1. What happens to the force required for an object to maintain circular motion if the period is halved (goes around twice as fast around the circle)?
a) force doubles
b) force quadruples
c) force is halved
d) force is quartered
my answer: c
2. Which is true
a) the acceleration of free fall objects on Earth is approximately 9.8 m/s^2 [down]
b) heavier objects in free fall accelerate faster than light objects
c) In projectile motion, the initial speed is always equal to the final speed
d) none are true
my answer: a
3. In a pulley problem involving an inclined plane:
a) the gravity needs to be resolved into components
b) the tension needs to be resolved into components
c) the friction needs to be resolved into components
d) the direction convention is the same for both blocks
my answer: c
1. What happens to the force required for an object to maintain circular motion if the period is halved (goes around twice as fast around the circle)?
The correct answer is b) force quadruples.
When the period is halved, the frequency doubles. According to the formula for the centripetal force required for circular motion (F = (m * v^2) / r), the force is directly proportional to the square of the velocity. Therefore, if the velocity doubles, the force required will quadruple.
2. Which is true?
The correct answer is a) the acceleration of free fall objects on Earth is approximately 9.8 m/s^2 [down].
Objects in free fall on Earth experience a acceleration due to gravity of approximately 9.8 m/s^2 downward. This acceleration is often represented by the symbol "g".
b) Heavier objects in free fall do not accelerate faster than lighter objects. In a vacuum or in the absence of air resistance, all objects (regardless of their mass) would fall with the same acceleration due to gravity.
c) In projectile motion, the initial speed is not always equal to the final speed. The initial speed and final speed depend on various factors like the angle of projection, air resistance, and gravitational pull.
3. In a pulley problem involving an inclined plane:
The correct answer is a) the gravity needs to be resolved into components.
In a pulley problem involving an inclined plane, the force due to gravity needs to be resolved into components in order to determine its effect along the direction of motion and perpendicular to it. This is because the gravitational force can be split into two components: one parallel to the inclined plane (which affects the motion) and one perpendicular to the inclined plane (which is usually countered by the normal force).
1. To determine what happens to the force required for an object to maintain circular motion if the period is halved (goes around twice as fast around the circle), we need to use the formula for centripetal force. The centripetal force is given by F = (m * v^2) / r, where m is the mass of the object, v is the velocity, and r is the radius of the circle.
If the period is halved, it means that the object is going around the circle twice as fast, so its velocity (v) becomes twice its original value. Since the force required is dependent on the square of the velocity, the force will be quadrupled. Therefore, the correct answer is b) force quadruples.
2. To determine which statement is true regarding the acceleration of free fall objects on Earth, we need to recall that the standard acceleration due to gravity on Earth is approximately 9.8 m/s^2, directed downwards. Thus, statement a) "the acceleration of free fall objects on Earth is approximately 9.8 m/s^2 [down]" is true.
On the other hand, statement b) "heavier objects in free fall accelerate faster than light objects" is false because all objects, regardless of their mass, fall with the same acceleration due to gravity.
Similarly, statement c) "In projectile motion, the initial speed is always equal to the final speed" is false because in most cases, the initial and final speeds are not equal in projectile motion.
Therefore, the correct answer is a) the acceleration of free fall objects on Earth is approximately 9.8 m/s^2 [down].
3. In a pulley problem involving an inclined plane, we need to analyze the forces acting on the system. The inclined plane introduces a component of the force of gravity that needs to be considered. Therefore, we need to resolve the force of gravity into components.
The correct answer is a) the gravity needs to be resolved into components.
In this type of problem, it is important to break down the weight of the objects into the parallel and perpendicular components relative to the inclined plane. This allows us to analyze the forces acting in different directions and make accurate calculations.
Therefore, to correctly solve pulley problems involving an inclined plane, we need to resolve the gravity (weight) of the objects into components.