Three people pull simultaneously on a stubborn donkey. Jack
pulls directly ahead of the donkey with a force of 79.9 N, Jill pulls with 93.1
N in a direction 45° to the left, and Jane pulls in a direction 45° to the
right with 189 N. (Since the donkey is involved with such uncoordinated people,
who can blame it for being stubborn?) Find the magnitude of the net force the
people exert on the donkey. What is the direction of the net force?
Express this as the angle from straight ahead between 0° and 90°, with a
positive sign for angles to the left and a negative sign for angles to the
To better understand the concept of static equilibrium a laboratory
procedure asks the student to make a calculation before performing the
experiment. The apparatus consists of a round level table in the center of
which is a massless ring. There are three strings tied to different spots on
the ring. Each string passes parallel over the table and is individually strung
over a frictionless pulley (there are three pulleys) where a mass is hung. The
table is degree marked to indicate the position or angle of each string. There
is a mass m1 = 0.145 kg located at θ1 = 26.5° and a second mass m2 = 0.219 kg
located at θ2 = 283°. Calculate the mass m3, and location (in degrees), θ3,
which will balance the system and the ring will remain stationary.
A 1.85-kg object hangs in equilibrium at the end of a rope
(taken as massless) while a wind pushes the object with a 18.5-N horizontal
force. Find the magnitude of the tension in the rope, and the rope\'s angle
from the vertical. The acceleration due to gravity is 9.81 m/s2.
A unstretched spring hangs from the ceiling with a length of
0.31 m. A 8.7-kg block is hung from the spring and the spring stretches to be
0.42 m long. How long will the spring be if a 2.1-kg block is hung from the
spring? For both cases, all vibrations of the spring are allowed to settle down
before any measurements are made.