V^2 =U^2 +2AS
V^2 = 25 ^2 + 2x9.5x10
V^2 = 625 + 1900 = 2525
V = 50.25
Answer:
a) 0.83984 i + 0.41992 j - 2.0996 k KN
b) T_ac = 1.972888 KN
Explanation:
Given:
- The tension in cable AB = 2.3 KN
Find:
a) Determine the vector expression for the tension T as a force acting on member AD.
b) Also find the magnitude of the projection of T along the line AC.
Solution:
part a)
- Find unit vector AB:
vector (AB) = 2 i + j - 5 k
mag (AB) = sqrt (2^2 + 1^2 + 5^2)
mag (AB) = sqrt(30)
unit (AB) = ( 1 / sqrt(30) )* ( 2 i + j - 5 k )
- Find Tension vector:
vector (T) = unit(AB)* 2.3 KN
= 0.83984 i + 0.41992 j - 2.0996 k
- The projection of T onto AC can be found from the dot product of vector T to unit vector (AC)
- For unit vector (AC)
vector (AC) = 2 i - 2 j - 5 k
mag (AC) = sqrt (2^2 + 2^2 + 5^2)
mag (AC) = sqrt(33)
unit (AC) = ( 1 / sqrt(33) )* ( 2 i - 2 j - 5 k )
- Compute the projection:
T_ac = vector T . unit (AC)
T_ac = (0.83984 i + 0.41992 j - 2.0996 k) . ( 1 / sqrt(33) )* ( 2 i - 2 j - 5 k )
T_ac = 0.2923947572 - 0.146973786 - 1.827467232
T_ac = 1.972888 KN
The volume of the rod is 1.26×10⁻⁵ m³, and the linear charge density of the rod is 3.64 C/m
<h3>What is volume?:</h3>
This is the product of the height of a solid object and its crossectional area.
The Volume of the rod is can be calculated using the formula below.
Note: A rod has the shape of a cylinder.
Formula:
- V = πr²h............... Equation 1
Where:
- V = Volume of the rod
- r = radius of the rod
- h = height of the rod.
From the question,
Given:
- r = 4mm = 0.004 m
- h = 25 cm = 0.25 m
- π = 3.14
Substitute these values into equation 1
- V = 3.14(0.004²)(0.25)
- V = 1.26×10⁻⁵ m³
<h3>What is linear charge density:</h3>
This is the ratio of the charge on an object to the length of the object.
The linear charge density of the rod can be calculated using the formula below.
- D = Q/h.................... Equation 2
Where:
- D = Linear charge density of the rod
- Q = Charge on the rod.
- h = height or length of the rod
From the question
Given:
- Q = 0.91 C
- h = 25 cm = 0.25 m
Substitute these values into equation 2
- D = 0.91/0.25
- D = 3.64 C/m
Hence, The volume of the rod is 1.26×10⁻⁵ m³, and the linear charge density of the rod is 3.64 C/m
Learn more about charge density here: brainly.com/question/14568868
Answer:
Mutualism, commensalism, parasitism, competition, and predation.
Explanation:
mutualism- relationship between two or more organisms where both are benefited. Example-oxpecker with rhino/zebra. They eat bugs off of them which means that they are getting food, while the rhino/zebra are getting cleaned up with pest control.
commensalism- relationship between two organisms where one benefits and the other isn't benefited or harmed. EX- tree frogs use plants as protectioin.he frog is benefited, and the plant is neither harmed nor benefited. Remora fish have a disk on their heads that they use to attach themselves to larger animals for protection. The animals they attach to are neither harmed nor benefited.
parasitism- in a relationship where an organism benefits at the expense of the other. (one is benefited while the other is harmed) ex- fleas and ticks that live on cats and dogs, tape worms that live in people and animals that eat the food which means that the people aren't getting the food or nutrition that they eat. lice, etc
competition- interaction within organisms/species in which both the organisms/species are harmed and is apart of natural selection. Examples may include two males fighting over a mate, animals competing over food, limited habitats that they are fighting over, territory, etc.
predation- the preying of one animal on another. It's where the predator hunts and eats another organism which is its prey. categorized within-(1) carnivory, (2) herbivory, (3) parasitism, and (4) mutualism. Each type of predation can by categorized based on whether or not it results in the death of the prey.ex- owls hunting mice, wolves hunting rabbits, lion hunting gazelle, etc.