A purple beam is hinged to a wall to hold up a blue sign. The beam has a mass of mb = 6.7 kg and the sign has a mass of ms = 17.
2 kg. The length of the beam is L = 2.78 m. The sign is attached at the very end of the beam, but the horizontal wire holding up the beam is attached 2/3 of the way to the end of the beam. The angle the wire makes with the beam is θ = 33.9°.
What is the tension in the wire? What is the net force the hinge exerts on the beam? The maximum tension the wire can have without breaking is
T=936 N. What is the maximum mass sign that can be hung from the beam?
What is the tension in the wire? What is the net force the hinge exerts on the beam? The maximum tension the wire can have without breaking is
T=936 N. What is the maximum mass sign that can be hung from the beam?
1 answer:
Answer:
wire tension =1003.8N
force in the hinge=894.15N
mass of sign=15.8Kg
Explanation:
Hello!
To solve this problem you must follow the following steps the complete procedure is in the attached images
1. draw the complete free body diagram of the situation
2. Raise Newton's equilibrium equations that establish that for a body to be in equilibrium, the sums of its vertical, horizontal forces and moments with respect to point A must be equal to zero.
3. Use the moment equilibrium equation with respect to point A (see attached image) to find the cable tension.
4. Use the equilibrium equations of vertical and horizontal forces to find the total reaction force on the hinge.
5. Use the equilibrium equation of moments with respect to point A (see attached image) to find the mass of the sign.
Remember to use algebra correctly to find the variables.
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A) The total energy of the system is sum of kinetic energy and elastic potential energy:
where
m is the mass
v is the speed
k is the spring constant
x is the elongation/compression of the spring
The total energy is conserved, so we can calculate its value at any point of the motion. If we take the point of maximum displacement:
then the velocity of the system is zero, so the total energy is just potential energy, and it is equal to
b) When the position of the object is
the potential energy of the system is
and so the kinetic energy is
since the mass is
, and the kinetic energy is given by
we can re-arrange the formula to find the speed of the object:
c) The potential energy when the object is at
is
Therefore the kinetic energy is
d) We already found the potential energy at point c, and it is given by
where
m is the mass
v is the speed
k is the spring constant
x is the elongation/compression of the spring
The total energy is conserved, so we can calculate its value at any point of the motion. If we take the point of maximum displacement:
then the velocity of the system is zero, so the total energy is just potential energy, and it is equal to
b) When the position of the object is
the potential energy of the system is
and so the kinetic energy is
since the mass is
we can re-arrange the formula to find the speed of the object:
c) The potential energy when the object is at
is
Therefore the kinetic energy is
d) We already found the potential energy at point c, and it is given by