MCAT Physical : Translational Motion
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Example Questions
Example Question #11 : Momentum
A 
This is a case of inelastic collision because the objects stay in contact after the impact. The total momentum in a system is always conserved, regardless of collision type. Here, the momentum before the collision is given by the sum of the individual momentum of each car, and the momentum after the collision is given by the singular momentum of the joined vehicles.
We are given the mass of each car and their initial velocities, allowing us to completely solve the left side of this equation.
We can now use the combined mass of both cars to solve for their final velocity.
Example Question #12 : Momentum
A 
Momentum is conserved in all situations. Here, we have an elastic collision, meaning that the objects do not stick together after the impact. Momentum is simply the product of mass and velocity, and it has the units 
We can solve this problem by setting the initial and final momentum of the system equal to each other. The momentum of the system will be the sum of the momentum of the parts.
The second ball contributes no momentum initially, because its initial velocity is zero. The total initial momentum comes from the initial velocity of the larger ball.
We know the mass of each ball and the final velocity of the smaller ball. Using these values, we can solve for the final velocity of the larger ball.
Example Question #11 : Momentum
An object of mass 
Momentum is given by the equation 
The initial momentum is given by the sum of the initial momentums of the two objects. Because the second mass starts from rest, it becomes irrelevant in the equation.
After a perfectly inelastic collision, the two objects will stick together and their masses will add. The final velocity will apply to the combined mass of the two objects.
Since we know that 
The mass of the second object must be 2kg.
Example Question #1 : Understanding Elastic And Inelastic Collisions
Ball A, traveling 
A perfectly inelastic collision is when the two bodies stick together at the end. At the beginning the two balls are traveling separately with individual momentum values. Using the momentum equation 
Note: ball B's velocity is negative because they are traveling in opposite directions.
The negative sign indicates the direction in which the two balls are traveling. Since the sign is negative and we indicated that traveling to the left is negative, the two balls must be traveling 2m/s to the left after the perfectly inelastic collision.
Example Question #11 : Momentum
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 
Collision 2:
Child 1 and child 2 are sliding in the same direction. Child 2, moving at 
Collision 3:
The two children collide while traveling in opposite directions at 
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 all of the above scenarios, which of the following quantities is conserved?
I. Kinetic energy
II. Potential energy
III. Momentum
I and II
II and III
III only
I and III
I, II, and III
III only
Kinetic energy and potential energy are interconverted. While total energy is conserved, kinetic energy is allowed to increase or decrease, provided that potential energy does the opposite. For example, as the child in collision 1 is starting at the top of a ramp, she has potential energy, but no kinetic energy. At the bottom of the ramp, all the potential energy has been turned into kinetic energy.
Momentum, on the other hand, is conserved in every collision.
Example Question #15 : Momentum
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 
Collision 2:
Child 1 and child 2 are sliding in the same direction. Child 2, moving at 
Collision 3:
The two children collide while traveling in opposite directions at 
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, with what velocity will the children be traveling after the collision?
Assume that the velocity with which child 1 hits child 2 is the same as the velocity with which child 1 reaches the surface of the lake. Also assume that the original direction of travel for child 1 is positive. Ignore friction and wind resistance.
Momentum is always conserved in collisions, and is equal to the product of mass and velocity.
Example Question #11 : Momentum
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 
Collision 2:
Child 1 and child 2 are sliding in the same direction. Child 2, moving at 
Collision 3:
The two children collide while traveling in opposite directions at 
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 4, what is the final velocity of child 1? Ignore friction and air resistance.
Cannot be determined from the information given
This is a reverse collision, and momentum is still conserved. The original momentum is zero.
Example Question #11 : Momentum
Which of the following is a correct description of an inelastic collision?
Neither kinetic energy nor momentum is conserved
Momentum is conserved, but kinetic energy is not
Kinetic energy is conserved, and momentum may be conserved
Kinetic energy is conserved, but momentum is not
Both kinetic energy and momentum are conserved
Momentum is conserved, but kinetic energy is not
Momentum is conserved in any collision, but kinetic energy is only conserved in elastic collisions. So, an inelastic collision has conservation of momentum, but not conservation of kinetic energy.
Example Question #12 : Momentum
In an elastic collision, which of the following quantities is not conserved?
Mechanical energy
Potential energy
Kinetic energy
All of these are conserved
Momentum
All of these are conserved
In an inelastic collision, kinetic energy is not conserved. In an elastic collision, kinetic energy is conserved and there is no transfer of energy to the surroundings.
Momentum is conserved regardless of the type of collision. All of the given quantities are conserved during an elastic collision.
Example Question #1 : Motion In One Dimension
A 2kg mass is suspended on a rope that wraps around a frictionless pulley attached to the ceiling with a mass of 0.01kg and a radius of 0.25m. The other end of the rope is attached to a massless suspended platform, upon which 0.5kg weights may be placed. While the system is initially at equilibrium, the rope is later cut above the weight, and the platform subsequently raised by pulling on the rope.
The rope is cut right above the 2 kgmass. What is the acceleration of the platform with the individual weights as it falls to the ground?
19.6m/s2
9.8m/s2
0m/s2
4.9m/s2
9.8m/s2
Remember that Newton’s second law is applicable regardless of whether we are talking about kinematics, torque, electric, magnetic, or gravitational force, thus, F = ma. We know that the only force acting in free-fall in an environment where we can neglect air resistance (i.e. most of the problems on the MCAT) is gravity. The acceleration due to gravity is 9.8m/s2. The sign could be + or – depending on how you decided to orient.
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