Question

Gibbons, small Asian apes, move by brachiation, swinging below a handhold to move forward to the next handhold. A 9.0 kg gibbon has an arm length (hand to shoulder) of 0.60 m. We can model its motion as that of a point mass swinging at the end of a 0.60-m-long, massless rod. At the lowest point of its swing, the gibbon is moving at 3.2 m/s .

What upward force must a branch provide to support the swinging gibbon?

Express your answer to two significant figures and include the appropriate units.

(Textbook is College Physics by:Knight, Jones, and Field.)

Answer 1

Answer:

2.4 x 10² N

Explanation:

$m$ = mass of the gibbon = 9.0 kg

$r$ = arm length of the gibbon = 0.60 m

$v$ = speed of gibbon at the lowest point of swing = 3.2 m/s

$W$  = weight of the gibbon in downward direction

$F$ = Upward force provided by the branch

weight of the gibbon in downward direction is given as

$W$ = $m$ g

$W$  = (9.0) (9.8)

$W$  = 88.2 N

Force equation for the motion of gibbon at the lowest point is given as

$F - W = \frac{mv^{2}}{r}$

$F - 88.2 = \frac{(9.0)(3.2)^{2}}{0.60}$

$F$ = 241.8 N

$F$ = 2.4 x 10² N

Answer 2

The upward force by a branch provide to support the swinging gibbon (small Asian apes) is 241.8 N.

What is centripetal force?

Centripetal force is the force which is required to keep rotate a body in a circular path. The direction of the centripetal force is inward of the circle, towards the center of rotational path.

The centripetal force of moving body in a circular path can be given as,

$F_c=\dfrac{mv^2}{r}$

Here, (m) is the mass of the body, (v) is the speed of the body, and (r) is the radius of the circular path.

At the lowest point of its swing, the gibbon is moving at 3.2 m/s. The mass of the Gibbon is 9 kg and the arm length of the gibbon is 0.60 m. This is the radius of the path at which the Gibbon is moving.

Thus, The centripetal force it is experiencing is found out by the above formula as,

$F_c=\dfrac{9\times(3.2)^2}{0.6}\\F_c+153.6\rm N$

The gravitational force experience by Gibbons is,

$F_g=-mg\\F_g=-9\times9.8\\F_g=-88.2\rm N$

Negative sign is for downward direction.

The net force acting on the body is,

$F_{up}+F_g=F_c\\F_{up}-88.2=153.6\\F_{up}=241.8\rm N$

Thus, the upward force by a branch provide to support the swinging gibbon (small Asian apes) is 241.8 N.

Learn more about the centripetal force here;

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