Newton's Laws of Motion

Position function

Force applied

Velocity function

Displacement

Increasing the density of water would have little to no effect on the system's equilibrium because the buoyant force already balances gravity for the submerged block.

Increasing the density of water would cause the system to tilt, thus tilting the pulley and making it unstable.

Increasing the density of the water would cause the first block to sink further due to increased buoyant force on the second.

Increasing the density of water would raise the second block slightly until a new equilibrium is established.

The maximum height reached will be exactly half the original height.

The maximum height reached will be less than half the original height.

The maximum height reached will exceed the original height due to lesser air resistance at lower velocity.

The maximum height reached will be more than half but less than the original height.

Spin objects with different shapes at consistent angular velocities and measure their respective angular decelerations when subject to identical torques.

Place differently shaped objects on an incline plane covered in sandpaper measuring delay before they start sliding down due to increased static friction.

Drop objects from the same height and record time taken to hit the ground checking for any deviations due to air resistance.

Compress springs using objects of various shapes equally then release to compare projected distances.

The wall pushes back with an equal, but opposite force.

The wall applies no force.

The wall moves inwards.

The wall pulls you towards itself.

The velocity doubles.

The mass doubles.

There is no change in the state of motion.

The acceleration doubles.

None reach the bottom simultaneously since all objects fall at the same rate regardless of their internal structure provided a frictionless environment.

Both reach the bottom at the same time due to various factors like air resistance and material properties could influence outcomes unless specified otherwise.

The hollow cylinder reaches the bottom first due to its shape allowing it greater stability and therefore faster descent down the slope.

The solid sphere reaches the bottom first because it has a smaller moment of inertia than does the hollow cylinder resulting in a larger fraction translated into linear kinetic energy compared to rotational kinetic energy.

The vertical component will gradually increase during ascent and decrease during descent since there is no air resistance to alter its horizontal velocity.

The vertical component slowly increases as the ball rises and reaches a maximum just before impact.

The vertical component will remain constant throughout the entire trajectory with the same value present at the start and end.

The vertical component will decrease until it reaches a turning point, then increases back to its original value at impact.

The translational acceleration is twice r times the angular acceleration (a = 2rα).

The translational acceleration equals r times the angular acceleration (a = r*α).

There is no relation between translational and angular accelerations for pure rolling motion.

The translational acceleration is half r times the angular acceleration (a = 0.5rα).

Only the particle with increased mass experiences a reduction in acceleration due to its greater inertia.

Both particles will have lower magnitudes of acceleration but inversely proportional to their respective masses.

The particle with decreased mass now experiences greater acceleration than prior to the mass increase of the other particle.

No change in either particles' accelerations since momentum conservation dictates no net force acts on them.