All MCAT Physical Resources
Example Questions
Example Question #213 : Mcat Physical Sciences
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.
After reaching maximum velocity at the bottom of a frictionless hill identical to the one in the question, Sam deploys a parachute. How much energy must the parachute dissipate before Sam comes to a stop?
30J
30000kJ
30kJ
300kJ
300J
30kJ
The parachute must dissipate all of the kinetic energy that Sam has at the bottom of the hill, since there is no friction to slow him. He has 30kJ of energy, as per the equation PE = mgh.
PE = 60kg * 10m/s2 * 50m = 30,000J = KE at the bottom of the hill
Example Question #1 : Kinetic Energy
How much energy is required to a accelerate a block from rest to a final speed of ?
From an energy stand-point, the block starts with zero kinetic energy and zero potential energy. At the end, the block still has zero potential energy, but has a non-zero kinetic energy. Assuming there is no friction, all energy added to the block have been converted to kinetic energy.
Using the change in velocity, we can solve for the energy used to move the block.
We are given our mass and the change in velocity, allowing us to solve for the change in kinetic energy.
Example Question #23 : Work, Energy, And Power
What is the kinetic energy of a bullet moving at ?
Kinetic energy is given by the formula:
We are given the mass of the bullet and its velocity, allowing us to calculate kinetic energy from this formula.
Work is often expressed in Newton-meters, but energy is usually expressed as Joules, although the units are equivalent.
Example Question #1 : Kinetic Energy
Two children are playing on an icy lake. Child 1 weighs 50kg, and child 2 weighs 38kg. Child 1 has a backpack that weighs 10kg, and child 2 has a backpack that weighs 5kg.
Over the course of the afternoon, they collide many times. Four collisions are described below.
Collision 1:
Child 1 starts from the top of a ramp, and after going down, reaches the lake surface while going and subsequently slides into a stationary child 2. They remain linked together after the collision.
Collision 2:
Child 1 and child 2 are sliding in the same direction. Child 2, moving at , slides into child 1, moving at .
Collision 3:
The two children collide while traveling in opposite directions at each.
Collision 4:
The two children push off from one another’s back, and begin moving in exactly opposite directions. Child 2 moves with a velocity of .
In collision 1, imagine that child 2 was not present on the ice. How much energy would child 1 have to dissipate to the lake surface before he came to a stop? Ignore wind resistance.
The amount of kinetic energy that child 1 has after she reaches the lake surface is the amount of energy she will dissipate to the lake before coming to a complete stop.
Example Question #2 : Kinetic Energy
What is the kinetic energy of a 0.1kg projectile traveling at ?
We can calculate the kinetic energy using the equation:
Use the given values for the mass and velocity to solve:
Example Question #1 : Potential Energy (Gravitational And Spring)
A spring in a pinball machine is compressed from its equilibrium position. It is released and it fires the pinball at a velocity of into play. No energy is lost to friction and all of the energy in the spring is transferred to the pinball. What is the spring constant in the spring?
The energy in a spring is given by the equation , where is the spring constant and is the displacement from the equilibrium position. The energy is transferred into kinetic energy in the pinball.
The kinetic energy in the pinball is found using the equation .
Now that we have kinetic energy, we can find the equal energy that was stored in the spring to begin.
Example Question #221 : Mcat Physical Sciences
A 2kg mass is attached to a massless spring with force constant 100N/m. The system rests on a frictionless horizontal surface. If the spring is compressed 5cm, then released, what is the maximum velocity of the mass?
35.4cm/s
12.5cm/s
10.2cm/s
50cm/s
25cm/s
35.4cm/s
Use conservation of energy to compare the point of maximum compression and the point of maximum velocity. At maximum compression, all energy is spring potential energy, where , and at maximum velocity all energy is kinetic, where . Since energy must be conserved, these two energies must be equal: .
Plugging in the given information for Es and solving for v gives the following series of calculations:
Example Question #1 : Potential Energy (Gravitational And Spring)
If a ball is attached to a spring that has a spring constant of 20N/m and is compressed 0.1m, what is the total energy of the oscillation?
The total energy of a simple harmonic oscillating system can be determined by the equation . A is the amplitude of the oscillation, k is the spring constant, and E is the total energy. Plugging in values given by the equation, the total energy is equal to 0.1J.
Example Question #2 : Potential Energy (Gravitational And Spring)
A massless spring rests horizontally on a table, with its right end attached to a block and with its left end attached to a wall. The block is then pushed against the spring, compressing it from its equilibrium position. After being released, the block's velocity as it moves back through the equilibrium point is . What is the spring constant of this spring?
Use conservation of energy to equate the initial spring potential energy and the final kinetic energy:
The initial situation is defined when the spring and block are compressed, and the final situation is defined to be when the block moves back through the equilibrium point. For a spring, the potential energy is maximal when the spring is compressed and the kinetic energy is maximal when the mass passes equilibrium. We can set up a equation based on these factors.
Use the equations for spring potential energy and for kinetic energy to incorporate the appropriate variables into the equation.
We are given values for the displacement, mass, and final velocity. Using these values, we can isolate the spring constant.
Example Question #1 : Potential Energy (Gravitational And Spring)
A block with mass, , is attached to a spring with a spring constant, . The spring is compressed a maximum distance, , and released. What is the maximum velocity the block reaches after the spring is released?
The spring potential is given by the equation and the equation for kinetic energy is given by .
When is at a maximum distance (the amplitude) the velocity is zero, and the spring ONLY has potential energy. When it is released, the total energy is part kinetic and part potential. When the amplitude is at zero (equilibrium), the velocity is at a maximum and all the potential energy is converted into kinetic energy. We can then set the two equations equal to each other to solve the maximum velocity.
Certified Tutor
Certified Tutor