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Two cars are traveling at the same speed of 27 m/s on a curve thathas a radius of 120 m. Car A has a mass of 1100 kg and car B has amass of 1600 kg. Find the centripetal acceleration and thecentripetal force for each car.

User Zadubz
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1 Answer

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Answer:


a_(cA) = 6.075 m/s²


a_(cB) = 6.075 m/s²


F_(cA) = 6682.5 N


F_(cB) = 9720 N

Step-by-step explanation:

Normal or centripetal acceleration measures change in speed direction over time. Its expression is given by:


a_(c) = (v^(2) )/(r) Formula 1

Where:


a_(c) : Is the normal or centripetal acceleration of the body ( m/s²)

v: It is the magnitude of the tangential velocity of the body at the given point

.(m/s)

r: It is the radius of curvature. (m)

Newton's second law:

∑F = m*a Formula ( 2)

∑F : algebraic sum of the forces in Newton (N)

m : mass in kilograms (kg)

Data


v_(A) = 27 (m)/(s)


v_(B) = 27 (m)/(s)


m_(A) = 1100 kg


m_(B) = 1600 kg

r= 120 m

Problem development

We replace data in formula (1) to calculate centripetal acceleration:


a_(cA) = ((27)^(2) )/(120)


a_(cA) = 6.075 m/s²


a_(cB) = ((27)^(2) )/(120)


a_(cB) = 6.075 m/s²

We replace data in formula (2) to calculate centripetal force Fc) :


F_(cA) = m_(A) *a_(cA) = 1100kg*6.075(m)/(s^(2) )


F_(cA) = 6682.5 N


F_(cB) = m_(B) *a_(cB) = 1600kg*6.075(m)/(s^(2) )


F_(cB) = 9720 N

User Djsp
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