A 9.5 kg monkey is hanging by one arm from a branch and is swinging in a vertica

Question

A 9.5 kg monkey is hanging by one arm from a branch and is swinging in a vertical circle. The distance between the monkey's mass and the branch is 85 cm. As the monkey swings through the lowest point in the circle, it has a speed of 2.8 m/s. Find the magnitude of the tension in the monkey's arm. A)5.4 N B) 120 N C) 180 N D) 93 N E) 210 N A force in the +x direction with a magnitude of 18.0 Nis applied to a 6.00 kg box that is sitting on the horizontal, frictionless surface of a frozen lake. If this is the only horizontal force on the box and it is initially at rest at x = 0, what is the speed after it has traveled 14.0 m? A)9.2 m/s B) 7.7 m/s C) 18 m/s D) 84 m/s E) 26 m/s

Explanation / Answer

12. Given : m= 9.5 kg , v = 2.8 m/s , R = 85 cm ~ 0.85 m

Acceleration can be find out as: a = v2/R = (2.8)2/ 0.85 = 9.22 m/s2

Centripetal force F = ma = (9.5)(9.22)= 87.59 N

Tension can be given as : T = m(a+g)= 9.5(9.22+9.81) = 180 N

(B) is the correct option.

13. Given : m = 6 kg, F = 18 N , d = 14 m

We know that F = ma

a = F/m = 18/6 = 3 m/s2

Using equation of motion

v2= u2+2as [ u=0]

v2= 2(3)(14)

v = 9.16 m/s~ 9.2 m/s

(A) is the correct option

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