MCAT Physical : Newtonian Mechanics and Motion
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Example Questions
Example Question #2 : Force Equilibrium
As a skydiver jumps out of a plane, he comes to terminal velocity as air resistance brings his fall to a constant speed. At what point is the net force on the skydiver the greatest?
The net force is constant through the fall
When he is halfway to the earth's surface
When he has reached terminal velocity
Right when he jumps out of the plane
Right when he jumps out of the plane
The skydiver’s velocity (along the y-axis) will be zero when he initially jumps out of the plane, however, his net force will be greatest at that point.
As the skydiver first jumps, there is only the force of gravity acting on him. As he approaches terminal velocity, however, the force of wind resistance becomes equal and opposite to the force of gravity, and he begins to move at constant velocity with a net force of zero.
Example Question #1 : Force Equilibrium
A mass hanging in equilibrium is attached to a fixed surface on the ceiling by a spring. The mass is pulled down from the ceiling, then released and allowed to move in simple harmonic motion. The mass does not lose energy due to friction or air resistance. At what point does the mass have maximum velocity?
At maximum downward displacement from the equilibrium position
At maximum upward displacement from the equilibrium position
Its velocity is constant
At the equilibrium position
At the equilibrium position
The velocity of the mass will be the greatest at the equilibrium position. Although the restoring force on the mass due to the spring will be the greatest at maximum displacement from the equilibrium position, this force is being applied to the mass as it moves in the opposite direction. As the mass moves towards the equilibrium position from maximum displacement, the restoring force due to the spring is applied in the same direction as the velocity of the mass. Because of this, the object is accelerating. After the mass passes through the equilibrium position, the spring begins to apply a force in the direction opposite to the motion of the mass, resulting in the deceleration of the mass. The mass experiences its maximum velocity at the equilibrium position.
Example Question #3 : Force Equilibrium
If a wooden block is decelerating across a surface, in what direction is the net force on the object?
Opposite to the motion
Initially opposite the direction of motion, then in the direction of the motion
There is no net force
Initially in the direction of the motion, then opposite the direction of motion
The same direction as the motion
Opposite to the motion
When an object is decelerating, there is a net force in the opposite direction of the motion of the object. Usually, this force is friction, which always acts counter to the net velocity. Even if there is a force in the direction of the object's motion, the net force is backwards if the object is decelerating.
Mathematically, we can prove this concept using Newton's second law. The direction of the object's motion will be positive, while the opposite (backwards) direction will be negative.
If the object is decelerating, then the acceleration is negative.
From this calculation, the force must be negative, acting counter to the direction of motion.
Example Question #1 : Force Equilibrium
What is the net force on a falling object at terminal velocity?
When an object is at terminal velocity, the upward force on the object from air resistance is equal to the force of gravity. These equal, but opposing, forces cancel each other out and the net force is zero. This results in a zero acceleration, allowing the object to fall at a constant (terminal) velocity.
Example Question #32 : Forces
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.
What is the tension in the rope if the system is at equilibrium?
19.6N
23N
5N
9.8N
19.6N
Consider that tension is a contact force that acts over a distance. Assuming the rope does not stretch and has no mass (as we should for the MCAT), we can think of tension as a force that acts directly on the mass. We can draw a force diagram below.
 
If the system is stationary (at equilibrium), we can see that tension is equal to the weight, T = mg.
T = (2 kg)(9.8 m/s2) = 19.6N
Example Question #4 : Force Equilibrium
Two positively charged particles are placed near one another in an otherwise isolated environment. Their charges are 
At a particular moment, the magnitude of particle A's acceleration is 
Use Newton's second law, 
The two charges exert equal-magnitude and opposite-direction forces on one another according to Newton's third law, so 
Plugging in our given values allows us to solve for 
Example Question #5 : Force Equilibrium
A potted plant is hanging from a rope attached to a hook. The plant exerts 25N of force in the downward direction. Assume the rope is weightless.
What is the tension of the rope?
The rope is weightless, so it cannot have tension
In order for the potted plant to stay still, the net force on the plant must be 0N. The tension of the rope is the force that allows an object to hang without falling. In order to keep the plant stationary, the tension must be equal to 25N in the upward direction.
Example Question #1 : Force Equilibrium
A skydiver with a mass of 100kg jumps out of an airplane and reaches a terminal velocity of 
What is the total force acting on the skydiver at this point in his jump?
The man has reached a terminal velocity, which means that he has an acceleration of 
Example Question #11 : Force Equilibrium
A man stands in the middle of a boat on a steady lake. As he walks toward one end the boat will __________.
stay still ans not move
move perpendicular to the man
move in the opposite direction from the man
move in the same direction as the man
move in the opposite direction from the man
The motion of the boat (
This scenario can also be solved by looking at momentum. Both the man and the boat start from rest, so in order for momentum to be conserved once the man gains positive velocity, the boat must gain negative velocity.
Example Question #402 : Mcat Physical Sciences
A box of mass 
There are only two forces acting on the box: the force of gravity and the force of tension in the rope. Since the box is not in motion, we can assume that the system is in equilibrium and the net force is equal to zero.
Rearranging, we can see that gravity and the force of tension will be equal and opposite.
Calculate the force of gravity using Newton's second law.
Note that the force of gravity is negative, since it acts in the downward direction. Use this value to solve for the force of tension.
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