Hooke's Law
What does a larger spring constant (k) tell you about a spring's stiffness?
The spring is stiffer and harder to stretch/compress (requires more force for the same displacement)
Does the Universal Law of Gravitation apply only to massive objects like planets and stars, most objects, or to all objects with mass?
All objects with mass.
What is the correct way to write 0.0000000000667 in scientific notation?
6.67 x 10^-11
If you double the mass of ONE object while keeping the distance between them constant, what happens to the gravitational force between them? What kind of relation is this?
It doubles. Directly proportional relation.
What is the "equilibrium position" of a spring? Does it ever change?
It is the spring's natural, unstretched/uncompressed resting length. This position can change depending on the forces acting on the spring, like a hanging mass.
In the equation F = -kx, what does x represent, and how is it different from the spring's total length?
x is the change in length (stretch or compression distance), found by subtracting the unstretched length from the total length.
What are the units of the fundamental gravitational constant? (G)
Newtons x meters squared per kilogram squared
N*m^2/kg^2
What are the SI units for force, stretch distance, and spring constant?
Force = Newtons (N), Distance = meters (m), Spring constant = N/m.
What kind of relation does Kinetic Energy have with velocity?
KE = 1/2 m * v^2
Quadratic, KE is proportional to velocity squared.
If pulling a spring to stretch it 5cm requires a force of 10 N to the right, how much force is required to push/compress that same spring by 5 cm to the left?
The same amount, 10 N. Hooke's Law works symmetrically for stretching and compressing.
If you apply twice as much pulling force to an ideal spring, what happens to the distance it stretches?
It stretches twice as far (force and stretch distance are directly proportional).
Earth exerts a gravitational force pulling down on a watermelon. According to Newton's 3rd Law, does the watermelon exert a gravitational force on Earth? If so, how strong is it?
Yes, the watermelon exerts an equal and opposite gravitational force pulling upward on the Earth.
A spring with k = 200N/m is stretched by 0.5m. What is the spring force?
100 N
Two objects attract each other with a gravitational force of 20 N. If the distance between them is cut in half, what is the new force of attraction?
80 N. Halving distance quadruples force.
How does velocity relate to position? How does acceleration relate to velocity?
Velocity is the rate of change of position, acceleration is the rate of change of velocity.
Two springs, A and B, are stretched by the same distance. Spring A requires twice as much force to stretch as Spring B. How do their spring constants compare?
Spring A's spring constant (k_A) is twice as large as Spring B's (k_A = 2k_B)
What is the main difference between mass (m) and weight (F_g)?
Mass is the amount of matter in an object (constant everywhere), while weight is the gravitational force acting on that mass (changes with gravitational field strength).
What are the units of acceleration? What do they mean?
Meters per second squared. (m/s^2) They mean meters per second per second.
What's changing is the number of meters per second, in other words, the rate of change of the velocity.
Two asteroids exert a gravitational force on each other. If the distance between their centers is doubled, what happens to the gravitational force?
The force becomes 1/4 of what it was before, because gravity follows an inverse-squared relationship with distance.
A block hangs at rest from a spring suspended from the ceiling. Is the spring currently at its "natural" unstretched length? Which two forces are balancing each other to create this new equilibrium point?
The spring is being stretched beyond it's "natural" equilibrium length. Gravity is pulling down, and the spring is pulling up, balancing out at a new equilibrium position.
A heavy block hangs at rest from a spring. If you take this exact setup to the Moon, will the spring stretch more, less, or the same amount as on Earth?
Less, because the downward gravitational force on the block is smaller on the Moon, requiring less upward spring force to stay in balance.
Why don't you feel the gravitational attraction between you and your desk or pencil in a classroom?
Because the gravitational constant (G) is extremely small (6.67 times 10^-11), making the force between small masses negligible.
A spring has a spring constant of 50 N/m. How far does a 100 N force stretch it? How far would a 10 N force stretch it?
2m for the 100N force, 0.2m for the 10N force.
If you double the mass of BOTH attracting objects AND double the distance between their centers, what happens to the net gravitational force between them?
The force stays the same.
Doubling both masses -> x2 x2 = x 4
Doubling distance -> x 1/4
They cancel out.
Why is Hooke's Law often written with a negative sign (F = -kx)? What does that negative sign tell us about the direction of the spring force relative to the stretch or compression?
It indicates that the spring force is a restoring force—it always points in the direction opposite to the displacement x to push or pull the spring back toward its equilibrium position.