A kg loudspeaker is suspended m below the ceiling by two -m-long cables that angle outward at equal angles. What is the tension in the cables?
The tension in the cable = .
The pulling force transferred axially by a string, cable, chain, or similar item, or by each end of a rod, truss member, or similar three-dimensional object is known as tension.
Mass of a loudspeaker = kg, Distance of the loudspeaker from the ceiling = m and the length of each cable = m
The arrangement's free body diagram is seen below.
From the figure, formula to calculate the angle is,
= the cable's angle with the vertical.
= loudspeaker height from the ceiling.
= rope's length.
Substitute m for and m for to find .
Mass of a loudspeaker = kg, Height of the loudspeaker from the ceiling = m and the length of each cable = m.
For the vertical equilibrium requirement, Newton's second law is used,
In the y-direction, resolving the components of forces in the ropes,
T = Tension in the cable.
= Angle made by the cable with the vertical.
= mass of the loudspeaker.
= acceleration due to gravity.
Substitute kg for , for and for to find T.
Hence, the tension in the cable = .
In an electricity experiment, a plastic ball is suspended on a -cm-long string and given an electric charge. A charged rod brought near the ball exerts a horizontal electrical force on it, causing the ball to swing out to a angle and remain there.
a. What is the magnitude of ?
b. What is the tension in the string
A block pushed along the floor with velocity slides a distance d after the pushing force is removed.
a. If the mass of the block is doubled but its initial velocity is not changed, what distance does the block slide before stopping?
b. If the initial velocity is doubled to but the mass is not changed, what distance does the block slide before stopping?
An accident victim with a broken leg is being placed traction. The patient wears a special boot with a pulley attached to the sole. The foot and boot together have a mass of 4.0 kg and the doctor has decided to hang a 6.0 kg mass from the rope. The boot is held suspended by the ropes, as shown in FIGURE P6.41, and does not touch the bed a. Determine the amount of tension in the rope by using Newton’s laws to analyze the hanging mass. b. The net traction force needs to pull straight out on the leg. What is the proper angle u for the upper rope? c. What is the net traction force pulling on the leg? Hint: If the pulleys are frictionless, which we will assume, the tension in the rope is constant from one end to the other.
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