Equilibrium & Momentum Flashcards
From the basics of rotational equilibrium to the complexities of torque, use these cards to master the topic of equilibrium and momentum as tested on the MCAT.
Define:
net force
- It is the sum of all forces on an object, added as vectors.
- The product of the object’s acceleration and its mass.
The SI unit of force is the newton (N). 1N = 1 kg*m/s2.
What quantity is generally measured in newtons (N)?
force
1 N is equal to 1 kg*m/s2.
What is the force on an object for which m = 2 kg and a = 10 m/s2?
20 N
F = ma = (2 kg) (10 m/s2) = 20 N
What is the force on an object for which m = 4kg, ∆v = 20 m/s, and ∆t = 1s?
80 N
Acceleration is equal to the change in velocity over time. Here:
a = (20 m/s) / (1 s) = 20 m/s2
F = ma = (4 kg) (20 m/s2) = 80 N
What is the force on an object for which ∆p = 10kg*m/s and ∆t = 10 s?
1 N
Change in momentum (∆p) is equal to the product of force and time, so force = ∆p/∆t. Here:
F = (10 kg*m/s) / (10 s) = 1 N
Define:
momentum (p)
It is a value that quantifies an object’s tendency to remain moving in a certain direction. The momentum of an object equals its mass times its current velocity.
The SI unit of momentum is kg*m/s.
What is the momentum of an object for which m = 2 kg and v = 15 m/s?
30 kg*m/s
p = mv = (2 kg) (15 m/s) = 30 kg*m/s
Note that momentum can be positive or negative, depending on direction of velocity.
What is the momentum of an object for which m = 10 kg and v = 0 m/s?
0 kg*m/s
p = mv = (10 kg) (0 m/s) = 0 kg*m/s
Note that momentum can be positive or negative, depending on direction of velocity.
Define:
impulse
It is the change in momentum of an object due to a net force applied over some change in time. Impulse is calculated as the product of average force and time.
The units used for impulse are N*s, or kg*m/s.
What is the impulse on an object if it has a Δmv of 8 kg*m/s and an average force of 4 N?
8 kg*m/s
Impulse is equal to change in momentum, which is given here as Δmv. Note that impulse can be positive or negative, depending on direction of velocity change.
What change in Δp will cause the force on an object to be halved?
Momentum per unit time must also be halved.
Since Δp = (Favg)(Δt), momentum and force are directly proportional. Halving force requires momentum to be reduced by half as well.
What momentum change occurs for an object that experiences a force that doubles its velocity?
Momentum also doubles.
Since Δp = mΔv, a change in momentum is directly proportional to a change in velocity. Doubling one will double the other.
One mass experiences a certain force for a given time, while another is subjected to half of that force for twice the length of time. How do their impulses compare?
The impulses are equal.
Original impulse = F1*t1
Since F2 = F1/2 and t2 = 2t1, the new impulse is equal to F2*t2 = (F1/2)*(2t1) = F1*t1 .
Describe why airbags can limit the injuries of passengers in a car accident.
Airbags lengthen the amount of time that a crash victim experiences deceleration forces. This decreases the average force on the victim.
According to the formula impulse = Favg*Δt, force and time are inversely proportional. Therefore, if the time increases, the force is decreased.
Describe Newton’s first law of motion with regards to force.
For an object to change its motion, a net force must act on it.
If all forces cancel to zero, the object will not experience any change in motion. This can either cause an object to stay at rest or to continue moving with a constant velocity.
Describe Newton’s first law of motion with regards to momentum.
An object with directional momentum will continue with that momentum unless acted on by a net force.
Similarly, an object with zero momentum will continue to remain at rest until acted on by a net force.
With regard to force, how can an object at rest gain velocity?
The object must experience a net force.
Since all forces cancel to zero at rest, a net force is required to change velocity.
With regard to momentum, how can an object at rest gain velocity?
The object must have experienced an impulse, or change in momentum, from a net force.
Since all forces cancel to zero at rest, a net force is required to change velocity. Velocity will change in a way that is directly proportional to any change in momentum.
In physics, what is meant by the term translation?
It is the net movement or change in location of an object. This may be thought of as a non-zero displacement in any direction.
For example, a hockey puck experiences translation when it begins at one end of an ice rink and moves to the other end.
Define:
translational equilibrium
This occurs when the sum of all of the forces acting on an object cancel to zero. The object will not accelerate, since the net force applied on it is zero.
This situation includes objects at rest as well as objects moving with constant velocity.
A skydiver is falling from a plane and has not yet reached terminal velocity. Is the skydiver in translational equilibrium?
No
The skydiver is accelerating (changing velocity), which must be due to a non-zero net force. Translational equilibrium only exists when net force is zero.
Specifically, the downward force due to gravity is greater than the upward force due to air resistance.
In a rotating system, what are the fulcrum and the lever arm?
- The fulcrum is the point of an object that remains fixed during rotation.
- The lever arm is the distance from the fulcrum to the point where a force is applied.
Define:
torque
- It is the ability of a force to create a change in the angular orientation of an object, by rotation about a fulcrum point.
- Torque can also be thought of as the component of work perpendicular to a lever arm.
The units used to describe torque are N*m.
What equation gives the relationship between the lever arm radius and the applied force?
τ = r*F sinθ
Here, r is the distance between the applied force and the fulcrum point, F is the magnitude of force applied, and θ is the angle between the lever arm and the force vector.
Only the component of force perpendicular to the lever arm will generate torque, since sin 0 = sin 180 = 0.