Question

A stunt man whose mass is 70 kg swings from the end ofa 4.0 m long rope along thearc of a vertical circle. Assuming that he starts from rest whenthe r

Other
ANSWERED
asked 2021-04-25
A stunt man whose mass is 70 kg swings from the end ofa 4.0 m long rope along thearc of a vertical circle. Assuming that he starts from rest whenthe rope is horizontal, find the tensions in the rope that are required to make him follow his circular path at each of the following points.
(a) at the beginning of his motion N
(b) at a height of 1.5 m above the bottom of the circular arc N
(c) at the bottom of the arc N

Expert Answers (1)

2021-04-27
m = 70 kg, L = 4.0 m,
(a) at the beginning of his motion T=0
b) h = 1.5 m
\(\displaystyle{m}{g}{L}={m}{g}{h}+{m}\frac{{v}^{{2}}}{{2}}\)
so \(\displaystyle{m}{v}^{{2}}={2}{m}{g{{\left({L}-{h}\right)}}}\)
\(\displaystyle{T}-{m}{g}{\cos{\theta}}={\frac{{{m}{v}^{{2}}}}{{{L}}}}\) where \(\displaystyle{\cos{\theta}}={\frac{{{L}-{h}}}{{{L}}}}\)
\(\displaystyle\therefore{T}={m}{g}{\frac{{{L}-{h}}}{{{L}}}}+{2}{m}{g}{\frac{{{L}-{h}}}{{{L}}}}={3}{m}{g}{\frac{{{1}-{h}}}{{{L}}}}={1286}\ {N}\)
c) let h=0 in \(\displaystyle{T}={3}{m}{g}{\frac{{{1}-{h}}}{{{L}}}}\)
So T=3mg=2058 N
42
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours

Relevant Questions

asked 2021-02-19
A 10 kg objectexperiences a horizontal force which causes it to accelerate at 5 \(\displaystyle\frac{{m}}{{s}^{{2}}}\), moving it a distance of 20 m, horizontally.How much work is done by the force?
A ball is connected to a rope and swung around in uniform circular motion.The tension in the rope is measured at 10 N and the radius of thecircle is 1 m. How much work is done in one revolution around the circle?
A 10 kg weight issuspended in the air by a strong cable. How much work is done, perunit time, in suspending the weight?
A 5 kg block is moved up a 30 degree incline by a force of 50 N, parallel to the incline. The coefficient of kinetic friction between the block and the incline is .25. How much work is done by the 50 N force in moving the block a distance of 10 meters? What is the total workdone on the block over the same distance?
What is the kinetic energy of a 2 kg ball that travels a distance of 50 metersin 5 seconds?
A ball is thrown vertically with a velocity of 25 m/s. How high does it go? What is its velocity when it reaches a height of 25 m?
A ball with enough speed can complete a vertical loop. With what speed must the ballenter the loop to complete a 2 m loop? (Keep in mind that the velocity of the ball is not constant throughout the loop).
asked 2021-05-04
Until he was in his seventies, Henri LaMothe excited audiences by belly-flopping from a height of 13 m into 35 cm. of water. Assuming that he stops just as he reaches the bottom of the water and estimating his mass to be 72 kg, find the magnitudes of the impulse on him from the water.
asked 2021-03-24
A man with mass 70.0 kg stands on a platform withmass 25.0 kg. He pulls on the free end of a rope thatruns over a pulley on the ceiling and has its other end fastened tothe platform. The mass of the rope and the mass of the pulley canbe neglected, and the pulley is frictionless. The rope is verticalon either side of the pulley.
a) With what force does he have to pull so that he and theplatform have an upward acceleration of \(\displaystyle{1.80}\frac{{m}}{{s}^{{2}}}\)?
b) What is the acceleration of the rope relative to him?
asked 2021-03-12
A 75.0-kg man steps off a platform 3.10 m above the ground. Hekeeps his legs straight as he falls, but at the moment his feettouch the ground his knees begin to bend, and, treated as aparticle, he moves an additional 0.60 m before coming torest.
a) what is the speed at the instant his feet touch theground?
b) treating him as a particle, what is his acceleration(magnitude and direction) as he slows down, if the acceleration isassumed to be constant?
c) draw his free-body diagram (see section 4.6). in termsof forces on the diagram, what is the net force on him? usenewton's laws and the results of part (b) to calculate the averageforce his feet exert on the ground while he slows down. expressthis force in newtons and also as a multiple of his weight.
...