Calculate Frictional Force Driving Up Inclined Hill - 4270kg Car

[jbowser]

Okay, I have tried this problem 13 times, used up 13 sheets of paper and I just don't know how to do this. Do ask me what I don't know, because I just don't understand physics, and no one I have asked can explain it to me in a way that I can understand it. Please I hope someone can expain how to set this up and find my answer.

You are sitting in a stopped car on a hill that is inclined at an angle of 52.7o with respect to the vertical. The combined mass of you and the car is 4270 kg.

You push down on the gas pedal and begin to travel up the hill. After 17.3 s have elapsed, your height has increased by 194 m.

Assuming that the frictional force was constant as you drove up the hill, what was the magnitude of the frictional force from the road on the car's tires?

 

[Nate810]

To solve this problem, you need to use Newton's Second Law and the equation F=ma. Newton's Second Law states that "the rate of change of momentum of a body is proportional to the net force acting on it and takes place in the direction of the force". In this case, the force that is acting on the car is the friction force from the road on the car's tires, so we can re-write the equation as Ffriction = ma. We can then solve for the magnitude of the frictional force by rearranging the equation: Ffriction = m(a) = (4270 kg)(a). Now, since you know the acceleration (a) of the car, you can substitute that into the equation. Since the height has increased by 194 m after 17.3s have elapsed, the acceleration of the car must be 11.2 m/s2. Therefore, the magnitude of the frictional force from the road on the car's tires is 47,744 N.

 

[quicknote]

First of all, it is important to understand the concept of frictional force. Frictional force is the force that opposes the motion of an object when it is in contact with another surface. In this case, the frictional force is the force that the road exerts on the car's tires as it moves up the inclined hill.

To calculate the frictional force, we need to use the formula F = μN, where F is the frictional force, μ is the coefficient of friction, and N is the normal force. The normal force is the force that the road exerts on the car perpendicular to its surface.

In this problem, we are given the angle of inclination, the time elapsed, and the change in height. To find the normal force, we can use the formula N = mgcosθ, where m is the mass of the car and g is the acceleration due to gravity (9.8 m/s^2). Plugging in the values, we get N = (4270 kg)(9.8 m/s^2)cos(52.7o) = 2.9 x 10^4 N.

Next, we need to find the coefficient of friction. This value depends on the type of surface in contact and the materials involved. Without knowing this information, we cannot accurately calculate the frictional force. However, we can make an assumption and use a typical coefficient of friction for a car on a dry road, which is around 0.7.

Finally, we can plug in all the values into the formula F = μN to find the frictional force. F = (0.7)(2.9 x 10^4 N) = 2.0 x 10^4 N. This is the magnitude of the frictional force from the road on the car's tires.

In summary, to calculate the frictional force driving up an inclined hill for a 4270 kg car, we need to use the formula F = μN, where N = mgcosθ and μ is the coefficient of friction. Without knowing the coefficient of friction, we can only make an assumption and use a typical value to get an estimate of the frictional force. I hope this explanation helps in understanding the concept and solving the problem.