Newtons laws, dynamics questions

[Nelonski]

Homework Statement

1) A 1000-kg Car is parked on a 10 degree slope. Determine the magnitude of the frictional force acting on the car

2) A 2000-kg car traveling at an initial speed of 10m/s skids to a stop with a constant acceleration. The coefficient of friction between the tired and the road is 0.4. determine the length of the skid marks

Homework Equations

Newtons 2nd law f=ma

(f_s) = static friction
f_k= kinetic friction
w= weight
n= normal force

The Attempt at a Solution

For the first part (1) . The free body diagram I drew was on a slant to show that the normal force is perpendicular to the slanted road so it is in the positive y direction, the force of static friction is to the negative x axis, and the weight force is downwards (with two components x and y)

F_x = -f_s + wsin∅ = 0
F_y= n-wcos∅=0

Essentially, I just solved the x component equation, given that wsin∅ is 9800sin10.

This was then equal to the static friction force.

This feels wrong, it was too simple, but maybe I could just be overthinking/underthinking.

Is this correct?



2)The normal force is pointing up in the positive y axis, the weight force is pointing down, and the kinetic friction force is poiting to the negative x axis(left) for the free body diagram.

Equations:

F_x= -f_k=ma_x
F_y= n-w=0

I esentially solved for the normal force in the y direction, then plugged that into f_k=μkn , to solve for the kinetic friction force. after solving the friction, I plugged that into F_x and determined the acceleration (which is negative).

After knowing the acceleration, initial and final velocities I used the equation

v_f^2=v_i^2+2aΔx

Solved for x, and think i found the answer.

Is this right as well? (the mah is entirely tough to type out so I simply gave my steps for solving)

Thanks so much

 

[Dick]

Homework Statement

1) A 1000-kg Car is parked on a 10 degree slope. Determine the magnitude of the frictional force acting on the car

2) A 2000-kg car traveling at an initial speed of 10m/s skids to a stop with a constant acceleration. The coefficient of friction between the tired and the road is 0.4. determine the length of the skid marks

Homework Equations

Newtons 2nd law f=ma

(f_s) = static friction
f_k= kinetic friction
w= weight
n= normal force

The Attempt at a Solution

For the first part (1) . The free body diagram I drew was on a slant to show that the normal force is perpendicular to the slanted road so it is in the positive y direction, the force of static friction is to the negative x axis, and the weight force is downwards (with two components x and y)

F_x = -f_s + wsin∅ = 0
F_y= n-wcos∅=0

Essentially, I just solved the x component equation, given that wsin∅ is 9800sin10.

This was then equal to the static friction force.

This feels wrong, it was too simple, but maybe I could just be overthinking/underthinking.

Is this correct?



2)The normal force is pointing up in the positive y axis, the weight force is pointing down, and the kinetic friction force is poiting to the negative x axis(left) for the free body diagram.

Equations:

F_x= -f_k=ma_x
F_y= n-w=0

I esentially solved for the normal force in the y direction, then plugged that into f_k=μkn , to solve for the kinetic friction force. after solving the friction, I plugged that into F_x and determined the acceleration (which is negative).

After knowing the acceleration, initial and final velocities I used the equation

v_f^2=v_i^2+2aΔx

Solved for x, and think i found the answer.

Is this right as well? (the mah is entirely tough to type out so I simply gave my steps for solving)

Thanks so much

The method seems ok on both of those.