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. To determine what happens to the force required for an object to maintain circular motion if the period is halved, let's start by understanding the relationship between force and period. The force required for an object to maintain circular motion is given by the formula: centripetal force = mass × (velocity^2 / radius).

When the period is halved, it means the object completes one revolution in half the time. Since velocity is distance divided by time, halving the period implies a doubling of the angular velocity (the rate at which the object rotates).

Doubling the angular velocity has the effect of doubling the linear velocity of the object (assuming a constant radius). As a result, the object will experience a greater force to maintain circular motion.

Therefore, the correct answer is a) force doubles.

2. Let's evaluate the given statements to determine which one is true:

a) The acceleration of free fall objects on Earth is approximately 9.8 m/s^2 [down].
This statement is true. The acceleration due to gravity on Earth is approximately 9.8 m/s^2, and objects in free fall experience this acceleration.

b) Heavier objects in free fall accelerate faster than light objects.
This statement is false. In the absence of air resistance, all objects, regardless of their mass, fall at the same rate. This principle is known as the equivalence principle.

c) In projectile motion, the initial speed is always equal to the final speed.
This statement is false. In projectile motion, the initial speed and final speed may be different. The final speed depends on the total time of flight and the vertical displacement of the projectile.

d) None are true.
Since statement (a) is true, this option is incorrect.

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, let's review the options:

a) The gravity needs to be resolved into components.
In a pulley problem involving an inclined plane, the gravitational force acting on the objects will need to be resolved into components along the plane's surface and perpendicular to it. This is essential to accurately analyze the forces involved.

b) The tension needs to be resolved into components.
For a pulley problem involving an inclined plane, there may be tensions in the strings that need to be resolved into components to determine their effect on the system. However, this is not a specific requirement for all pulley problems involving inclined planes.

c) The friction needs to be resolved into components.
In a pulley problem involving an inclined plane, it is important to resolve the friction force into components, particularly the component parallel to the plane's surface. This allows for a more accurate analysis of the forces affecting the system.

d) The direction convention is the same for both blocks.
The direction convention refers to the choice of positive and negative directions for forces and displacements. It is crucial to establish a consistent direction convention for both blocks to ensure accurate calculations. However, this is not directly tied to pulley problems involving inclined planes.

Therefore, the correct answer is c) the friction needs to be resolved into components.