Dynamics block problem

In summary, the problem involves a 40-kg package at rest on an incline, with a force P applied to it. The goal is to determine the magnitude of P if it takes 4 seconds for the package to travel 10 meters up the incline. The coefficients of static and kinetic friction are given as 0.3 and 0.25, respectively. Using Newton's 2nd Law and the equation x=x0+v0t+0.5at^2, the normal force and acceleration are calculated to be 368.73 N and 1.25 m/s^2, respectively. However, this results in a value for P of 355.35 N, which is different from the expected
  • #1
srh
7
0

Homework Statement


A 40-kg package is at rest on an inlcine when a force P is applied to it. Determine the magnitude of P if 4s is required for the package to travel 10 m up the incline. The static (us) and kinetic (uk) coefficients of friction between the package and the incline are 0.3 and 0.25 respectively.


Homework Equations


Newton's 2nd Law : sum of forces = mass x acceleration
x=x0+v0t+0.5at^2

The Attempt at a Solution


First I changed my coordinate system to make the x plane parallel w/ the incline. I then summed the forces in the y direction in equilibrium to find the value of the N, normal force. I found this to be 368.73 N. (N-mgcos(20)=0)

THen I summed the x forces and set equal to mass x acceleration:
Pcos(50)-(uk)(N)=ma

To find a I used the relation x=x0+v0t+0.5at^2:
x-x0 = 10m
v0=0
t=4s
I found a to be 1.25 m/s^2.

Plugging in all the known values I got P = 355.35 N. I know that P is supposed to be 612 N. I was wondering if it was obvious where I was going wrong?
 

Attachments

  • dynam.JPG
    dynam.JPG
    4.2 KB · Views: 364
  • freebod.JPG
    freebod.JPG
    4.4 KB · Views: 387
Last edited:
Physics news on Phys.org
  • #2
Thread moved from Engineering to Intro Physics.

Could you list all of the forces acting normal to the plane and parallel to it? I think you might be missing a term or two from the force pushing down and sideways on the block.
 
  • #3


Based on your attempt at a solution, it seems like you have correctly set up the equations and calculated the normal force and acceleration. However, there may be a mistake in your calculation for P. It should be Pcos(50) + (uk)(N) = ma, since the force of friction is acting in the opposite direction of P. Also, make sure you are using the correct values for the coefficient of kinetic friction, which should be 0.25. Double check your calculations and equations to see if you can find where the error is, and then re-calculate P.
 

1. What is a dynamics block problem?

A dynamics block problem is a type of physics problem that involves calculating the motion of a block or object as it moves through a system of forces and interactions.

2. How do you solve a dynamics block problem?

To solve a dynamics block problem, the basic steps include drawing a free body diagram, applying Newton's laws of motion, and using equations of motion to solve for the unknown variables.

3. What are some common forces involved in dynamics block problems?

Some common forces involved in dynamics block problems include weight, normal force, friction, tension, and applied forces such as pushing or pulling.

4. What is the difference between static and dynamic equilibrium in a dynamics block problem?

In a dynamics block problem, static equilibrium refers to when the block is at rest or moving at a constant velocity. Dynamic equilibrium refers to when the block is accelerating at a constant rate.

5. What are some real-life applications of dynamics block problems?

Dynamics block problems have many real-life applications, such as calculating the motion of objects on an inclined plane, analyzing the forces acting on a car or airplane during motion, and understanding the movement of objects in simple machines.

Similar threads

  • Introductory Physics Homework Help
Replies
10
Views
692
  • Introductory Physics Homework Help
Replies
13
Views
861
  • Introductory Physics Homework Help
Replies
15
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
5K
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
18
Views
2K
  • Introductory Physics Homework Help
Replies
24
Views
892
  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
17
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
929
Back
Top