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Vertical Centripetal Forces quiz

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  • What is the formula for centripetal acceleration in circular motion?
    Centripetal acceleration is given by a_c = v^2 / r, where v is velocity and r is the radius of the circle.
  • Why is the speed not constant in vertical circular motion?
    The speed is not constant because gravity (mg) acts on the object, changing its speed as it moves through the loop.
  • At the bottom of a vertical loop, which forces act on a roller coaster cart?
    At the bottom, the normal force from the seat acts upward and gravity (mg) acts downward.
  • How do you determine the sign of forces in centripetal force problems?
    Forces pointing toward the center of the circle are positive, those pointing away are negative, and perpendicular forces contribute zero.
  • What is the centripetal acceleration at the bottom of the loop if v = 30 m/s and r = 10 m?
    The centripetal acceleration is a_c = 30^2 / 10 = 90 m/s^2.
  • How do you calculate the normal force at the bottom of the loop?
    The normal force at the bottom is n_b = m(a_c + g), where a_c is centripetal acceleration and g is gravity.
  • What is the normal force at the bottom for a 70 kg mass, a_c = 90 m/s^2, and g = 9.8 m/s^2?
    n_b = 70 × (90 + 9.8) ≈ 7000 N.
  • What is the centripetal acceleration at the top of the loop if v = 20 m/s and r = 10 m?
    The centripetal acceleration is a_c = 20^2 / 10 = 40 m/s^2.
  • How do the directions of normal force and gravity compare at the top of the loop?
    At the top, both the normal force and gravity act downward, toward the center of the loop.
  • How do you calculate the normal force at the top of the loop?
    The normal force at the top is n_t = m(a_c - g), since both forces act in the same direction.
  • What is the normal force at the top for a 70 kg mass, a_c = 40 m/s^2, and g = 9.8 m/s^2?
    n_t = 70 × (40 - 9.8) ≈ 2100 N.
  • Why is the normal force at the bottom of the loop greater than at the top?
    The normal force is greater at the bottom because the velocity (and thus centripetal acceleration) is higher, and the normal force must also counteract gravity.
  • What equation is used to relate the sum of forces to centripetal acceleration?
    The equation is ΣF = m a_c, where ΣF is the sum of forces toward the center.
  • What happens to the normal force if the speed at the top of the loop decreases further?
    If the speed decreases, a_c decreases, and the normal force becomes smaller; if it drops below g, the cart may lose contact with the track.
  • What is the main difference in calculating forces at the top versus the bottom of a vertical loop?
    At the bottom, the normal force and gravity act in opposite directions, while at the top, both act toward the center, so their effects are added or subtracted accordingly.