Help with work and energy problem

[NAkid]

Hi i need help with this problem. The first part asks
A car (m = 890.0 kg) traveling on a level road at 27.0 m/s (60.5 mph) can stop, locking its wheels, in a distance of 60.0 m (196.9 ft). Find the size of the horizontal force which the car applies on the road while stopping on the road. First solve this problem using work/energy concepts and then check your answer using kinematics/force law concepts.

I solved this by finding the acceleration and plugging into formula F=ma=5402N

The second part asks
Find the stopping distance of that same car when it is traveling up a 18.9deg slope, and it locks its wheels while traveling at 27.0 m/s (60.5 mph). Assume that muk does not depend on the speed.

I drew a free body diagram and came up with the following relationships
F-fk-mgsin(18.9)=ma where F=5402N
N-mgcos(18.9)=0

How do I solve for the horizontal distance? Is it just the vertical component of the Force?

 

[NAkid]

I just tried using the formula Vf^2 = v0^2 + 2adx -- where final velocity=0, initial velocity is given, and i solved for a using the above equation F-ukmgcos(18.9)-mgsin(18.9)=ma. But I still didn't get the right answer..

 

[Moetasim]

For the first part of the problem, using work/energy concepts, we can determine the size of the horizontal force by using the equation W = Fd, where W is the work done, F is the force applied, and d is the distance traveled. In this case, the work done is equal to the change in kinetic energy, which can be calculated using the equation KE = 1/2mv^2. By solving for F, we get F = (m*v^2)/2d, which gives us a force of 5402 N.

To check our answer using kinematics/force law concepts, we can use the equation F = ma, where F is the net force, m is the mass, and a is the acceleration. We know the mass and the acceleration (which can be calculated using the formula a = v^2/2d), so we can solve for F, which again gives us a force of 5402 N.

For the second part of the problem, we can use the same equations to calculate the stopping distance on the slope. The only difference is that we now have to take into account the component of the force due to gravity acting on the car along the slope. This can be calculated using the equation Fg = mg*sinθ, where θ is the angle of the slope. We can then use this value to modify the equation for acceleration (a = v^2/2d) to include the gravitational force, giving us a = (v^2/2d) - (Fg/m). By solving for d, we can find the stopping distance on the slope. It is not just the vertical component of the force, as the force is acting at an angle and will contribute to both the horizontal and vertical components of acceleration.