Question

A rope that is 6 m long can sustain a maximum tension of 700 Newtons before breaking. A person stands with the rope angled 45 degrees from the vertical and swings off a ledge in a circular arc. What is the maximum mass the person can have, in order to not break the rope. Answer in kilograms.

Answer #1

T = maximum tension force in the rope = 700 N

L = length of the rope = 6 m

= Angle = 45 deg

h = height dropped

height dropped to reach the bottom is given as

h = L (1 - Cos)

h = (6) (1 - Cos45)

h = 1.76 m

Using conservation of energy

Kinetic energy gained = Potential energy lost

(0.5) m v2 = mgh

v = sqrt(2gh)

v = sqrt(2(9.8)(1.76))

v = 5.873 m/s

At the bottom, force equation for the motion of the person is given as

T - mg = m v2/L

T = mg + m v2/L

T = mg + m v2/L

700 = 9.8 m + (5.873)2 m/6

m = 45.02 kg

7) A rope of length R has one end tied to a fixed point and the
other end tied to a pail full of water. The pail of water of mass M
is brought into vertical circular motion. The rope can sustain a
tension of To and no more before breaking. a) What is the minimum
speed of the pail at the top of the circle if no water is to spill
out? What is the tension in the rope...

A stuntman whose mass is 70 kg swings from the end of a
4.0-m-long rope along the arc of a vertical circle. Assuming he
starts from rest when the rope is horizontal, find the tensions in
the rope that are required to make him follow his circular path (a)
at the beginning of his motion, (b) at a height of 1.5 m above the
bottom of the circular arc, and (c) at the bottom of the arc

A stuntman whose mass is 76 kg swings from the end of a 3.5-m-long
rope along the arc of a vertical circle. Assuming that he starts
from rest when the rope is horizontal, find the magnitudes of the
tensions in the rope that are required to make him follow his
circular path at each of the following points.

Suppose that the maximum amount of tensile stress a ligament can
endure before breaking is 500 Pascals (Pascal = N/m2).
If the total area of the ligament is 0.05 m2, what is
the maximum tensile force it can endure before breaking? Show your
work.
6. For Problem 5, suppose that total area of the ligament is now
0.2 m2, what is the maximum tensile force it can endure
before breaking? Show your work.
7. Suppose the maximum strain of a...

m = 100g mass ball at the end of a
thin rope r = 0.5m long, The ball starts moving while standing
still on the x axis and accelerates clockwise with . If the string
can withstand a maximum tensile force of 5.8 N; a) When does the
rope break? b) How many turns the ball rolls before the rope
breaks. c) What is the acceleration of the ball just before the
rope breaks? (The equation to use: )

A 21 kg wood ball hangs from a 2.0-m-long wire. The maximum
tension the wire can withstand without breaking is 367 N. A 1.2 kg
projectile traveling horizontally hits and embeds itself in the
wood ball. What is the largest speed this projectile can have
without causing the cable to break?
A 31 g dart is shot straight up at 9.6 m/s. At the same instant,
a 20 g ball of cork is dropped from 2.0 m above the dart....

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 23 minutes ago

asked 27 minutes ago

asked 30 minutes ago

asked 34 minutes ago

asked 34 minutes ago

asked 40 minutes ago

asked 59 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago