Minimum horizontal force to slide a 4 kg block up a 37° ramp

[Toila]

Homework Statement

What is the minimum horizontal force that must be applied to the stationary 4.0kg block so that the block will start to slide up the ramp? the ramp is inclined at a 37degrees angle and the coefficient of static friction between the block and the ramp is 0.23.

Homework Equations

Ff = μN
---

The Attempt at a Solution

y-direction
0 = N - mgcosθ
N = mgcosθ
N = 4(9.8)cos37 = 31.3
------
x-direction
0 = Fcos(θ) - Ff − mgsinθ
F = (mgsinθ + Ff)/cos(θ)
F = [39.2sin(37) + (.23(39.2)(cos37)]/cos37
F = 38.6
==================================================
I have the wrong answer because the correct answer is
N = 59.4N, F = 46.6
Also, i think the way i use to solve F is right but i believe my N is wrong because when i plug in the N of the correct answer i get the same F as the result. Hope you can help me solve this problem thanks a lot

 

[alphysicist]

Hi Toila,

Homework Statement

What is the minimum horizontal force that must be applied to the stationary 4.0kg block so that the block will start to slide up the ramp? the ramp is inclined at a 37degrees angle and the coefficient of static friction between the block and the ramp is 0.23.

Homework Equations

Ff = μN
---

The Attempt at a Solution

y-direction
0 = N - mgcosθ
N = mgcosθ
N = 4(9.8)cos37 = 31.3
------
x-direction
0 = Fcos(θ) - Ff − mgsinθ

Notice here that you have the x-component of the applied force. But you have not taken into account the y-component of the applied force anywhere.

F = (mgsinθ + Ff)/cos(θ)
F = [39.2sin(37) + (.23(39.2)(cos37)]/cos37
F = 38.6
==================================================
I have the wrong answer because the correct answer is
N = 59.4N, F = 46.6
Also, i think the way i use to solve F is right but i believe my N is wrong because when i plug in the N of the correct answer i get the same F as the result. Hope you can help me solve this problem thanks a lot