Physics 170 - Mechanics
Lecture 12
Strings & Springs
Pulleys and Ropes
An ideal pulley is one that simply changes the
direction of the tension:
Pulleys
Strings and ropes often pass over
pulleys that change the direction of
the tension. In principle, the friction
and inertia in the pulley could modify
the transmitted tension.
Therefore, it is conventional to
assume that such pulleys are massless
and frictionless.
Example: Connected Masses
A block of mass m1 is connected by a string and pulley to a
hanging mass m2. Find the acceleration a and string tension T.
1
2,y
1
T2 - m22g = - m2a
2
T2 =T1
Translational Equilibrium
A person lifts a bucket of water from the bottom of a well with a
constant speed v. Because the speed is constant, the acceleration
must be zero, and the net force on the bucket is zero, so T1 = W.
.
Springs
Stretching a Spring
The unloaded spring has a length L0. Hang a weight of
mass m on it and it stretches to a new length L.
Δs=L-L0 vs. the applied force Fsp=mg.
We find that Fsp=kΔs, where k is the “spring constant”.
Hooke’s Law for Springs
force increases linearly with the amount the
spring is stretched or compressed:
The constant k is called the spring constant.
k has units of N/m or kg/s2.
Hooke’s Law
The linear proportionality between
force and displacement is found to be
valid whether the spring is stretched
or compressed, and the force and
displacement are always in opposite
directions.
Therefore, we write the forcedisplacement relation as:
Spring Forces
The force always opposes the compression or extension of the spring.