How Fast Does a 80 kg Weight Move After Being Pulled 1.5 m on a Rough Plane?

[Garicup]

Homework Statement

A weight, mass m = 80 kg , is pulled over a rough horizontal plane, mu = 0.15, by a force of magnitude F = 359 N, making an angle of 43 degrees with the plane, away from the plane. Calculate the speed of the weight d= 1.5 m away from its initial position assuming that it started from rest.

Homework Equations

F_f = muF_n

Vf² = Vi² + 2ad

The Attempt at a Solution

The applied force is evaluated in the x direction only (since the object remained on the floor)

therefore : Fapp_x = 359 cos 43 = 262.56N

Fn = mg , therefore
F_f = 0.15(80)(9.8) = 117.6N
sumF_x = 262.56 - 117.6 = 144.96N

which means:::: ma = 144.96N
80a = 144.96
a = 1.812

given Vf² = Vi² + 2ad, and vi = 0 (rest)

then Vf² = 2 (1.812)(1.5)

Vf = 2.33 m/s-------> This is what I've done on the question, I am having doubts though, can anyone please verify / correct anywhere I am wrong? Please and Thank you

 

[JoAuSc]

It seems right to me. Why do you have doubts?

 

[baba89]

.

I would first clarify any assumptions or uncertainties in the problem, such as the type of surface the weight is being pulled on and whether there is any external friction acting on the weight. I would also double check the values given in the problem to ensure accuracy.

With that being said, your solution appears to be correct. You have correctly identified and used relevant equations to solve for the final velocity of the weight. Your use of trigonometry to find the horizontal component of the applied force is also accurate. Overall, your solution is clear and well-organized.

One suggestion I would make is to provide units for your final answer (m/s) to ensure completeness and accuracy in your solution. Additionally, you could also include a brief explanation of your reasoning behind each step, which would make your solution more thorough and easier to follow for someone else reading it. Great work overall!