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Question: A monkey is sitting on a tree limb. The limb exerts a normal force of \[48N\] and a frictional force...

A monkey is sitting on a tree limb. The limb exerts a normal force of 48N48N and a frictional force of 20N20N. Find the magnitude of the total force exerted by the limb on the monkey.
(A)23N(A)23N
(B)36N(B)36N
(C)  48N(C)\;48N
(D)52N  (D)52N\;

Explanation

Solution

Once we have two bodies that are in contact with one another, then there acts a force in between them. Since this force is acting because of the contact between the two bodies, it is termed as the contact force. This contact force may be resolved in two components. The vertical component of the contact force is understood because the normal reaction force and also the horizontal component is called the frictional force. The normal reaction force is that which acts perpendicular to the surfaces in contact. And also the frictional force is that which resists the motion between two surfaces.

Formula used:
The resultant magnitude of the force R=(Fn)2+(Ff)2R = \sqrt {{{\left( {{F_n}} \right)}^2} + {{\left( {{F_f}} \right)}^2}}
Where, Fn{F_n}-Normal force and Ff{F_f}-Frictional force

Complete step-by-step solution:
The limb exerts a normal force of 48N and a frictional force of 20N then the magnitude of the entire force exerted by the limb on the monkey is
R=(Fn)2+(Ff)2R = \sqrt {{{\left( {{F_n}} \right)}^2} + {{\left( {{F_f}} \right)}^2}}
⇒R=(48)2+(20)2\Rightarrow R = \sqrt {{{\left( {48} \right)}^2} + {{\left( {20} \right)}^2}}
⇒R=2304+400=2704\Rightarrow R = \sqrt {2304 + 400} = \sqrt {2704}
⇒R=52N\Rightarrow R = 52N
The magnitude of the total force exerted by the limb on the monkey is52N52N.
Hence, option D is correct.

Additional information:
The coefficient of friction (COF) may be a dimensionless number and COF is termed as the ratio between friction force and normal force. The material which has COF smaller than 0.10.1 are considered lubricous materials. COF depends on the character of the materials and surface roughness.

Note: When two bodies are placed in grips, attractive forces act between their particles at the surface of contact. As a result, each body exerts a contact force on another body. These mutual forces are equal and opposite by obeying Newton’s third law. A component of the contact force is termed the frictional force.