Calculation of forces acting on an object on an inclined plane

Key:
N = Normal force that is perpendicular to the plane
m = Mass of object
g = Acceleration due to gravity
θ (theta) = Angle of elevation of the plane, measured from the horizontal
f = frictional force of the inclined plane

To calculate the forces on an object placed on an inclined plane, consider the three forces acting on it. Air resistance may be neglected for most calculations, except at high speeds.

1. The normal force (N) exerted by the plane onto the body,
2. the force due to gravity (mg - acting vertically downwards) and
3. the frictional force (f) acting parallel to the plane.

We can decompose the gravitational force into two vectors, one perpendicular to the plane and one parallel to the plane. Since there is no movement perpendicular to the plane, the component of the gravitational force in this direction (mgcosθ) must be equal and opposite to normal force exerted by the plane, N. If the remaining component of the gravitational force parallel to the surface (mgsinθ) is greater than the static frictional force f_s - then the body will slide down the inclined plane with acceleration (gsinθ - f_k/m), where f_k is the kinetic friction force - otherwise it will remain stationary.

When the slope angle (θ) is zero, sinθ is also zero so the body does not move.

External links

• An interactive simulation of Physics inclined plane

Lumped Vs Distributed Systems

• A lumped system is one in which the dependent variables of interest are a function of time alone. In general, this will mean solving a set of ordinary differential equations (ODEs)
• A distributed system is one in which all dependent variables are functions of time and one or more spatial variables. In this case, we will be solving partial differential equations (PDEs)

For example, consider the following two systems:

• The first system is a distributed system, consisting of an infinitely thin string, supported at both ends; the dependent variable, the vertical position of the string is indexed continuously in both space and time.
• The second system, a series of ``beads'' connected by massless string segments, constrained to move vertically, can be thought of as a lumped system, perhaps an approximation to the continuous string.
• For electrical systems, consider the difference between a lumped RLC network and a transmission line
  
  
• The importance of lumped approximations to distributed systems will become obvious later, especially for waveguide-based physical modeling, because it enables one to cut computational costs by solving ODEs at a few points, rather than a full PDE (generally much more costly)

How do I find out if my Lan (NIC) card working at full or halt duplex mode / speed under Linux?

LAN card or NIC is use to send and receive data. Technically, we use word Duplex for this functionality. Full duplex means you are able to send and receive data (files) simultaneously. In half duplex, you can either send or receive data at a time (i.e. you cannot send receive data (files) simultaneously). Obviously, full duplex gives you best user experience. However, how can I find out whether I am using full duplex/half duplex speed/mode?
Here full duplex, half duplex and auto-negotiation have the following meanings.

Full Duplex - Logic that enables concurrent sending and receiving. This is usually desirable and enabled when your computer is connected to a switch.

Half Duplex - This logic requires a card to only send or receive at a single point of time. When your machine is connected to a Hub, it auto-negotiates itself and uses half duplex to avoid collisions.

Auto-negotiation - This is the process of deciding whether to work in full duplex mode or half duplex mode. An Ethernet card supporting autonegotiation will decide for itself which mode is the optimal one depending on the network it is attached to.

Task: Find full or half duplex speed

You can use dmesg command to find out your duplex mode:

# dmesg | grep -i duplex
Output:
eth0: link up, 100Mbps, full-duplex, lpa 0x45E1

ethtool command

Uss ethtool to display or change Ethernet card settings. To display duplex speed, enter:

# ethtool eth1
Output:

Settings for eth1:
        Supported ports: [ TP ]
        Supported link modes:   10baseT/Half 10baseT/Full
                                100baseT/Half 100baseT/Full
                                1000baseT/Full
        Supports auto-negotiation: Yes
        Advertised link modes:  10baseT/Half 10baseT/Full
                                100baseT/Half 100baseT/Full
                                1000baseT/Full
        Advertised auto-negotiation: Yes
        Speed: 10Mb/s
        Duplex: Full
        Port: Twisted Pair
        PHYAD: 0
        Transceiver: internal
        Auto-negotiation: on
        Supports Wake-on: umbg
        Wake-on: g
        Current message level: 0x00000007 (7)
        Link detected: yes

mii-tool command

You can also use mii-tool to find out your duplex mode. Type following command at shell prompt:
# mii-tool
Output:

eth0: negotiated 100baseTx-FD flow-control, link ok

Remember,

1. 100baseTx-FD: 100Mbps full duplex (FD)
2. 100baseTx-HD: 100Mbps half duplex (HD)
3. 10baseT-FD: 10Mbps full duplex (FD)
4. 10baseT-HD: 10Mbps half duplex (HD)

mii-tool utility checks or sets the status of a network interface’s Media Independent Interface (MII) unit. Most fast ethernet adapters use an MII to autonegotiate link speed and duplex setting. If you are using old card then this utility may not work (use dmesg command).
This utility is useful for forcing specific Ethernet speed and duplex settings too, setup 100Mbps full duplex speed under Linux:
# mii-tool -F 100baseTx-FD
Setup 10Mbps half duplex:
# mii-tool -F 10baseT-HD       

Determine / Find ethernet connection speed

You need to use ethtool command todisplay or change Ethernet card settings. It is used for querying settings of an Ethernet device such as
=> Link speed
=> Autonegotiation
=> Coalescing settings
=> Change the rx/tx ring parameters
=> Setup new speed and much more
Most intelligent network devices use an autonegotiation protocol to communicate what media technologies they support, and then select the
fastest mutually supported media technology.

How do I determine Ethernet connection speed?

Type the following command to get speed for eth0:

$ ethtool eth0 | less

OR
 
$ ethtool eth0 | grep -i speed