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Kruka [31]
2 years ago
13

A 2.00-kg box is suspended from the end of a light vertical rope. A time-dependent force is applied to the upper end of the rope

, and the box moves upward with a velocity magnitude that varies in time according to v(t)=(2.00m/s2)t+(0.600m/s3)t2. Part A What is the tension in the rope when the velocity of the box is 15.0 m/s ?
Physics
1 answer:
Alex2 years ago
4 0

Answer:

T = 27.92 N

Explanation:

For this exercise let's use Newton's second law

      T - W = m a

The weight

      W = mg

The acceleration can be found by derivatives

     a = dv / dt

     v = 2 t + 0.6 t²

     a = 2 + 0.6 t

We replace

      T - mg = m (2 + 0.6t)

      T = m (g + 2 + 0.6 t)               (1)

Let's look for the time for the speed of 15 m / s

       15 = 2 t + 0.6 t²

       0.6 t² + 2 t - 15 = 0

We solve the second degree equation

        t = [-2 ±√(4 - 4 0.6 (-15))] / 2 0.6

        t = [-2 ±√40] / 1.3 = [-2 ± 6.325] / 1.2

We take the positive time

       t = 3.6 s

Let's calculate from equation 1

       T = 2.00 (9.8 + 2 + 0. 6  3.6)

        T = 27.92 N

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Oceanographers use submerged sonar systems, towed by a cable from a ship, to map the ocean floor. In addition to their downward
KATRIN_1 [288]

Answer:

Tension in the cable is T = 16653.32 N

Explanation:

Give data:

Cross section Area A = 1.3 m^2

Drag coefficient CD = 1.2

Velocity V = 4.3 m/s

Angle made by cable with horizontal  =30 degree

Density \rho \ of\  water= 1000 kg/m3

 Drag force FD is given as

F_{D} = \fracP{1}{2} \rho v^{2} C_{D} A

        = 0.5\times 1000\times 4.32\times  1.2\times 1.3

Drag force = 14422.2 N acting opposite to the motion

As cable made angle  of 30 degree with horizontal  thus horizontal component is take into action to calculate drag force

TCos30 = F_D

T = \frac{F_D}{cos30}

T =\frac{ 14422.2}{cos 30}

T = 16653.32 N

7 0
2 years ago
An air-track glider undergoes a perfectly inelastic collision with an identical glider that is initially at rest. what fraction
DiKsa [7]
Refer to the diagram shown below.

The initial KE (kinetic energy) of the system is
KE₁ = (1/2)mu²

After an inelastic collision, the two masses stick together.
Conservation of momentum requires that
m*u = 2m*v
Therefore
v = u/2

The final KE is
KE₂ = (1/2)(2m)v²
       = m(u/2)²
       = (1/4)mu²
      = (1/2) KE₁

The loss in KE is
KE₁ - KE₂ = (1/2) KE₁.

Conservation of energy requires that the loss in KE be accounted for as thermal energy.

Answer:  1/2 

5 0
2 years ago
Read 2 more answers
What is the electric potential vtot at the center of the square? make the usual assumption that the potential tends to zero far
Romashka-Z-Leto [24]
Missing figure of the problem: http://tsephysics.weebly.com/uploads/5/1/9/3/51934203/477140_orig.jpg

Solution:
Assuming the potential is zero at infinite distance from the charge, then the potential at a certain distance r from a single point charge is 
V(r)=k_e  \frac{q}{r}
where k_e=8.99\cdot 10^9 Nm^2C^{-2} is the Coulomb's constant.

In our problem, we just have to superimpose the potential generated by every charge. The diagonal of the square is \sqrt{2} d, therefore the distance between each charge and the center of the square is \frac{ \sqrt{2} }{2} d.
So, the total potential is:
V=V_1+V_2+V_3+V_4=
=k_e \frac{q}{ \frac{ \sqrt{2}d }{2} }+ k_e \frac{2q}{ \frac{ \sqrt{2}d }{2} }+k_e \frac{5q}{ \frac{ \sqrt{2}d }{2} }-k_e \frac{3q}{ \frac{ \sqrt{2}d }{2} }=
=5 \sqrt{2} k_e  \frac{q}{d}
7 0
2 years ago
A person pushes horizontally on a 50-kg crate, causing it to accelerate from rest and slide across the surface. If the push caus
Marina CMI [18]

Answer:

v_{f} =4.9\frac{m}{s}  :  velocity of the crate after the person has pushed the crate a distance of 6 meters

Explanation:

Crate kinetics

Crate moves with uniformly accelerated movement

v f²=v₀²+2a*d (formula 1)

d:displacement in meters (m)

v₀: initial speed in m/s

vf: final speed in m/s

a: acceleration in m/s²

Known data

v₀=0 The speed of the crate is equal to zero because part of the rest.

a= 2m/s²

d= 6m

Distance calculating

We replace data in the Formula (1)

v f²=0+2*2*d

v f²=2*2*6

v f²=24

v_{f} =\sqrt{24}

v_{f} =4.9\frac{m}{s}

7 0
2 years ago
In an experiment you are performing, your lab partner has measured the distance a cart has traveled: 28.4inch. You need the dist
alexgriva [62]

As per the question the distance travelled by  a car is 28.4 inch.

we are asked to determine the  conversion factor in centimeter  which when multiplied with 28.4 inch will give a unit.

we know that one inch =2.54 centimeter.

Hence 28.4 inch = 2.54  ×28.4 cm

                            =72.136 cm.

Now we have to determine the conversion factor .The multiplication factor is calculated as    P =\frac{28.4 inch*2.54cm}{1 inch}

                         p= 72.136 cm        [p is the multiplication factor.]

Hence the multiplication factor is 72.137 cm which will give unit conversion when multiplied with 28.4 inch.

                 

                             


4 0
1 year ago
Read 2 more answers
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