Question

In the figure, a ladder of length L = 10 m and mass m = 44 kg leans against a slick (frictionless) wall. The ladder's upper end is at height h = 7.9 m above the pavement on which the lower end rests (the pavement is not frictionless). The ladder's center of mass is L/3 from the lower end. A firefighter of mass M = 68 kg climbs the ladder. Let the coefficient of static friction μs between the ladder and the pavement be 0.51. How far (in percent) up the ladder must the firefighter go to put the ladder on the verge of sliding?

Answer #1

Ans:-

Given data: L= 10m, m= 44kg, h= 7.9m, M= 68kg,μs= 0.51

Since there is no friction at the wall, the normal force on the
ground is the sum of the weights of the ladder and the
firefighter:

Fn = (44 + 68)kg * 9.8m/s² = 1097.6 N

so the maximum friction force is

Ff = µ*Fn = 0.51 * 1097.6N = 559.78N

The angle between the ground and the ladder is

Θ = arcsin(7.9/10) = 52.19º

Now sum the moments about the base:

ΣM = 0 = firefighter's torque + ladder's torque - wall force's
torque

0 = 68kg*9.8m/s²*x*10m*cos52.19 + 44kg*9.8m/s²*(10m/3)*cos52.19 -
Fw*7.9m

where Fw is the horizontal force at the wall which, at the
threshold, is equal to the friction force at the floor (the only
two horizontal forces on the ladder).

0 =4085.33Nm*x +881.15Nm -4422.26Nm

0= 4085.33*x Nm -3541.11Nm

x = 3541.11N·m / 4085.33N·m = 0.8667 = 0.87=87%

A ladder of length L = 2.7 m and mass m = 21 kg rests on a floor
with coefficient of static friction μs = 0.55. Assume the wall is
frictionless.
1)What is the normal force the floor exerts on the ladder? 205.8
N
2)What is the minimum angle the ladder must make with the floor
to not slip?
3)A person with mass M = 68 kg now stands at the very top of the
ladder. What is the normal...

A ladder of length L = 2.4 m and mass m = 15 kg rests on a floor
with coefficient of static friction μs = 0.56. Assume
the wall is frictionless.
1)
What is the normal force the floor exerts on the ladder? N
2)
What is the minimum angle the ladder must make with the floor to
not slip?
3)
A person with mass M = 62 kg now stands at the very top of the
ladder.
What is...

A ladder whose length L is 12 m and mass m are 45 kg rests
against a wall. Its upper end is a distance h of 9.3 m above the
ground. The center of mass of the ladder is one-third of the way up
the ladder. A fire fighter whose mass M is 72 kg climbs the ladder
until his center of mass is halfway up. Assume the wall but not the
ground is frictionless. What forces are exerted on...

Romeo takes a uniform 11.5-m ladder and leans it against the
smooth wall of the Capulet residence. The ladder's mass is 24.0kg,
and the bottom rests on the ground 2.80m from the wall. When Romeo,
whose mass is 70 kg, gets 87.0 percent of the way to the top, the
ladder begins to slip. What is the coefficient of static friction
between the ground and the ladder?

A ladder having a uniform density and a mass m rests
against a frictionless vertical wall, making angle 49.0° with the
horizontal. The lower end rests on a flat surface where the
coefficient of static friction is µs = 0.410. A window
cleaner with mass M = 2m attempts to climb the
ladder. Given a ladder length of L, what fraction of the
length of the ladder (x / L) will the worker have reached
when the ladder begins to...

A ladder having a uniform density and a mass m rests
against a frictionless vertical wall, making angle 50.0° with the
horizontal. The lower end rests on a flat surface where the
coefficient of static friction is µs = 0.420. A window
cleaner with mass M = 2m attempts to climb the
ladder. Given a ladder length of L, what fraction of the
length of the ladder (x / L) will the worker have reached
when the ladder begins to...

A 16.0-m uniform ladder weighing 490 N rests against a
frictionless wall. The ladder makes a 61.0° angle with the
horizontal.
(a) Find the horizontal and vertical forces the ground exerts on
the base of the ladder when an 820-N firefighter has climbed 4.30 m
along the ladder from the bottom.
Horizontal Force
magnitude
__N
direction
- towards the wall or away from the wall?
Vertical Force
magnitude
N
direction
up or down?
(b) If the ladder is just on...

A 16.0-m uniform ladder weighing 490 N rests against a
frictionless wall. The ladder makes a 57.0° angle with the
horizontal.
(a) Find the horizontal and vertical forces the ground exerts on
the base of the ladder when an 850-N firefighter has climbed 4.20 m
along the ladder from the bottom.
Horizontal Force
magnitude
direction
Vertical Force
magnitude
direction
(b) If the ladder is just on the verge of slipping when the
firefighter is 9.10 m from the bottom, what...

A 16.0-m uniform ladder weighing 490 N rests against a
frictionless wall. The ladder makes a 55.0° angle with the
horizontal.
(a) Find the horizontal and vertical forces the ground exerts on
the base of the ladder when an 820-N firefighter has climbed 4.20 m
along the ladder from the bottom.
Horizontal Force
magnitude
N
direction
---Select--- towards the wall away from the wall
Vertical Force
magnitude
N
direction
---Select--- up down
(b) If the ladder is just on the...

A uniform ladder of length l and mass m rests against a smooth,
vertical wall. The coefficient of static friction between ladder
and ground is 0.35. Find the minimum angle at which the ladder does
not slip. (Consider the torques about an axis perpendicular to the
page through O)

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 8 minutes ago

asked 8 minutes ago

asked 9 minutes ago

asked 9 minutes ago

asked 16 minutes ago

asked 23 minutes ago

asked 29 minutes ago

asked 32 minutes ago

asked 35 minutes ago

asked 38 minutes ago

asked 46 minutes ago

asked 48 minutes ago