How Long Does It Take for a Block to Slow Down on an Inclined Plane?

[suspenc3]

Homework Statement

A block A (mass m) is projected up a slope at 17 m/s. The coefficient of dynamic friction is 0.27 and θ = 15˚. How long will it take for the mass's speed to drop to 5 m/s?

**Let x direction be along the incline, y direction is normal to incline

Homework Equations

$$L_1+IMP_{1-2}=L_2$$
1 being point of initial velocity
2 being point of final velocity

The Attempt at a Solution

$$L_1+IMP_{1-2}=L_2$$
$$mv_i-\mu_dNt=mv_f$$ (1)

sum forces in y direction:$$N-mgcos(\theta)$$ (2)

Sub 2 into 1: $$mv_i-\mu_dmgcos(\theta)t=mv_f$$

m (MASS) cancels out and we are left with: $$t=\frac{v_f-v_i}{\mu_dmgcos(\theta)}$$

Giving me a value of 3.55 s, whereas the answer should be 1.66 s.

Any help would be appreciated!

 

[PhanthomJay]

Homework Statement

A block A (mass m) is projected up a slope at 17 m/s. The coefficient of dynamic friction is 0.27 and θ = 15˚. How long will it take for the mass's speed to drop to 5 m/s?

**Let x direction be along the incline, y direction is normal to incline

Homework Equations

$$L_1+IMP_{1-2}=L_2$$
1 being point of initial velocity
2 being point of final velocity

The Attempt at a Solution

$$L_1+IMP_{1-2}=L_2$$
$$mv_i-\mu_dNt=mv_f$$ (1)

sum forces in y direction:$$N-mgcos(\theta)$$ (2)

Sub 2 into 1: $$mv_i-\mu_dmgcos(\theta)t=mv_f$$

m (MASS) cancels out and we are left with: $$t=\frac{v_f-v_i}{\mu_dmgcos(\theta)}$$

Giving me a value of 3.55 s, whereas the answer should be 1.66 s.

Any help would be appreciated!

I would shy away from trying to solve this problem using momentum change, which is a result of the net forces acting on the object (you left out gravity), because you can get messed up very quickly. Instead, identify all the forces acting and use Newton2 to solve for the acceleration , and basic kinematics to solve for the time. Or use energy methods if you're familiar with that approach.

 

[suspenc3]

Yea, It is a bit safer your way, and I got it using Impulse/Momentum change too, Thanks for your help Phanthom