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23 Nov 2019

A 3.0 kg object is to be hung by some massless rope. 1 rope hangsat a 53 degree angle and the other is at a 140 degree angle.

a) What is the tensions of the two ropes?

b) If the 140 degree angle rope were to suddenly snap, what wouldbe the magnitude and direction of the acceleration at that instant?HINT: Use the 53 degree angle rope's tension value from part (a)

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Jarrod Robel
Jarrod RobelLv2
9 Aug 2019

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

A 215-kg robotic arm at an assembly plant is extended horizontally. The massless support rope attached to point B makes an angle of 15.0° with the horizontal, and the center of mass of the arm is at point C.

(a) What is the tension in the support rope?

(b) What are the magnitude and direction of the force exerted by hinge A on the robotic arm to keep the arm in the horizontal position?

This problem introduces the concept of tension. The example is a rope, oriented vertically, that is being pulled from both ends. Let Fu and Fd (with u for up and d for down) represent the magnitude of the forces acting on the top and bottom of the rope, respectively. Assume that the rope is massless so that its weight is negligible compared with the tension. (This is not a ridiculous approximation-modern rope material such as Kevlar can carry tensions thousands of times greater than the weight of tens of meters of such rope.)

Consider the three sections of rope labeled a, b, and c in the figure.

  • At point 1, a downward force of magnitude Fad acts on section a.
  • At point 1, an upward force of magnitude Fbu acts on section b.
  • At point 1, the tension in the rope is T1.
  • At point 2, a downward force of magnitude Fbd acts on section b.
  • At point 2, an upward force of magnitude Fcu acts on section c.
  • At point 2, the tension in the rope is T2.

(A) What is the magnitude Fad of the downward force on section a?

(B) What is the magnitude Fbu of the upward force on section b?

(C) The magnitude of the upward force on c, Fcu, and the magnitude of the downward force on b, Fbd, are equal because of which of Newton's laws?

(D) The magnitude of the force Fbu is ______ Fbd.

(E) Now consider the forces on the ends of the rope. What is the relationship between the magnitudes of these two forces?

(a) Fu > Fd

(b) Fu = Fd

(c) Fu < Fd

(F) The ends of a massless rope are attached to two stationary objects (e.g., two trees or two cars) so that the rope makes a straight line. For this situation, which of the following statements are true?

(a) The tension in the rope is everywhere the same.

(b) The magnitudes of the forces exerted on the two objects by the rope are the same.

(c) The forces exerted on the two objects by the rope must be in opposite directions.

(d) The forces exerted on the two objects by the rope must be in the direction of the rope.

Question Two

A rocket is fired at an angle from the top of a tower of height ho = 50.0 m. Because of the design of the engines, its position coordinates are of the form

x(t) = A + Bt2 and y(t) = C + Dt3

where A, B, C, and D, are constants.

Furthermore, the acceleration of the rocket 1.00 s after firing is a = (4.00i + 3.00j) m/s .

Take the origin of coordinates to be at the base of the tower.

(a) Find the constants A, B, C, and D, including their SI units.

(b) At the instant after the rocket is fired, what are its acceleration vector and its velocity?

(c) What are the x- and y-components of the rocket's velocity 10.0 s after it is fired, and how fast is it moving?

(d) What is the position vector of the rocket 10.0 s after it is fired?

 

Question Four

 

Figure 2

A bowling ball weighing 71.2 N is attached to the ceiling by a 3.80-m rope. The ball is pulled to one side and released; it then swings back and forth as a pendulum. As the rope swings through the vertical, the speed of the bowling ball is 4.20 m/s.

(a) What is the acceleration of the bowling ball, in magnitude and direction, at this instant?

(b) What is the tension in the rope at this instant? (10 marks)

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