A student placed a pencil in a cup of water. The pencil appears broken because light- always travels in a straight line makes th

mass₃<mass₁=mass₅<mass₂=mass₄

Explanation:

Data points:-

1. mass:  m      speed: v

2. mass: 4 m   speed: v

3. mass: 2 m   speed: ¼ v

4. mass: 4 m   speed: v

5. mass: 4 m   speed: ½ v

We know that the formula for Kinetic energy (KE) is ½ mv²

Where m represents the mass of the object

           v represents the object's velocity

<psubstituting the="" given="" values="" for="" mass="" and="" speed="" from="" previous="" data:="">

The KE of Body 1(mass₁) = ½*m*v²             = mv²/2

KE of Body 2(mass₂) = ½*4m*v²         = 2mv²

KE of Body 3(mass₃) = ½*2m*(1/4v)²  =  mv²/16

KE of Body 4(mass₄) = ½*4m*v ²        =  2mv ²

KE of Body 5(mass₅) = ½*4m*(1/2v)²  =   mv²/2

</psubstituting>

In static equilibrium, all forces balance out. Therefore, to simplify, start by breaking down F1 into its horizontal and vertical components. Since no other forces act horizontally, F1's horizontal component is known to be 40N. This information can be used to determine the vertical component using the Pythagorean theorem. Once the components are established, simply add the vertical components to calculate the difference between the upward and downward forces.

Answer:

d_total = 12 m

Explanation:

In this kinematics scenario illustrated in the graph provided, we determine the distance traveled over a 24-second duration.

The comprehensive distance can be calculated as follows:

d_total = d₁ + d₂ + d₃

Given that d₂ on the graph is level (v=0), its distance equates to zero, hence d₂ = 0.

The distance for d₁ is calculated as:

d₁ = 12 - 6 = 6 m

For distance d₃:

d₃ = 6 - 0 = 6 m

Thus, the overall distance covered is:

d_total = 6 + 0 + 6

d_total = 12 m

Answer:

b = 0.6487 kg / s

Explanation:

In the context of oscillatory motion, friction is related to velocity,

               fr = - b v

where b represents the friction coefficient.

Upon solving the equation, the angular velocity is represented as

               w² = k / m - (b / 2m)²

In this case, we're given an angular frequency w = 1Hz, the mass m = 0.1 kg, and the spring constant k = 5 N / m. This allows us to derive the friction coefficient.

             

Let’s denote

               w₀² = k / m

               w² = w₀² - b² / 4m²

               b² = (w₀² -w²) 4 m²

Now, let's calculate the angular frequencies.

             w₀² = 5 / 0.1

             w₀² = 50

             w = 2π f

             w = 2π 1

             w = 6.2832 rad / s

Substituting values yields

               b² = (50 - 6.2832²) 4 0.1²

               b = √ 0.42086

                b = 0.6487 kg / s

Answer:

223 degrees

Explanation:

We have the following information:

Magnitude of the resultant vector = 8 units

The resultant vector makes a counterclockwise angle with the positive x-axis

Our goal is to determine the magnitude and angle of the equilibriant vector.

We understand that the equilibrium vector has the same magnitude but is oriented in the opposite direction of the given vector.

Thus, the equilibrium vector's magnitude = 8 units

x-component of a vector=

Where v = Magnitude of vector

Using the formula:

x-component of the resultant vector=

y-component of the resultant vector=

x-component of the equilibrium vector=

y-component of the equilibrium vector=

Because the equilibrium vector lies in the third quadrant

The angle is in the third quadrant

In the third quadrant, the angle =

The angle of the equilibrium vector measured from the positive x-axis in a counterclockwise direction is 180+43=223 degrees