravity acting on the automobile:
The force of gravity can be calculated using the formula F = mg, where m is the mass and g is the acceleration due to gravity.
Given: mass (m) = 1500 kg and acceleration due to gravity (g) = 9.8 m/s^2.
F = (1500 kg) * (9.8 m/s^2) = 14700 N.
2. Calculate the force of friction:
The force of friction can be calculated using the formula Ff = μN, where μ is the coefficient of friction and N is the normal force.
The normal force can be calculated using the formula N = mgcosθ, where θ is the angle of the incline.
Given: coefficient of friction (μ) = 0.12 and angle of the incline (θ) = 30°.
N = (1500 kg) * (9.8 m/s^2) * cos(30°) = 12753 N.
Ff = (0.12) * (12753 N) = 1530.36 N.
3. Calculate the net force acting on the automobile:
The net force can be calculated using the formula Fnet = F - Ff.
Fnet = 14700 N - 1530.36 N = 13169.64 N.
4. Calculate the acceleration of the automobile:
The acceleration can be calculated using the formula a = Fnet / m.
a = (13169.64 N) / (1500 kg) = 8.78 m/s^2.
Therefore, the acceleration of the automobile is approximately 8.78 m/s^2.
To determine the acceleration of the automobile, we can use Newton's second law, which states that the net force on an object is equal to the product of its mass and acceleration (F = m * a).
In this case, we need to consider the forces acting on the automobile. The two main forces are the gravitational force (pulling the automobile down) and the frictional force (opposing its motion on the incline).
1. Gravitational force: The gravitational force can be calculated using the formula Fg = m * g, where m is the mass of the automobile (1500 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Fg = 1500 kg * 9.8 m/s^2
2. Frictional force: The frictional force is calculated using the formula Ff = μ * N, where μ is the coefficient of friction (0.12) and N is the normal force acting on the automobile.
The normal force acting on the automobile can be found by decomposing the gravitational force into components. Since the incline is at an angle of 30° from the horizontal, the normal force can be calculated as follows:
N = m * g * cos(θ)
where θ is the incline angle (30°).
N = 1500 kg * 9.8 m/s^2 * cos(30°)
3. Net force: The net force on the automobile is the difference between the gravitational force and the frictional force.
Net force (Fnet) = Fg - Ff
4. Acceleration: Finally, we can use Newton's second law to calculate the acceleration:
Fnet = m * a
Substituting the values we have calculated:
1500 kg * a = Fg - Ff
a = (Fg - Ff) / 1500 kg
Now you can plug in the values for Fg (calculated in step 1) and Ff (calculated in step 2) to find the acceleration of the automobile.