Finding the velocity of an object being pushed up an angular slope

In summary: These are the gravity force of 9.8 N downward, the static friction force of 8.487 N in the same direction, and the upward force of 11 N.The work done against the static friction force is 8.487 N*d*cos(Θ), and the work done against the downward force is 9.8 N*d*cos(Θ). The total work done is 19.05 N.In summary, a box is pushed up an incline by a force of 11 N, and the resulting kinetic energy is 3.2 [M/s].
  • #1
Murph
4
0
1. A box mass m=1 kg is pushed up an incline of an angle theta=30 degrees that has a coefficient of kinetic friction u_k=.5. Find the velocity of the object after it pushed for d=2m by a force of magnitude F=11N directed upward alone the incline.


W_g=m*g*d*cos(90+theta)
W_constant force=F*d*cos(theta)
F_f=m*g*u_k
F_n=m*g
W(which is the sum of the work done on the box)=1/2*m*v^2


First off I solved for the W_g, which is just straight substitution W_g=1*9.8*2*cos(120)=-9.8. After that I solved for the constant force W_constant force= 11[N]*2*cos(30)=19.05. Now this is the part where I try to determine the work that friction affects the box which is F_f=1*9.8*.5=4.9 and I am not for sure if I need to solve for the work done by friction W_f=4.9*2*cos(30) or not and i know the normal force is 0 since F_n is perpendicular to the displacement ... I know the answer is 3.2 [M/s] but I am off by a bit every time.
Please help!
 

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  • #2
Let's consider your expression for the work done by the constant force for a moment. You have

W = Fd.cos(Θ)

What is the definition of the angle Θ?
 
  • #3
Would it not just be the angle of 30 degrees which the slope is angled at?
 
  • #4
Murph said:
Would it not just be the angle of 30 degrees which the slope is angled at?
Nope, what is the defintion of Θ in the equation for work done by a constant force?
 
  • #5
Oh yea... I have been poking in numbers for a while i did the angle of that to be zero as well so then my work done for the constant is W_c=11*2*cos(0degrees).. or am I still wrong... haha..which is 22
 
  • #6
Murph said:
Oh yea... I have been poking in numbers for a while i did the angle of that to be zero as well so then my work done for the constant is W_c=11*2*cos(0degrees)
Looks better to me :approve:

Θ is the angle between the applied force and the displacement, in this case the force and displacement are parallel and hence the angle is zero.
 
  • #7
ok so I have W_g=-9.8 my W_c=22 and my W_friction=-8.487, so then I add those sums to get my total work done which is W=3.713 then I plug that into the Kinetic energy theorem and have the v=sqrt(2*W/m)...sqrt(2*3.713/1)=2.72...and the answer is 3.2[M/s]...am I still making errors?
 
  • #8
You may want to recheck your calculation of the normal force. The normal is not zero as you stated in your opening post, and it is not simply the weight of the object as you have in your calculations.

Start by resolving the forces acting on the block into the components perpendicular to the slope.
 

1. What is the formula for finding the velocity of an object being pushed up an angular slope?

The formula for finding the velocity of an object being pushed up an angular slope is: v = √(2gh sinθ), where v is the velocity, g is the acceleration due to gravity, h is the height of the slope, and θ is the angle of the slope.

2. How do you determine the acceleration due to gravity in this scenario?

The acceleration due to gravity can be determined by using the formula a = g sinθ, where a is the acceleration and θ is the angle of the slope. This formula takes into account the gravitational force acting on the object as it moves up the slope.

3. Can the angle of the slope affect the velocity of the object?

Yes, the angle of the slope can affect the velocity of the object. As the angle of the slope increases, the velocity of the object will decrease, and vice versa. This is because a steeper slope will require the object to work against a greater gravitational force, resulting in a slower velocity.

4. What other factors can impact the velocity of an object being pushed up an angular slope?

Aside from the angle of the slope, other factors that can impact the velocity of an object being pushed up an angular slope include the mass of the object, the force applied to push the object, and any external forces acting on the object such as friction.

5. Are there any limitations to using this formula to find the velocity of an object on an angular slope?

Yes, there are some limitations to using this formula. It assumes that there is no air resistance or other external forces acting on the object, and that the slope is a perfect angle. In reality, these conditions may not always be present, so the calculated velocity may differ from the actual velocity of the object.

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