Finding the applied force at an angle?

[Bethany]

Homework Statement

A 2000 kg car is driving up a 20° grade at a speed of 85 km/h. What force must be applied to the car to accelerate it up to 100 km/h in 10s?

m= 2000 kg
θ= 20°
V_o= 85 km/hr = 23.6 m/s
V_f = 100 km/hr = 27.8 m/s
t = 10 s

Homework Equations

F = ma (F_x = ma_x)
F_x= Fcosθ
V_ox = V_o cosθ
V_oy = V_o sinθ
V_x = V_ox + a_xt
V_x= V_ox +a_xt

The Attempt at a Solution

I found these using the cos or sin equations above:
V_ox = 22.1 m/s
V_oy = 8.07 m/s
V_x = 26.1 m/s
V_y = 9.51 m/s

Using the last equation, I found a_x = 0.4 m/s²

F_x= 800 N

I then solved for F using the second equation by dividing F_x by cosθ, making F= 851 N. I think I did something wrong when I solved for a, and my guess is that I couldn't use 10s for that since it was the incline, when I used it for the x values. I'm stuck on how to fix it, or on how to solve the problem a different way. These are practice problems that I have the answers to, but no solutions, so I know that F=7.5 kN.

I tried working backward and got that a=3.75 m/s² and a_x=3.52 m/s². Using F=ma and the cos, I got F_x = 7040 N, which gets me the right answer however I do it. This makes me fairly certain that I'm doing something wrong with getting the acceleration.

Thanks in advance!

 

[PhanthomJay]

Homework Statement

A 2000 kg car is driving up a 20° grade at a speed of 85 km/h. What force must be applied to the car to accelerate it up to 100 km/h in 10s?

m= 2000 kg
θ= 20°
V_o= 85 km/hr = 23.6 m/s
V_f = 100 km/hr = 27.8 m/s
t = 10 s

Homework Equations

F = ma (F_x = ma_x)
F_x= Fcosθ
V_ox = V_o cosθ
V_oy = V_o sinθ
V_x = V_ox + a_xt
V_x= V_ox +a_xt

The Attempt at a Solution

I found these using the cos or sin equations above:
V_ox = 22.1 m/s
V_oy = 8.07 m/s
V_x = 26.1 m/s
V_y = 9.51 m/s

Using the last equation, I found a_x = 0.4 m/s²

F_x= 800 N

I then solved for F using the second equation by dividing F_x by cosθ, making F= 851 N. I think I did something wrong when I solved for a, and my guess is that I couldn't use 10s for that since it was the incline, when I used it for the x values. I'm stuck on how to fix it, or on how to solve the problem a different way. These are practice problems that I have the answers to, but no solutions, so I know that F=7.5 kN.

I tried working backward and got that a=3.75 m/s² and a_x=3.52 m/s². Using F=ma and the cos, I got F_x = 7040 N, which gets me the right answer however I do it. This makes me fairly certain that I'm doing something wrong with getting the acceleration.

AThanks in advance!

you are making the problem complex by not choosing the x-axis parallel to the incline and the y-axis perpendicular to the incline. You are also not noting that it is the net force that produces the acceleration , not just the applied force, regardless of how you choose your axes. Draw a free body diagram.