still i cant find the normal force without mass of automabile. is normal force mass times gravity sin theta?
on a level road the stopping distance for an automobile is 35.0m for an initail speed of 90 km/hr what is the stopping distance of the same automobile on a simalr road with the slope 1:10
physics - bobpursley, Saturday, October 30, 2010 at 7:42am
Assume the coefficent of friction is the same.
F=mu*Normal force=ma
a= normalforce*mu/mass
Vf^2=Vi^2+2ad
solve for mu on the level road, knowing normalforce is mg.
Then, knowingmu, look at the slope
normal force=mg*SinTheta
Vf^2=Vi^2+2mgSinTheta*mu/m * d
solve for distance.
since Theta is a small angle, SinTheta=TanTheta= 1/10
To find the stopping distance of the automobile on the slope, you first need to find the coefficient of friction (mu) on the level road.
On the level road, the force of friction (F) is equal to mu times the normal force (F=mu*Normal force), which is equal to the mass (m) times acceleration (a) (F=ma). Rearrange the equation to solve for a: a = F/m.
Using the equation for final velocity (Vf^2 = Vi^2 + 2ad), where Vf is the final velocity, Vi is the initial velocity (which is given as 90 km/hr), a is the acceleration, and d is the stopping distance (which is given as 35.0m), you can solve for mu.
Rearrange the equation to solve for mu:
mu = (Vf^2 - Vi^2) / (2ad)
Now that you have mu, you can find the normal force on the slope. The normal force (Normal force = mg * SinTheta) is equal to the mass (m) times gravity (g) times the sin of the slope angle (Theta). In this case, since the slope is given as 1:10, the sin of the slope angle is equal to the value of the slope (1/10).
Now, using the equation Vf^2 = Vi^2 + 2mgSinTheta(mu/m) * d, where Vf is the final velocity (which is 0 since the automobile comes to a stop), Vi is the initial velocity, m is the mass (which you don't have), g is the acceleration due to gravity (which is approximately 9.8 m/s^2), SinTheta is the sin of the slope angle (which is 1/10), mu is the coefficient of friction, and d is the stopping distance (which is what you are trying to find), you can solve for d.
Rearrange the equation to solve for d:
d = (Vf^2 - Vi^2) / (2mgSinTheta(mu/m))
Remember that Theta is a small angle, so SinTheta is approximately equal to TanTheta, which in this case is 1/10.
So, this is the step-by-step process to find the stopping distance on the slope. However, without knowing the mass of the automobile, it is not possible to find the normal force or the stopping distance.