Work and Energy
Define work in physics and state the condition under which work is zero.
Work is the energy transferred to or from an object by a force acting on it. W = Fdcos(theta)
Define momentum
Momentum is a measure of an object's motion, defined as the product of mass and velocity:
two identical springs. One is compressed 10 cm the other is stretched 10cm. Which one has a greater amount of stored potential energy
equal
Uspring = 0.5kx^2
A 1500 kg car accelerates from rest to 20 m/s. Calculate the work done by the net force on the car.
300 KJ
A 2 kg block moving at 6 m/s collides elastically with a 4 kg block initially at rest on a frictionless surface.
(a) Calculate the final velocities of both blocks.
(b) Verify that kinetic energy is conserved.
(c) Calculate the impulse delivered to the 4 kg block.
a) -2 m/s and 4 m/s
b) 36 J
c) 16 kgm/s
Explain the difference between kinetic energy and potential energy, and give one example of each.
Kinetic energy is the energy of motion. Potential energy is stored energy due to position or configuration.
State the impulse-momentum theorem and explain how impulse relates to changes in momentum.
The impulse-momentum theorem states that the impulse (force applied over time) equals the change in momentum. J = Favg*t = pf - pi.
This shows that a force applied for a longer time or a larger force produces a greater change in momentum.
A student calculates the speed of a roller coaster at the bottom of the first loop using conservation of mechanical energy equations (Eg = Ek). However, when she looks up the data on the actual speed of the coaster, it is lower than her predicted result. Why does her calculated value not match the real-world value?
She didn't consider non-conservative forces like friction
Calculate the impulse of this F vs t graph (drawn by Mr. G)
1.8 Ns
A 3 kg object moving at 8 m/s collides inelastically with a 5 kg object at rest. After collision, they move together.
(a) Find the final velocity.
(b) Calculate the kinetic energy before and after collision.
(c) How much energy is lost
a) vf = 3m/s
b) KEf = 36J
c) KElost = 60 J
State the work-energy theorem and explain what it tells us about the relationship between work and kinetic energy.
The work-energy theorem states that the net work done on an object equals the change in its kinetic energy. W = Change in EK. This tells us that work is the mechanism by which kinetic energy changes—positive net work increases kinetic energy, negative net work decreases it.
Explain the law of conservation of momentum and state the condition under which it applies
The law of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act on it.
pf = pi
This applies when the system is isolated (no net external force) or when considering internal forces only
A hiker, moving at constant velocity, walks up a hill carrying a 15 kg bag. What is the net work done on the backpack
net work is zero
A 0.5 kg ball moving at 4 m/s collides with a stationary 0.5 kg ball in a perfectly inelastic collision. Calculate the velocity of the combined mass after collision.
2 m/s
A 10 kg block is pushed across a horizontal surface with a constant applied force of 50 N at an angle of 30° above the horizontal. The coefficient of kinetic friction is 0.2. The block travels 15 m.
(a) Calculate the net work done on the block
(b) If the block starts from rest, what is its final kinetic energy and final speed?
a) Wnet = 424.5
b) v = 9.2 m/s
Define mechanical energy and explain what it means for mechanical energy to be conserved in a system.
Mechanical energy is the sum of kinetic and potential energy.
Conservation of mechanical energy occurs when only conservative forces (gravity, elastic forces) act on a system
Distinguish between elastic and inelastic collisions. What is conserved in each type?
Elastic collisions: Objects bounce apart; both momentum and kinetic energy are conserved.
Inelastic collisions: Objects may stick together or deform; momentum is conserved but kinetic energy is not.
Explain why it is advantageous to "follow through" when playing sports like tennis, badminton, golf, or hockey. Use physics principles
greater amount of time spent in contact means greater impulse, meaning greater change in momentum, meaning greater increase in speed
J = Fnet*t
A 12 kg object is suspended from a spring. If the spring was stretched 13 cm away from equilibrium, determine the spring constant.
905 N/m
A 15 kg box slides down a frictionless ramp starting from a height of 5m. At the bottom of the ramp it travels 1.2 m across a surface with a coefficient of kinetic friction of 0.11 before colliding with a spring with spring constant k = 6500 N/m.
determine the distance the spring is compressed
x = 0.47 m
Distinguish between conservative and non-conservative forces. Give one example of each
Conservative forces (gravity, elastic forces, electric forces) do work that is independent of path and can be associated with potential energy. Non-conservative forces (friction, air resistance) depend on the path taken and dissipate energy as heat or sound. When non-conservative forces act, mechanical energy decreases
Two identical balls are dropped from the same height. Ball A bounces elastically back to its original height. Ball B is deforms and doesn't bounce up at all. Compare the impulse delivered by the ground to each ball.
the impules of ball A is twice that of ball b. It not only loses the momentum it has but gains an equal amount in the opposite direction
Order the following situations in order of "most to least" for the amount of work done by friction. Assume the surfaces in contact are the same in each case and the distance the box moves is the same:
a) a box sliding down a ramp at an angle of 12 degrees
b) a box sliding up a ramp at an angle of 12 degrees
c) a box sliding across a horizontal surface
horizontal > up ramp = down ramp
An asteroid explodes into 2 sections. A 13,500 kg piece flies [left] and a 8,500 piece flies [right]. Find the speed of both pieces if the total energy of both pieces after the explosion is 3.8 x 10^6 J
v1 = 14.7 m/s
v2 = 23.4 m/s
A 3 kg ball is traveling east at a speed of 3.5 m/s, and a 5 kg ball is traveling north at a speed of 2 m/s. The two balls of playdough collide inelastically.
a) Find the magnitude and direction of the velocity of the wreckage after the collision, assuming that the vehicles undergo a perfectly inelastic collision and assuming that friction between the vehicles and the road can be neglected.
b) how much energy was lost in the collision?
a) v = 1.8 m/s [E 43.6 N]
b) Elost = 15.2 J