What is 6.9 × 107 written in standard form?
2 answers:
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Answer:
6.86 m/s
Explanation:
This problem can be solved by doing the total energy balance, i.e:
initial (KE + PE) = final (KE + PE). { KE = Kinetic Energy and PE = Potential Energy}
Since the rod comes to a halt at the topmost position, the KE final is 0. Therefore, all the KE initial is changed to PE, i.e, ΔKE = ΔPE.
Now, at the initial position (the rod hanging vertically down), the bottom-most end is given a velocity of v0. The initial angular velocity(ω) of the rod is given by ω = v/r , where v is the velocity of a particle on the rod and r is the distance of this particle from the axis.
Now, taking v = v0 and r = length of the rod(L), we get ω = v0/ 0.8 rad/s
The rotational KE of the rod is given by KE = 0.5Iω², where I is the moment of inertia of the rod about the axis of rotation and this is given by I = 1/3mL², where L is the length of the rod. Therefore, KE = 1/2ω²1/3mL² = 1/6ω²mL². Also, ω = v0/L, hence KE = 1/6m(v0)²
This KE is equal to the change in PE of the rod. Since the rod is uniform, the center of mass of the rod is at its center and is therefore at a distane of L/2 from the axis of rotation in the downward direction and at the final position, it is at a distance of L/2 in the upward direction. Hence ΔPE = mgL/2 + mgL/2 = mgL. (g = 9.8 m/s²)
Now, 1/6m(v0)² = mgL ⇒ v0 =
Hence, v0 = 6.86 m/s
1. Weight is the gravitational pull with which the earth attracts the body towards the center of the earth. The S.I unit is Newton (N)
2. The weight of an object is related to its mass with the below equation.
W = mg
Where W = weight, m = mass and g = acceleration due to gravity
3. The mass m = 50 kg and g = 9.8 m/
Substitute the parameters in the equation above.
W = 50 x 9.8
W = 490 N
4. An object is accelerating when it speeds up. If the object slows down, it means it is decelerating. The correct answer is option A
5. Newton's second law of motion is:
F = ma
Where F = force applied, m = mass and a = acceleration
Therefore, Newton's second law of motion relates an object's acceleration to its net force acting on it. The correct answer is option C
6. According to Newton's second law of motion which relates an object's acceleration to its mass, doubling the net force acting on an object a doubles its acceleration. Because mass is always constant.
7. Since the weight of an object is related to its mass with the equation.
W = mg, If the mass of an object doubles, its weight will also doubles. Option A is the correct answer.
8. If you know the mass of an object, you can calculate its weight with the formula F = mX when X = 9.8m/
9. Force is expressed in unit as Newton (N)
10. The parameters given are :
mass m = 20kg
Force F = 40N
To calculate acceleration, use the formula F = ma
Substitute all the parameters into the equation.
40 = 20a
a = 40/20
a = 2m/
The correct option is D
Learn more here : brainly.com/question/18835375