PHYSICS Vector Lab Help?

Question

 

Link for The Lab Handout:

http://facstaff.gpc.edu/~jseymour/Physics%201111L-2211L/Lab_02_Force_Table_004.pdf

Questions:

1) State how this experiment has demonstrated the vector addition of forces.

2) If you have four pulleys (four forces acting on a particle), could all four pulleys be placed in the same quadrant or in two adjacent quadrant and still be in equilibrium? Explain.

3) State the condition for the equilibrium of a particle.

4) The forces used in this experiment are the weights of known masses, that is, the forces exerted on these masses by gravity. Bearing this in mind, explain the function of the pulleys?

5) The analytical method of adding vectors expressed in terms of their components maybe applied to vectors in three dimensions, for which graphical work is inconvenient. Find the magnitude of the resultant of the vectors A= 12 i – 37 j + 58 k and B = 5 i + 30 j – 42 k, where i, j and k are unit vectors along the x, y and z axes respectively.

6) The x and y component of a certain force are measured and found to be 68 (+/-3) N and 42 (+/-) N, respectively. Calculate the direction and magnitude of this force, expressing your results to the proper number of significant figures and showing the error in both magnitude and angle. Note that the error in the latter is obtained from the error in its tangent. Devise a procedure for doing this and show your work. 

Help needed with questions.

 

 

Answer 1

(1)

Force Table experiment helps us in finding the resultant of vector forces .

In force table experiment ,  vector addition of forces can be evaluated  using the concept of equilibrium .

The vectors are forces supplied by the weight of the masses that hang over the pulleys. Masses hanging over pulleys

placed at given angles are balanced by another mass over a pulley at another angle .

 

Two forces are applied on the force table by hanging masses over pulleys positioned at certain angles.

Then the angle and mass hung over a third pulley are adjusted until it balances the other two forces. 

This third force is called the equilibrant (F_E ) since it is the force that establishes equilibrium.

The equilibrant is not the same as the resultant (F_R).

The resultant is the addition of the two forces. While the equilibrant is equal in magnitude to the

resultant, it is in the opposite direction because it balances the resultant . So the equilibrant is the

negative of the resultant.

 

Answer 2

(4)

We must bear in your mind that there is a significant difference between the mass and weight .

Mass is amount of the matter contained with an object. 

Weight is the force that Earth’s gravity exerts on the object .

A pulley is a wheel on an axle that is designed to support movement and change of direction of a cable or belt along its circumference.

The pulleys allow the change of direction of the gravitational force without introducing friction .

In Force Table experiment , we use pulleys to avoid the friction with force table for applying the weight using the strings . 

Answer 3

(3)

We say that a body is in equilibrium if the vector sum of the forces and torques are zero.

We call them Translational Equilibrium and Rotational Equilibrium, respectively. 

In Force Table experiment :

Two forces are applied on the force table by hanging masses over pulleys positioned at certain angles.

Then the angle and mass hung over a third pulley are adjusted until it balances the other two forces. 

This third force is called the equilibrant (F_E ) since it is the force that establishes equilibrium.

The resultant is the addition of the two forces. While the equilibrant is equal in magnitude to the

resultant, it is in the opposite direction because it balances the resultant . So the equilibrant is the

negative of the resultant.

The figure below depects the same 

 

Mathematically condition for equilibrium is 

The equilibrium condition is 

 

 

Answer 4

(5)

Vectors  A= 12 i – 37 j + 58 , B = 5 i + 30 j – 42 k

The resultant  vector 

 The magnitude of the resultant  vector is 24.37

Answer 5

(6)

Step 1:

The x and y components of the force are N and N.

Find the magnitude and direction of the resultant force.

When and , then the magnitude of the resultant force is .

The magnitude of the resultant force is 79.92 N.

When and , then the direction of the resultant force with respect to the horizontal direction is .

The direction of the resultant force is 31.70°.

The resultant force is N.

Step 2:

The maximum angle occurs when x is a minimum and y is a maximum.

Minimum value of x is N.

Maximum value of y is N.

The magnitude of the resultant force is .

The magnitude of the resultant force is 78.49 N.

The direction of the resultant force is .

The direction of the resultant force is 34.095°.

The maximum resultant force is N.

Step 3:

The minimum angle occurs when x is a maximum and y is a minimum.

Maximum value of x is N.

Minimum value of y is N.

The magnitude of the resultant force is .

The magnitude of the resultant force is 81.49 N.

The direction of the resultant force is .

The direction of the resultant force is 29.396°.

The minimum resultant force is N.

Possible error in the magnitude of the resultant force is N.

Possible error in the direction of the resultant force is .

Therefore the resultant force with possible error is N.

Solution:

The resultant force is N.

The maximum resultant force is N.

The minimum resultant force is N.

The resultant force with possible error is N.