Chapter 6 - Linear Kinetics

Question 1

What is the law of inertia? (1st Law)

Answer 1

A body will maintain a state of rest or constant velocity unless acted on by an external force that changes the state.

For example, a skater has a tendency to continue gliding with constant speed and direction because of inertia.

Question 2

What is the law of acceleration? (2nd Law)

Answer 2

A force applied to a body causes acceleration of that body, of a magnitude proportional to the force, in the direction of the force, and inversely proportional to the body’s mass.
F = ma

Question 3

What is the law of reaction? (3rd Law)

Answer 3

For every action, there is an equal and opposite reaction.
When one body exerts a force on a second body, the second body exerts a reaction force that is equal in magnitude and opposite in direction on the first body.

For example, the weight of a box sitting on a table generates a reaction force by the table that is equal in magnitude and opposite in direction to the weight.

Another example: Ground reaction forces are sustained with every footfall during running.

Question 4

How are better sprinters fast?

Answer 4

Better sprinters are able to generate a forward-directed horizontal component (FH) of the total ground reaction force (F).

Question 5

What is friction?

Answer 5

Friction is a force acting over the area of contact between two surfaces.
Direction is opposite of motion or motion tendency.

Question 6

How to obtain the magnitude of friction?

Answer 6

Magnitude of friction is the product of the coefficient of friction (µ) and the normal reaction force (R)
F = µR

Question 7

What are static (motionless) bodies?

Answer 7

Static friction is the force that opposes the initiation of motion between two surfaces in contact when the object is at rest or in a state of equilibrium.
Friction is equal to the applied force

Question 8

What are dynamic bodies (in motion)?

Answer 8

Force that opposes the relative motion between two surfaces in contact when the object is already in motion.

Friction is constant and less than maximum static friction.

Question 9

What is the difference between static and dynamic bodies?

Answer 9

Static friction occurs when there is no relative motion between the surfaces, whereas dynamic friction occurs when there is relative motion.

Question 10

Question Example:
The coefficient of static friction between a sled and the snow is 0.18, with a coefficient of kinetic friction of 0.15. A 250-N boy sits on the 200-N sled. How much force directed parallel to the horizontal surface is required to start the sled in motion? How much force is required to keep the sled in motion?

Answer 10

To start the sled in motion:

Fm = µsR
= (0.18)(250N + 200N)
= 81N
(Applied force must be greater than 81N)

To maintain motion,
Fk = µkR
= (0.15)(250N + 200N)
= 67.5N
(Applied force must be at least 67.5N)

Question 11

What value must the coefficient of friction between a dancer’s shoes and the floor be to allow freedom of motion and prevent slippage?

Answer 11

The coefficient of friction between a dancer’s shoes and the floor must be small enough to allow freedom of motion but large enough to prevent slippage.

Question 12

What is momentum?

Answer 12

Momentum is the quantity of motion possessed by a body.

Question 13

What is momentum measuered in?

Answer 13

Measured as the product of a body’s mass and its velocity,
M = mv

Question 14

What is the principle of conservation of momentum?

Answer 14

In the absence of external forces, the total momentum of a given system remains constant.
M1 = M2
(mv)1 = (mv)2

Question 15

What causes momentum?

Answer 15

Impulse.

Question 16

What is impulse?

Answer 16

Impulse is the product of a force and the time interval over which the force acts

Question 17

What is the relationship between impulse and momentum?

Answer 17

Ft = ΔM
Ft = (mv)2 - (mv)1

Question 18

Question Example: A 90-kg hockey player traveling with a velocity of 6m/s collides head-on with an 80-kg player traveling at 7m/s. If the two players entangle and continue traveling together as a unit following the collision, what is their combined velocity?

Answer 18

Before collision = After collision

Before collision = (m1)(v1) + (m2v2)

After collision = (m1 + m2)(v)

(90kg)(6m/s)+(80kg)(-7m/s) = (90kg + 80kg)(v)

540kg.m/s - 560kg.m/s = (170kg)(v)

-20kg.m/s = (170kg)(v)

v = 0.12m/s in the 80-kg player’s original direction of travel.

Question 19

Question Example:
A toboggan race begins with the two crew members pushing the toboggan to get it moving as quickly as possible before they climb in. If crew members apply an average force of 100 N in the direction of motion of the 90-kg toboggan for a period of 7s before jumping in, what is the toboggan’s speed (neglecting friction) at that point?

Answer 19

Ft = (mv)2 - (mv)1
(100N)(7s) = (90kg)(v) - (90kg)(0)

v = 7.78m/s in the direction of force application

Question 20

What does the area under the curve represent in a Force (Body Weight) against Time (ms) graph represent?

Answer 20

The shaded area represents the impulse generated against the floor during the jump.

Question 21

What is impact?

Answer 21

Impact is a collision characterized by:
The exchange of a large force during a small time interval

Question 22

What happens following an impact?

Answer 22

It is dependent on:
1. Momentum present in the system
2. Nature of the impact

Question 23

What happens during impact?

Answer 23

This is described by the coefficient of restitution, a number that serves as an index of elasticity for colliding bodies; represented as e.

Question 24

What does the coefficient of restitution (e) describe?

Answer 24

-e = relative velocity after impact / relative velocity before impact
-e = v1 - v2 / u1 - u2

Question 25

What is the relationship between ball velocity before impact and after impact?

Answer 25

The differences in two balls’ velocities before impact is proportional to the difference in their velocities after impact. The factor of proportionality is the coefficient of restitution.
v1 - v2 = -e ( u1 - u2)

Question 26

What are the 2 types of impacts?

Answer 26

1. Perfectly elastic impact
2. Perfectly plastic impact

Question 27

What are perfectly elastic impacts?

Answer 27

velocity of the system is conserved; (e = 1)(superball bounce is close…)

Question 28

What are perfectly plastic impacts?

Answer 28

in which there is a total loss of system velocity; (e = 0) (spaghetti hits a wall)

Question 29

What is mechanical work?

Answer 29

Mechanical work is the product of a force applied against a resistance and the displacement of the resistance in the direction of the force
W = Fd

Question 30

What is mechanical power?

Answer 30

The rate of work production
Calculated as work divided by the time over which the work was done.
P = W / t

Question 31

A 580-N person runs up a flight of 30 stairs of riser (height) of 25cm during a 15-s period. How much mechanical work is done? How much mechanical power is generated?

Answer 31

For mechanical work:
W = Fd
= (580N)(30 x 0.25m)
= 4350 J

For mechanical power:
P = W / t
= 4350 J / 15 s
= 290 Watts

Question 32

What is mechanical energy?

Answer 32

The capacity to do work (J).

Question 33

What are the three forms of mechanical energy?

Answer 33

1. Kinetic energy
2. Potential energy
3. Thermal energy

Question 34

What is kinetic energy?

Answer 34

Energy of motion
KE = ½mv2

Question 35

What is potential energy?

Answer 35

Energy by virtue of a body’s position or configuration.
PE = (wt)(ht)

Question 36

What is the law of conservation of mechanical energy?

Answer 36

When gravity is the only acting external force, a body’s mechanical energy remains constant.
KE + PE = C
where C is a constant - a number that remains unchanged

Question 37

What is the principle of work and energy?

Answer 37

The work of a force is equal to the change in energy that it produces in the object acted upon.
W = ΔKE + ΔPE + ΔTE
(where TE is thermal energy)

Question 38

Question Example:
A 2-kg ball is dropped from a height of 1.5m. What is its velocity immediately before impact with the floor?

Answer 38

Total (constant) mechanical energy possessed by the ball:
PE + KE = C
(wt) (h) + 1/2mv^2 = C

(2kg)(9.81m/s^2)(1.5m) + 0 = C

C = 29.43 J

Velocity of the ball before impact:
PE + KE = 29.43 J

(wt)(h) + 1/2mv^2 = 29.43 J

(2kg)(9.81m/s^2)(0) + 1/2(2kg)v^2 = 29.43 J

v^2 = 29.43

v = 5.42m/s