A bar of soap when weighed in air has a weight of 5,2N . When completely immersed in water , however it has a weight of 3,7N . What is the volume of the bar of soap

Answer:

[tex]\displaystyle \sqrt{\frac{(5/2)\, (g - a)\, m\, R^{2}}{M^{2}\, a}}[/tex], assuming that the tension in the rope is the only tangential force on the sphere ([tex]g[/tex] denote the gravitational acceleration.)

Explanation:

The forces on the bucket are:

Since the weight of the bucket and the tension from the rope are in opposite directions, the magnitude of the net force would be:

[tex]\begin{aligned} \|\text{Net Force}\| =\; & \|\text{Weight}\| - \|\text{Tension}\| \end{aligned}[/tex].

The upward tension in the rope prevents the bucket from accelerating at [tex]g[/tex] (free fall.) Rather, the bucket is accelerating at an acceleration of only [tex]a[/tex]. The net force on the bucket would be thus [tex]m\, a[/tex].

Rearrange the equation for the net force on the bucket to find the magnitude of the tension in the rope would be:

[tex]\begin{aligned} & \|\text{Tension}\| \\ =\; & \|\text{Weight}\| - \|\text{Net Force}\| \\ =\; & m\, g - m\, a \\ =\; & (g - a)\, m\end{aligned}[/tex].

At a distance of [tex]R[/tex] from the center of the sphere, the tension in the rope [tex](g - a)\, m[/tex] would exert a torque of [tex](g - a)\, m\, R[/tex] on the sphere. If this tension is the only tangential force on this sphere, the net torque on the sphere would be [tex](g - a)\, m\, R\![/tex].

Let [tex]M[/tex] denote the mass of this sphere. The moment of inertia of this filled sphere would be [tex]I = (2/5)\, M^{2}[/tex].

Therefore, the magnitude of the angular acceleration of this sphere would be:

[tex]\begin{aligned}& \|\text{Angular Acceleration}\| \\ =\; & \frac{\|\text{Net Torque}\|}{(\text{Moment of Inertia})} \\ =\; & \frac{(g - a)\, m\, R}{(2/5)\, M^{2}} \end{aligned}[/tex].

The bucket is accelerating at a magnutide of [tex]a[/tex] downwards. The rope around the sphere need to unroll at an acceleration of the same magnitude, [tex]a\![/tex]. The tangential acceleration of the sphere at the surface would also need to be [tex]\! a[/tex].

Since the surface of the sphere is at a distance of [tex]R[/tex] from the center, the angular acceleration of this sphere would be [tex](a / R)[/tex].

Hence the equation:

[tex]\begin{aligned}& \frac{(g - a)\, m\, R^{2}}{(2/5)\, M^{2}} = \|\text{Angular Acceleration}\| = \frac{a}{R} \end{aligned}[/tex].

Solve this equation for [tex]M[/tex], the mass of this sphere:

[tex]\begin{aligned}& \frac{(g - a)\, m\, R^{2}}{(2/5)\, M^{2}} = \frac{a}{R} \end{aligned}[/tex].

[tex]\begin{aligned}M^{2} &= \frac{(g - a)\, m\, R^{2}}{(2/5)\, a} \\ &= \frac{(5/2)\, (g - a)\, m\, R^{2}}{a}\end{aligned}[/tex].

[tex]\begin{aligned}M&= \sqrt{\frac{(5/2)\, (g - a)\, m\, R^{2}}{a}}\end{aligned}[/tex].

The angular momentum is 200 kg m^2 s^-1

Angular momentum is the product of  linear momentum and the perpendicular distance. Linear momentum is the product of mass and velocity, where radius is the perpendicular distance

Angular momentum = mass * velocity * radius

Angular momentum = 5 * 2 * 20

Angular momentum = 200 kg m^2 s^-1

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Answer:

Isaac Newton came up with the 3 Laws of Motion

Answer:

Isaac Newton came up with three laws of motion

Answer:

Explanation:

I don't think so. Think about it. To compress the volume by a factor of 2 it takes 956 Joules.

Now you come along and you want to get the pressure for 1/12 of the volume. It's going to take a huge pressure to do that.

I would suggest that you have to use a modified form of the formula.

PV = 956

You need to compress the volume by 1/6

P(V/6) = 956

6 * PV/6 = 6 * 956

PV = 5736 J

Why did I only take 1/6? Because. 956 represents the pressure needed for 1/2 the volume. You need to multiply 1/2 * 1/6 to get 1/12

The material is at its phase change temperature and the thermal energy is going to change the phase instead of increase the temperature.

Latent heat is defined as the thermal energy absorbed or released during a phase change of a substance.

Latent heat can also be explained as the energy in hidden form which is supplied or extracted to change the state of a substance without changing its temperature.

From the above explanation, we can conclude that, the material is at its phase change temperature and the thermal energy is going to change the phase instead of increase the temperature.

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Answer:

M1 g L1 = 19 kg * 9.8 m/s^2 * 5 m = counter clockwise torque - Cassie at left end

M1 g L1 = M2 g L2        for torques to balance

L2 = M1 L1 / M2 = 19 * 5 / 31 = 3.06 M

Alex should sit at 3.1 m from the fulcrum (at 5 m from each end)

The type of heat transfer occurs in your stomach when you eat hot soup and an ice cold beverage is Conduction.

This is the process by which heat energy is transmitted through collisions between neighboring atoms or molecules.

This happens when they are in close contact with each other which was why Conduction was chosen as the most appropriate choice.

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Answer:

a

Explanation:

Distance is simply the distance travelled which in this case would be 4km + 3km = 7km

To work out displacement, try to imagine the situation.

Draw a straight line to the east (label it 3) and then draw another line from the end of the first line upwards (label this one 4). Thus, you've created a right angles triangle. Now use pythagorean theorem to work out the displacement

4^2 + 3^2 = 25

sqrt 25 = 5 = displacement

Answer:

C

because urine is waste product

Answer:

50 N

Explanation:

Let the natural length of the spring = L

so

100 = k(40 - L)       (1)

200 = k(60 - L)       (2)

(2)/(1):   2 = (60 - L)/(40 - L)

60 - L = 2(40 - L)

60 - L = 80 - 2L

2L - L = 80 - 60

L = 20

Sub it into (1):

100 = k(40 - 20) = 20k

k = 100/20 = 5 N/in

Now

X = k(30 - L) = 5(30 - 20) = 50 N

(a) The initial energy of the block due to its position is 1.96 J.

(b) The velocity of the block at the bottom of the loop is 3.96 m/s.

(c)  the velocity of the block at the top of the loop is 3.13 m/s.

The initial energy of the block due to its position is calculated as follows;

P.E = mgh

P.E = 0.25 X 9.8 X 0.8

P.E = 1.96 J

The velocity of the block at the bottom of the loop is determined by applying the principle of conservation of energy as shown below;

P.Ei + P.Ef = K.Ei + K.Ef

1.96 + 0 = 0 + ¹/₂mvf²

vf² = 2(1.96)/m

vf² = (2 x 1.96) / (0.25)

vf² = 15.68

vf = √15.68

vf = 3.96 m/s

The velocity of the block at the top is calculated by applying principle of conservation of energy,

P.Ei + P.Ef = K.Ei + K.Ef

1.96 = mghf + ¹/₂mvf²

where;

1.96 = 0.25 x 9.8 x 0.3   +   0.5 x 0.25vf²

1.225 = 0.125vf²

vf² = 1.225/0.125

vf² = 9.8

vf = 3.13 m/s

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Question :-

Answer :-

Explanation :-

As per the provided information in the given question, The Resistance is given as 330 Ohm . The Voltage is given as 5 Volt . And, we have been asked to calculate the Current .

For calculating the Current , we will use the Formula :-

[tex] \bigstar \: \: \: \boxed{ \sf{ \: Current \: = \: \dfrac{Voltage}{Resistance} \: }} [/tex]

Therefore , by Substituting the given values in the above Formula :-

[tex] \dag \: \: \: \sf {Current \: = \: \dfrac {Voltage}{Resistance} } [/tex]

[tex] \longmapsto \: \: \: \sf {Current \: = \: \dfrac {5}{330} } [/tex]

[tex] \longmapsto \: \: \: \sf {Current \: = \: \dfrac {1}{66} } [/tex]

[tex] \longmapsto \: \: \: \textbf {\textsf {Current \: = \: 66 }} [/tex]

Hence :-

[tex] \underline {\rule {180pt} {4pt}} [/tex]

Additional Information :-

[tex] \Longrightarrow \: \: \: \sf {Voltage \: = \: Current \: \times \: Resistance} [/tex]

[tex] \Longrightarrow \: \: \: \sf {Current \: = \: \dfrac {Voltage}{Resistance} } [/tex]

[tex] \Longrightarrow \: \: \: \sf {Resistance \: = \: \dfrac {Voltage}{Current} } [/tex]

Answer:

Step by step explanation:

Answer:

Explanation:

A television set is plugged into a 120 V outlet. The television circuit carries a current equal to 0.75 A. What is the overall resistance of the television set?​

V = IR

120 volt = 0.75A * R

R = 160 Ω

The si unit of force is newton.

so, F is eqal to m*g

Answer:

F=ma

Explanation:

force is actually a derived quantity

newton is a unit derived from kg.m/s^2

This is from Newton's second law of motion

F=ma

Alpha

I hope this helps you

:)

Answer:

H = 1/2 g t^2    where t is time to fall a height H

H = 1/8 g T^2   where T is total time in air  (2 t  = T)

R = V T cos θ       horizontal range

3/4 g T^2 = V T cos θ       6 H = R    given in problem

cos θ = 3 g T / (4 V)           (I)

Now t = V sin θ / g     time for projectile to fall from max height

T = 2 V sin θ / g

T / V = 2 sin θ / g

cos θ = 3 g / 4 (T / V)     from (I)

cos θ = 3 g / 4 * 2 sin V / g = 6 / 4 sin θ

tan θ = 2/3      

θ = 33.7 deg

As a check- let V = 100 m/s

Vx = 100 cos 33.7 = 83,2

Vy = 100 sin 33,7 = 55.5

T = 2 * 55.5 / 9.8 = 11.3 sec

H = 1/2 * 9.8 * (11.3 / 2)^2 = 156

R = 83.2 * 11.3 = 932

R / H = 932 / 156 = 5.97        6 within rounding

Answer:

Given:

m1 = 7 kg

V1 = 12 m/s

m2 = 25 kg

V2 = 6 m/s

To find:

Combined speed of two balls stick together after collision V = ?

Solution:

According to law of conservation of momentum,

m1V1 + m2V2 = (m1+m2)V

7×12 + 25×6 = (7+25)V

84 + 150 = 32V

V = 234/32

V = 7.31 m/s

Combined speed of two ball is 7.31 m/s

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Answer:

p = rho× g × h

Explanation:

p: pressure

rho : density

g : gravity acceleration

h : height

Answer:

M1 would seem to be slower because of a larger mass

x1 = A1 sin ω1 t1        describes the displacement

ω1 / ω2 = ((k1 / k2) / (m1 / m2))^1/2 = (m2 / m1)^1/2  since k's are equal

ω1 / ω2 = 1/2 from graph    (frequency of 2 is greater)

(m1 / m2)^1/2 = ω2 / ω1    from above

m1 / m2 = 2^2 = 4    so m1 would have 4 times the mass of m2

M1 would seem to be slower because of a larger mass

x1 = A1 sin ω1 t1      

ω1 / ω2 = ((k1 / k2) / (m1 / m2))^1/2 = (m2 / m1)^1/2  since k's are equal

ω1 / ω2 = 1/2 from graph   (frequency of 2 is greater)

(m1 / m2)^1/2 = ω2 / ω1   from above

m1 / m2 = 2^2 = 4    so m1 would have 4 times the mass of m2.

The two graphs shown represent the motion of two blocks with different masses, m1 and m2. The blocks are oscillating on identical springs. For the system consisting of the two blocks, the change in the kinetic energy of the system is equal to work done by gravity on the system. For the system consisting of the two blocks, the pulley and the Earth, the change in the total mechanical energy of the system is zero.

The two graphs shown represent the motion of two blocks with different masses, m1 and m2. The blocks are oscillating on identical springs. For the system consisting of the two blocks, the change in the kinetic energy of the system is equal to work done by gravity on the system.

Therefore, M1 would seem to be slower because of a larger mass

x1 = A1 sin ω1 t1      

ω1 / ω2 = ((k1 / k2) / (m1 / m2))^1/2 = (m2 / m1)^1/2  since k's are equal

ω1 / ω2 = 1/2 from graph   (frequency of 2 is greater)

(m1 / m2)^1/2 = ω2 / ω1   from above

m1 / m2 = 2^2 = 4    so m1 would have 4 times the mass of m2.

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#SPJ2

The momentum, in the x-direction, that was transferred to the more massive cart after the collision is 19.38 kgm/s.

The momentum transfered to the more massive cart is determined by applying the principle of conservation of linear momentum as shown below;

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

where;

⁻ΔP₁ = ΔP₂

ΔP₂ = m₂v₂ - m₂u₂

ΔP₂ = m₂(v₂ - u₂)

ΔP₂ = 3m₁(v₂ - u₂)

ΔP₂ = 3 x 3.8 x (1.7 - 0)

ΔP₂ = 19.38 kgm/s

Thus, the momentum, in the x-direction, that was transferred to the more massive cart after the collision is 19.38 kgm/s.

The complete question is beblow

A cart of mass 3.8 kg is traveling to the right (which we will take to be the positive x-direction for this problem) at a speed of 6.9 m/s. It collides with a stationary cart that is three times as massive. After the collision, the more massive cart is moving at a speed of 1.7 m/s, to the right.

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Answer:

For B it is 0

Explanation:

I think

The monocular cue of relative size

Answer:25

Explanation: because higher means less kinetic energ

Answer: 6067.5 N

Explanation:

Work = Change in Energy. To start, all of the energy is kinetic energy, so find the total KE using: KE = 1/2(m)(v^2). Plug in 1980 kg for m and 15.5 m/s for v and get KE = 237847.5 J.

Now, plug this in for work: Work = Force * Distance; so, divide work by distance to get 6067.5 N.

All of the following are examples of physical properties except tearing.

This is used to describe the state of a physical system and is usually measurable.

Examples include:

Tearing isn't an example of a physical property which was why option A was chosen as the most appropriate choice.

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