<< Chapter < Page Chapter >> Page >

Free body diagram

F x = F - N sin θ = 0 F = N sin θ

and

F y = N cos θ - mg = 0 mg = N cos θ

Taking ratio, we have :

F mg = tan θ F = mg tan θ

Pulley, string and block system

Problem 4 : A string going over a pulley “A” of mass “m” supports a mass “M” as shown in the figure. Find the magnitude of force exerted by the clamp “B” on pulley “A”.

Balanced force system

Solution : Here, we consider pulley as the body system. Let us also consider that clamp “B” exerts a force “F” in an arbitrary direction, making an angle with the horizontal. We should note that pulley, unless otherwise specified, is considered to be of negligible mass and friction-less. In this case, however, pulley has finite mass “m” and its weight should be considered to be an external force on the pulley.

Free body diagram of pulley

The string is single piece and mass-less, whereas pulley is not mass-less. However, pulley is static. As such, there is no torque involved. Hence, tension in the string all through out is same. From the consideration of block, we see that tension in the string is equal to the weight of the block i.e. Mg.

Now, the external forces on pulley are (i) Horizontal tension "T" (ii) Weight, mg, of the pulley (iii) Vertical Tension, T, and (iv) force, F applied by clamp “B”.

Free body diagram

F x = F x - T = F x - Mg = 0 F x = Mg

and

F y = F y - mg - T = F y - mg - Mg = 0 F y = ( M + m ) g

The force exerted by the clamp,F, is :

F = ( F x 2 + F y 2 ) = { ( Mg ) 2 + ( M + m ) 2 g 2 } F = g { M 2 + ( M + m ) 2 }

Two blocks system

Problem 5 : Two blocks "A" and "B", weighing 20 N and 10 N respectively are in contact with each other. If the blocks are at rest, then find the force "F" and the normal reactions between all contact surfaces.

Balanced force system

Solution : The question demands that we draw free body diagram of each of the block separately as we are required to know normal reactions at all surfaces. Here, there are three contact surfaces between (i) A and horizontal surface (ii) B and horizontal surface and (iii) A and B.

A preliminary assessment of forces on the blocks suggests that analysis of forces on B will provide values of unknown force(s). It is so because the forces on B are mutually perpendicular (thus, they would not need to be resolved), if appropriate coordinate system is chosen. Hence, we first analyze force on block B.

Free body diagram of B

The external forces are (i) weight of B = 10 N (ii) Normal force applied by A i.e. N 1 (say) (iii) Normal force applied by surface i.e. N 2 and (iv) external force of 20 N

Free body diagram

F x = N 1 - 20 = 0 N 1 = 20 N

and

F y = N 2 - 10 = 0 N 2 = 10 N

Free body diagram of B

The external forces are (i) weight of A, 20 N (ii) Normal force applied by B i.e. N 3 (say) = N 1 = 20 N (iii) Normal force applied by surface i.e. N 4 and (iv) force, F = ?

Free body diagram

F x = F cos 30 0 - N 3 = F cos 30 0 - N 1 = F cos 30 0 - 20 = 0 20 = F cos 30 0 F = 20 cos 30 0 = 20 3 2 = 40 3 N

and

F y = N 4 - F sin 30 0 - 20 = 0 N 4 = F sin 30 0 + 20 = 40 3 X 1 2 + 20 = 20 3 + 20 = 20 ( 1 + 3 3 ) N

Pulley, string and multiple blocks system

Problem 6 : The blocks A and B weighing 10 N and 20 N are connected by a string. The block B, in turn, is connected to block C with another string passing over a pulley. Friction forces at all interfaces is negligible. If the block system is in equilibrium, find the weight of C and tensions in the two strings.

Balanced force system

Solution : There are two strings. Hence, the tensions in the strings will be different. Let T 1 and T 2 be the tension in strings AB and BC respectively.

Looking at the various body systems, we guess that the simplest force system is the one associated with block C. However, force analysis of block C will not yield anything as we do not know its weight or the tension T 2 .

Thus, we begin with block A.

Free body diagram of A

Free body diagram

The external forces are (i) weight of A = 10 N (ii) Normal force applied by incline i.e. N 1 (say) (iii) tension in AB, T 1 .

F x = 10 sin 30 0 - T 1 = 0 T 1 = 10 sin 30 0 = 5 N

We need not analyze forces in y – direction as we are not required to determine normal force N 1 and it is not expected to be used for analyzing force on block B.

Free body diagram of B

The external forces are (i) weight of B, W C = 20 N (ii) Normal force applied by incline i.e. N 2 (say) (iii) tension in AB, T 1 and (iv) tension in BC, T 2 .

F x = 20 sin 30 0 + T 1 - T 2 = 0 T 2 = 20 x 1 2 + 5 = 15 N

Free body diagram of C

Free body diagram

The external forces are (i) weight of c = ? and (ii) tension in BC, T 2 .

F y = T 2 - W C = 0 W C = T 2 = 15 N

Acknowledgment

Author wishes to thank Scott Kravitz, Programming Assistant, Connexions for making suggestion to remove error in the module.

Questions & Answers

What are the system of units
Jonah Reply
A stone propelled from a catapult with a speed of 50ms-1 attains a height of 100m. Calculate the time of flight, calculate the angle of projection, calculate the range attained
Samson Reply
58asagravitasnal firce
Amar
water boil at 100 and why
isaac Reply
what is upper limit of speed
Riya Reply
what temperature is 0 k
Riya
0k is the lower limit of the themordynamic scale which is equalt to -273 In celcius scale
Mustapha
How MKS system is the subset of SI system?
Clash Reply
which colour has the shortest wavelength in the white light spectrum
Mustapha Reply
how do we add
Jennifer Reply
if x=a-b, a=5.8cm b=3.22 cm find percentage error in x
Abhyanshu Reply
x=5.8-3.22 x=2.58
sajjad
what is the definition of resolution of forces
Atinuke Reply
what is energy?
James Reply
Ability of doing work is called energy energy neither be create nor destryoed but change in one form to an other form
Abdul
motion
Mustapha
highlights of atomic physics
Benjamin
can anyone tell who founded equations of motion !?
Ztechy Reply
n=a+b/T² find the linear express
Donsmart Reply
أوك
عباس
Quiklyyy
Sultan Reply
Moment of inertia of a bar in terms of perpendicular axis theorem
Sultan Reply
How should i know when to add/subtract the velocities and when to use the Pythagoras theorem?
Yara Reply

Get the best Physics for k-12 course in your pocket!





Source:  OpenStax, Physics for k-12. OpenStax CNX. Sep 07, 2009 Download for free at http://cnx.org/content/col10322/1.175
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Physics for k-12' conversation and receive update notifications?

Ask