اختبار اختيار من متعدد تفاعلي: Centripetal Force Physics Assessment - inspire
Centripetal force is the inward force required to maintain an object's circular motion, acting perpendicular to its velocity and directed toward the center of the path. Its magnitude is determined by the object's mass, its speed, and the radius of the circular path according to the physical law \( F_c = \frac{mv^2}{r} \). This assessment explores these relationships through conceptual questions and practical calculations, such as determining the force on a rotating ball or calculating the required radius for a road turn based on safety acceleration limits. Understanding these principles is essential for engineering, aeronautics, and basic physics mechanics.
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A horse gallops around a circular arena. The centripetal force on the horse is ___.
Explanation
By definition, centripetal force is a center-seeking force that always acts toward the center of the circular path being followed.
Question 2
Points: 1
Which of the following increase the centripetal force?
Explanation
According to the formula \( F_c = \frac{m v^2}{r} \), the centripetal force is directly proportional to the square of the velocity; therefore, increasing velocity increases the force.
Question 3
Points: 1
Calculate the amount of centripetal force it takes for a softball pitcher to rotate a ball with a velocity of 3 m/s if the ball weighs .12 kg and her arm is .65 meters long.
Explanation
Using the formula \( F_c = \frac{m v^2}{r} \), where m = 0.12, v = 3, and r = 0.65. Calculation: \( \frac{0.12 \times 3^2}{0.65} = \frac{0.12 \times 9}{0.65} = \frac{1.08}{0.65} \approx 1.66 \text{ N} \).
Question 4
Points: 1
A bola is an old hunting instrument. If three rocks with a combined mass of 0.75 kg are spun at a speed of 20 m/s with a radius of 0.5 m, how much centripetal force is required to keep them spinning.
Explanation
Using the centripetal force formula \( F_c = \frac{m v^2}{r} \): \( F_c = \frac{0.75 \times 20^2}{0.5} = \frac{0.75 \times 400}{0.5} = \frac{300}{0.5} = 600 \text{ N} \).
Question 5
Points: 1
An engineer is planning a road with a turn. If the speed limit is 20 m/s and the centripetal acceleration cannot exceed 8.5 m/s/s, how big must the radius of the turn be?
Explanation
Centripetal acceleration is defined as \( a_c = \frac{v^2}{r} \). Rearranging for radius: \( r = \frac{v^2}{a_c} = \frac{20^2}{8.5} = \frac{400}{8.5} \approx 47.05 \text{ m} \). The closest option is 47 m.
Question 6
Points: 1
A car with mass m travels around a curve with velocity v. What do you know about the centripetal force if the velocity triples?
Explanation
Centripetal force is proportional to the square of the velocity (\( F_c \propto v^2 \)). If velocity is multiplied by 3, the force is multiplied by 32 = 9.
Question 7
Points: 1
A car with mass m travels around a curve with velocity v. What do you know about the centripetal force if the radius triples?
Explanation
Centripetal force is inversely proportional to the radius (\( F_c \propto \frac{1}{r} \)). If the radius is tripled, the force is reduced to one-third of its original value.
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