Hanging from the ceiling over a baby bed, well out of baby’s reach, is a string with plastic shapes, as shown here. The string is taut (there is no slack), as shown by the straight segments. Each plastic shape has the same mass m , and they are equally spaced by a distance d , as shown. The angles labeled θ describe the angle formed by the end of the string and the ceiling at each end. The center length of sting is horizontal. The remaining two segments each form an angle with the horizontal, labeled ϕ . Let T 1 be the tension in the leftmost section of the string, T 2 , be the tension in the section adjacent to it, and T 3 be the tension in the horizontal segment. (a) Find an equation for the tension in each section of the string in terms of the variables m , g , and θ . (b) Find the angle ϕ in terms of the angle θ . (c) If θ = 5.10 ° , what is the value of ϕ ?(d) Find the distance x between the endpoints in terms of d and θ .
Hanging from the ceiling over a baby bed, well out of baby’s reach, is a string with plastic shapes, as shown here. The string is taut (there is no slack), as shown by the straight segments. Each plastic shape has the same mass m , and they are equally spaced by a distance d , as shown. The angles labeled θ describe the angle formed by the end of the string and the ceiling at each end. The center length of sting is horizontal. The remaining two segments each form an angle with the horizontal, labeled ϕ . Let T 1 be the tension in the leftmost section of the string, T 2 , be the tension in the section adjacent to it, and T 3 be the tension in the horizontal segment. (a) Find an equation for the tension in each section of the string in terms of the variables m , g , and θ . (b) Find the angle ϕ in terms of the angle θ . (c) If θ = 5.10 ° , what is the value of ϕ ?(d) Find the distance x between the endpoints in terms of d and θ .
Hanging from the ceiling over a baby bed, well out of baby’s reach, is a string with plastic shapes, as shown here. The string is taut (there is no slack), as shown by the straight segments. Each plastic shape has the same mass
m
, and they are equally spaced by a distance
d
, as shown. The angles labeled
θ
describe the angle formed by the end of the string and the ceiling at each end. The center length of sting is horizontal. The remaining two segments each form an angle with the horizontal, labeled
ϕ
. Let
T
1
be the tension in the leftmost section of the string,
T
2
, be the tension in the section adjacent to it, and
T
3
be the tension in the horizontal segment. (a) Find an equation for the tension in each section of the string in terms of the variables
m
,
g
, and
θ
. (b) Find the angle
ϕ
in terms of the angle
θ
. (c) If
θ
=
5.10
°
, what is the value of
ϕ
?(d) Find the distance
x
between the endpoints in terms of
d
and
θ
.
A hoop of radius RH and mass mH and a solid cylinder of radius Rc and mass mc are released simultaneously at the top of a plane ramp of length L inclined at angle θ above horizontal. Which reaches the bottom first, and what is the speed of each there?
A small sphere with mass m is attached to a massless rod of length L that is pivoted at the top, forming a simple pendulum. The pendulum is pulled to one side so that the rod is at an angle θ from the vertical, and released from rest.
At this point, what is the linear acceleration of the sphere?
Express your answer in terms of g, θ
a nonuniform bar is suspended at rest in a horizontal position by two massless cords. One cord makes the angle u=36.9° with the vertical; the other makes the angle f =53.1° with the vertical. If the length L of the bar is 6.10 m, compute the distance x from the left end of the bar to its center of mass.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.