
A motorcyclist of mass is to negotiate a curve of radius with a speed . The minimum value of the coefficient of friction so that this negotiation may take place safely is?
A.
B.
C.
D.
Answer
156.6k+ views
Hint: Since there is a downward force (which equals the weight of the body) applied to a body. When a body takes a curve with radius there is a chance of slipping a body hence, to negotiate the slip the normal force acting opposite to the downward force must be balanced by the centrifugal force.
Complete answer:
Mass of a motorcyclist (given)
Since the gravity acts downward. Therefore, the weight of a body
Let us consider the normal force is equal to and opposite to the direction of weight of a body.
Now, we know that Centrifugal Force acting on the body:
where,
v = speed of a body
r = radius of curve taken by body
Also, we know that where,
F = Frictional Force and = Coefficient of friction
To avoid slip, the frictional force must be balanced by centrifugal force i.e.,
Substitute in the above expression, we get
Thus, the minimum value of the coefficient of friction so that this negotiation may take place safely is .
Hence, the correct option is (B) >
Note: Since this is a problem based on the balancing of two different forces hence, given conditions are to be analyzed very carefully and only after which the procedure of solving the problem is identified. To have a better understanding of the formulas used, it is essential to understand which kind of forces influences the problem.
Complete answer:
Mass of a motorcyclist
Since the gravity
Let us consider the normal force
Now, we know that Centrifugal Force acting on the body:
v = speed of a body
r = radius of curve taken by body
Also, we know that
F = Frictional Force and
To avoid slip, the frictional force must be balanced by centrifugal force i.e.,
Substitute
Thus, the minimum value of the coefficient of friction so that this negotiation may take place safely is
Hence, the correct option is (B)
Note: Since this is a problem based on the balancing of two different forces hence, given conditions are to be analyzed very carefully and only after which the procedure of solving the problem is identified. To have a better understanding of the formulas used, it is essential to understand which kind of forces influences the problem.
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