A heavy mirror that has a width of 2 m is to be hung on a wall as shown in the figure below. The mirror weighs 700 N and the wir
e used to hang it will break if the tension exceeds 700 N (breaking strength). What is the shortest length of wire L that can be used to hang the mirror without the wire breaking? (Ignore any friction forces between the mirror and the wall.)
2 answers:
The translational equilibrium condition allows finding that the response for cable length with a maximum tension is
L = 2.56 m
Newton's second law says that the force is proportional to the mass and the acceleration of the body, in the special case that the acceleration is zero, the relationship is called the translational equilibrium condition.
∑ F = 0
Where the bold indicates vectors, F is the force and the sum is for all external forces.
The reference systems are coordinate systems with respect to which the decomposition of the vectors is carried out and the measurements are made, in this case we will use a system with the horizontal x axis and the vertical y axis.
In the attachment we can see a free body diagram of the system, let's write the equilibrium condition for each axis.
x-axis
Tₓ -Tₓ = 0
y-axis
2 - W = 0
Let's use trigonometry to decompose the tension, we can see from the graph and the adjoint that each string is half the length, let's call the angle θ
cos θ =
sin θ =
Tₓ = T cos θ
= T sin θ
We substitute
2 T sin θ = W (1)
The text indicates that the length of the block is 2 m, so the distance to the midpoint is
x = 1 m
Let's use the Pythagoras' Theorem
H² = CA² + CO²
CO =
CA = x
CO =
Where CO is the opposite leg, CA is the adjacent leg and H is the hypotenuse indicating H = L / 2,
Let's write the trigonometry functions
sin θ =
Let's substitute
sin θ =
Let's subtitute in the equation 1
2 T ( \frac{2 \sqrt{\frac{L^2}{4} -1 } }{L} ) = W
Let's solve by squaring
They indicate that the maximum tension of the cable is T = 700N and the weight is worth W = 700N, we substitute the values
L = 2.31 m
In conclusion using the translational equilibrium condition we can find that the response for cable length with maximum tension is
L = 2.31 m
Learn more about translational equilibrium here:
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Answer:
a) u = 30.29 m/s
b) t = 2.09 s
Explanation:
given,
velocity = 45 m/s
angle (θ) = 50°
horizontal velocity = 45 cos 50°
time taken to reach 150 m.
times =
t = 5.19 s
a) height of arrow
s = 46.78 m
v² - u² = 2 g s
u² = 2 × 9.81 × 46.78
u = 30.29 m/s
b) time taken by the apple =
= 3.09 s
time after which it has to be thrown = 5.19-3.09 = 2.1 s
Answer:
Pressure, P = 32666.66 Pa
Explanation:
It is given that,
Surface area of foot of Bimaba is 150 cm² or 0.015 m².
Her weight is 50 kg
We need to find the pressure does she exert on the ground, as she stands on her one foot. The force acting per unit area is called pressure. It can be given by :
So, the pressure is 32666.66 Pa.
The time needed for the 7th car to pass is 13.2 s
Explanation:
The motion of the train is a uniformly accelerated motion, therefore we can use suvat equations.
We start by analzying the motion of the first car, by using the equation:
where
s is the distance covered by the first car in a time t, which corresponds to the length of one car
u = 0 is the initial velocity
a is the acceleration
t = 5.0 s is the time
The equation can be rewritten as
where L is the length of one car.
The same equation can be written considering the first 7 cars:
where
7L is the distance covered by the 7 cars
t' is the time needed
We still have
u = 0
And the acceleration is constant so it is
Substituting into the equation, we can find t':
In attachment the graph of the distance covered versus the time taken: since the motion is uniformly accelerated, the relationship between the two variables is quadratical.
Learn more about accelerated motion:
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