A 1500 kg car takes a 50-m-radius unbanked curve at 15 m/s. What is the size of

wurmiana6d

wurmiana6d

Answered question

2021-11-15

A 1500 kg automobile travels at 15 m/s around a 50 m-radius unbanked curve. What is the size of the friction force on the car?

Answer & Explanation

Helen Rodriguez

Helen Rodriguez

Beginner2021-11-16Added 9 answers

Step 1 
Given values: 
m=1500kg 
r=50m 
v=15ms 
Centripetal acceleration operates on a vehicle traveling in a circle.
According to Newtons

nick1337

nick1337

Expert2023-05-11Added 777 answers

Answer:
4500N
Explanation:
To solve this problem, we can use the concept of centripetal force. The centripetal force required to keep an object moving in a circular path is provided by the friction force in this case.
The centripetal force (Fc) can be calculated using the equation:
Fc=m·v2r
where m is the mass of the automobile, v is its velocity, and r is the radius of the curve.
Substituting the given values into the equation, we have:
Fc=1500kg·(15m/s)250m
Simplifying the expression, we find:
Fc=4500N
Therefore, the size of the friction force (Ff) acting on the car is equal to the centripetal force, which is 4500 N.
In conclusion, the size of the friction force on the car is 4500N.
Eliza Beth13

Eliza Beth13

Skilled2023-05-11Added 130 answers

The centripetal force (Fcentripetal) is given by the formula:
Fcentripetal=mv2r,
where m is the mass of the car, v is the velocity, and r is the radius of the curve.
In this case, the mass of the automobile (m) is 1500 kg, the velocity (v) is 15 m/s, and the radius of the curve (r) is 50 m. Substituting these values into the formula, we have:
Fcentripetal=(1500kg)(15m/s)250m.
Calculating the centripetal force:
Fcentripetal=6750N.
Now, the friction force (Ffriction) acts in the opposite direction to the car's motion and can be found using the formula:
Ffriction=μ·m·g,
where μ is the coefficient of friction and g is the acceleration due to gravity. Since the curve is unbanked, the friction force provides the centripetal force. Thus, Ffriction=Fcentripetal.
Now we can substitute the known values into the equation:
6750N=μ·(1500kg)·(9.8m/s2).
Simplifying the equation:
μ·1500·9.8=6750.
Dividing both sides by 1500·9.8:
μ=67501500·9.8.
Evaluating the expression:
μ0.459.
Therefore, the size of the friction force on the car is approximately 6750 N, and the coefficient of friction is approximately 0.459.
Don Sumner

Don Sumner

Skilled2023-05-11Added 184 answers

The gravitational force can be calculated using the formula:
Fg=m·g
where Fg is the gravitational force, m is the mass of the automobile, and g is the acceleration due to gravity. In this case, the mass of the automobile is 1500 kg.
Substituting the given values into the equation, we have:
Fg=1500kg·9.8m/s2
Next, we need to calculate the centripetal force acting on the automobile. The centripetal force can be determined using the formula:
Fc=m·v2r
where Fc is the centripetal force, m is the mass of the automobile, v is the velocity, and r is the radius of the curve. In this case, the velocity is 15 m/s and the radius is 50 m.
Substituting the given values into the equation, we have:
Fc=1500kg·(15m/s)250m
Now, we know that the friction force acts towards the center of the curve and provides the necessary centripetal force. Therefore, the friction force is equal to the centripetal force:
Ff=Fc
Substituting the calculated value of Fc into the equation, we find:
Ff=1500kg·(15m/s)250m
Simplifying the equation gives us the final result:
Ff=4500N
Therefore, the size of the friction force on the car is 4500N.

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