Force with friction problem(determine a force by the angle)

[suyashr99]

Homework Statement

A block of mass m rests on a horizontal table. The block is pulled by a massless rope with a force F at an angle θ. The coefficient of static friction is 0.60. The minimum value of the force needed to move the block depends on the angle θ

a)Discuss qualitatively how you would expect the magnitude of this force to depend on θ.
b) Compute the force for the angles θ = 0°, 10°, 20°, 30°, 40°, 50°, and 60°, and make a plot of F versus θ for mg = 421.3 N. From your plot, at what angle is it most efficient to apply the force to move the block?​

Homework Equations

F= ma
F(fric)= μ(N)

The Attempt at a Solution

For a) If the angle were to be increased, the normal force would be less. Therefore, the force of friction would less too, making the net force larger. If the net force is larger that means F would also be larger. This would be the opposite if the angle was decreased

For b) N = mg - Fsinθ
F(Fric) = Fcosθ
μ(mg- Fsinθ) = Fcosθ
Fcosθ - μFsinθ = μ*mg
F(cosθ -μsinθ) = μ*mg
F = μ*mg / cosθ - μsinθ
Using this, I only got force F at 0 degrees right. The rest were all wrong. Would I need calculus to solve this problem (haven't learned it yet.) Please guide me in the right direction for this problem.

[Edit: I made a simple sign mistake. I should have added μsinθ in the denominator.]

 

[SteamKing]

Homework Statement

A block of mass m rests on a horizontal table. The block is pulled by a massless rope with a force F at an angle θ. The coefficient of static friction is 0.60. The minimum value of the force needed to move the block depends on the angle θ

a)Discuss qualitatively how you would expect the magnitude of this force to depend on θ.
b) Compute the force for the angles θ = 0°, 10°, 20°, 30°, 40°, 50°, and 60°, and make a plot of F versus θ for mg = 421.3 N. From your plot, at what angle is it most efficient to apply the force to move the block?​

Homework Equations

F= ma
F(fric)= μ(N)

The Attempt at a Solution

For a) If the angle were to be increased, the normal force would be less. Therefore, the force of friction would less too, making the net force larger. If the net force is larger that means F would also be larger. This would be the opposite if the angle was decreased

For b) N = mg - Fsinθ
F(Fric) = Fcosθ
μ(mg- Fsinθ) = Fcosθ
Fcosθ - μFsinθ = μ*mg
F(cosθ -μsinθ) = μ*mg
F = μ*mg / cosθ - μsinθ
Using this, I only got force F at 0 degrees right. The rest were all wrong. Would I need calculus to solve this problem (haven't learned it yet.) Please guide me in the right direction for this problem.

We can't tell what you did wrong if you don't show your calculations.

 

[suyashr99]

We can't tell what you did wrong if you don't show your calculations.

Sorry, I ended up figuring out the answer. How do I delete this thread?

 

[SteamKing]

Sorry, I ended up figuring out the answer. How do I delete this thread?

You don't. It stays.

 

[suyashr99]

You don't. It stays.

Oh okay. I accidentally subtracted μsinθ instead of adding by it. Sorry for all the trouble.