MCAT Physical : MCAT Physical Sciences
Study concepts, example questions & explanations for MCAT Physical
All MCAT Physical Resources
Example Questions
Example Question #2 : Potential Energy (Gravitational And Spring)
Two children are playing with sleds on a snow-covered hill. Sam weighs 50kg, and his sled weighs 10kg. Sally weighs 40kg, and her sled weighs 12kg. When they arrive, they climb up the hill using boots. Halfway up the 50-meter hill, Sally slips and rolls back down to the bottom. Sam continues climbing, and eventually Sally joins him at the top.
They then decide to sled down the hill, but disagree about who will go first.
Scenario 1:
Sam goes down the hill first, claiming that he will reach a higher velocity. If Sally had gone first, Sam says they could collide.
Scenario 2:
Sally goes down the hill first, claiming that she will experience lower friction and thus reach a higher velocity. If Sam had gone first, Sally says they could collide.
Scenario 3:
Unable to agree, Sam and Sally tether themselves with a rope and go down together.
How much potential energy does Sally have at the top of the hill on her sled?
260000J
2.6kJ
260J
26,000kJ
26kJ
26kJ
This is a tricky question only because you have to keep your units straight. The formula is simply PE = mgh.
PE = 52kg * 10m/s2 * 50m = 26,000J = 26kJ
Example Question #31 : Work, Energy, And Power
A 2kg box slides down a ramp a distance of two meters before it reaches the ground. The ramp has an angle of 30o. The coefficient of kinetic friction for the ramp is 0.1.
What is the gravitational potential energy of the box relative to the ground when at the top of the ramp?
Gravitational potential energy is determined using the equation 
Now that we have the height, we simply plug the given values into the equation.
Example Question #11 : Potential Energy (Gravitational And Spring)
A spring is used to launch a 
What was the displacement of the spring required to launch the ball?
We can use conservation of energy to calculate the displacement. The spring must be displaced so that its potential energy is equal to the gravitational potential energy of the ball at its maximum height.
Substituting in the expressions for potential energy of the spring and gravitational potential energy, we can start to set up an equation using the given variables.
We are given the spring constant, the mass, and the maximum height. Using these values, and the acceleration for gravity, we can solve for the spring displacement.
Note that, since we are taking the square root, the displacement answer could be either positive or negative. Since the spring is being compressed to launch the ball (rather than stretched), the displacement should be negative.
Example Question #231 : Mcat Physical Sciences
What is the potential energy of a 
Our formula for gravitational potential energy is:
Example Question #12 : Potential Energy (Gravitational And Spring)
A 
It depends if the stone is raised vertically or along an incline
No matter how you raise the stone (all at once, in multiple vertical steps, or along a ramp) the final potential energy is the same. Gravitational potential energy of a given object is solely dependent on height.
Use the given mass, the acceleration of gravity, and the final height to calculate the potential energy of the system.
Since work is equal to the change in potential energy of a system, this value also gives the total work done to raise the stone.
Example Question #1 : Conservation Of Energy
A ball with mass of 2kg is dropped from the top of a building this is 30m high. What is the approximate velocity of the ball when it is 10m above the ground?
25m/s
14m/s
10m/s
30m/s
20m/s
20m/s
Use conservation of energy. The gravitational potential energy lost as the ball drops from 30m to 10m equals the kinetic energy gained.
Change in gravitational potential energy can be found using the difference in mgh.
So 400 Joules are converted from gravitational potential to kinetic energy, allowing us to solve for the velocity, v.
Example Question #1 : Conservation Of Energy
Consider a spring undergoing simple harmonic motion. When the spring is at its maximum velocity __________.
kinetic energy is at a maximum and potential energy is at a minimum
kinetic energy and potential energy are at a maximum
kinetic energy is at a minimum and potential energy is at a maximum
kinetic energy and potential energy are at a minimum
kinetic energy is at a maximum and potential energy is at a minimum
Kinetic energy is highest when the spring is moving the fastest. Conversely, potential energy is highest when the spring is most compressed, and momentarily stationary. When the force resulting from the compression causes the spring to extend, potential energy decreases as velocity increases.
Example Question #1 : Conservation Of Energy
A pendulum with a mass of 405kg reaches a maximum height of 2.4m. What is its velocity at the bottommost point in its path?
4.5m/s
48m/s
17m/s
6.9m/s
6.9m/s
First solve for the potential energy of the pendulum at the height of 2.4m.
PE = mgh
PE = (405kg)(10m/s2)(2.4m) = 9720J
This must be equal to the maximum kinetic energy of the object.
KE = ½mv2
9720J = ½mv2
Plug in the mass of the object (405 kg) and solve for v.
9720J = ½(405kg)v2
v = 6.9m/s
Example Question #2 : Conservation Of Energy
Two children are playing with sleds on a snow-covered hill. Sam weighs 50kg, and his sled weighs 10kg. Sally weighs 40kg, and her sled weighs 12kg. When they arrive, they climb up the hill using boots. Halfway up the 50-meter hill, Sally slips and rolls back down to the bottom. Sam continues climbing, and eventually Sally joins him at the top.
They then decide to sled down the hill, but disagree about who will go first.
Scenario 1:
Sam goes down the hill first, claiming that he will reach a higher velocity. If Sally had gone first, Sam says they could collide.
Scenario 2:
Sally goes down the hill first, claiming that she will experience lower friction and thus reach a higher velocity. If Sam had gone first, Sally says they could collide.
Scenario 3:
Unable to agree, Sam and Sally tether themselves with a rope and go down together.
At the bottom of a neighboring hill, a neighbor watches Sally and Sam come down the hill. Sally is traveling 15m/s and Sam is traveling 10m/s. From the moment the neighbor begins watching, to just after they both come to a stop, who has dissipated more heat in the form of friction? (Assume all friction is lost as heat).
Sam, because he has more momentum
Sally, because she has less momentum
Sam, because he has greater kinetic energy
Sally, because she has greater kinetic energy
They dissipate equal amounts because the coeffecients of friction are the same for both
Sally, because she has greater kinetic energy
Sally has greater kinetic energy in this example than does Sam. From the moment when the neighbor begins watching we can calculate the kinetic energy. Once stopped, all of the kinetic energy will have been dissipated.
Sally's KE = 1/2 (52kg) (15m/s)2 = 5850J
Sam's KE = 1/2 (60kg) (10m/s)2 = 3000J
All of this energy will be dissipated as friction before Sam and Sally come to a stop.
Example Question #1 : Conservation Of Energy
Ignoring air resistance, which of the following is true regarding the motion of a pendulum?
At the bottom of the oscillation potential energy is at a minimum and kinetic energy is at a maximum
At the bottom of the oscillation potential energy is at a minimum and kinetic energy is at a minimum
At the bottom of the oscillation potential energy is at a maximum and kinetic energy is at a maximum
At the bottom of the oscillation potential energy is at a maximum and kinetic energy is at a minimum
At the bottom of the oscillation potential energy is at a minimum and kinetic energy is at a maximum
Energy must be conserved through the motion of a pendulum. Let point 1 represent the bottom of the oscillation and point 2 represent the top. At point 1, there is no potential energy, using point 1 as our "ground/reference," thus all of the system energy is kinetic energy. At point 2, the velocity is zero; thus, the kinetic energy is zero and all of the system energy is potential energy. At the highest point in the swing, potential energy is at a maximum, and at the lowest point in the swing, kinetic energy is at a maximum.
Certified Tutor
Certified Tutor
All MCAT Physical Resources
