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11 days ago

A vector of magnitude 10 has an angle with the positive x axis (east) of 120 degrees. what are its components

1 answer:

3 0

The angle formed with the positive x-axis is 120 degrees. We can assume that this angle is determined in a counterclockwise direction from the positive x-axis. The x-component of the vector can be calculated as: x-component = 10 cos(120) = -5. The vector's y-component is determined as: y-component = 10 sin(120) = 8.66. The x-component equates to -5 while the y-component equals 8.66.

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The amount of kinetic energy an object has depends on its mass and its speed. Rank the following sets of oranges and cantaloupes

Sav [3153]

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

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

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6 0

1 month ago

Modern wind turbines generate electricity from wind power. The large, massive blades have a large moment of inertia and carry a

Yuliya22 [3333]

Answer:

Explanation:

a )

Each blade resembles a rod with its axis positioned near one end.

The moment of inertia for one blade is:

= 1/3 x m l²

where m stands for the mass of the blade

l represents the length of each blade.

Total moment of inertia for 3 blades is:

= 3 x $\frac{1}{3}$ x m l²

ml²

2 )

Details provided include:

m = 5500 kg

l = 45 m

Substituting these values produces:

moment of inertia of one blade:

= 1/3 x 5500 x 45 x 45

= 37.125 x 10⁵ kg.m²

Moment of inertia for 3 blades:

= 3 x 37.125 x 10⁵ kg.m²

= 111.375 x 10⁵ kg.m²

c )

Angular momentum

= I x ω

I denotes the moment of inertia of the turbine

ω symbolizes angular velocity

ω = 2π f

f indicates the rotational frequency of the blades

d )

We have I = 111.375 x 10⁵ kg.m² (Calculated)

f = 11 rpm (revolutions per minute)

= 11 / 60 revolutions per second

ω = 2π f

= 2π x 11 / 60 rad / s

Calculating angular momentum yields

= I x ω

111.375 x 10⁵ kg.m² x 2π x 11 / 60 rad / s

= 128.23 x 10⁵ kgm² s⁻¹.

4 0

1 month ago

In 2014, the Rosetta space probe reached the comet Churyumov Gerasimenko. Although the comet's core is actually far from spheric

ValentinkaMS [3465]

To tackle this issue, we will utilize concepts related to gravity based on Newtonian definitions. To find this value, we'll apply linear motion kinematic equations to determine the required time. Our parameters include:

Comet mass $M = 1.0*10^{13} kg$

Radius $r = 1.6km = 1600 m$

The rock is released from a height 'h' of 1 m above the surface.

The relationship for gravity's acceleration concerning a body with mass 'm' and radius 'r' is described by:

$g = \frac{GM}{R^2}$

Where G represents the gravitational constant and M denotes the mass of the planet.

$g = \frac{(6.67408*10^{-11})(1*10^{13})}{1600^2}$

$g = 2.607*10^{-4} m/s^2$

Now, let’s compute the time value.

$h = \frac{1}{2} gt^2$

$t = \sqrt{\frac{2h}{g}}$

$t = \sqrt{\frac{2(1)}{2.607*10^{-4}}}$

$t = 87.58s$

Ultimately, the time for the rock to hit the surface is t = 87.58s.

8 0

1 month ago

The same physics student jumps off the back of her Laser again, but this time the Laser is

Yuliya22 [3333]

a) The student's speed after jumping is 1.07 m/s

b) The final speed of the laser is 10.4 m/s

Explanation:

This issue can be approached through the momentum conservation principle: In the absence of external forces, the combined momentum of the student and the laser must remain unchanged. Hence, we can express:

$p_i = p_f\\0=mv+MV$

where:

The initial momentum is zero

m = 42 kg signifies the mass of the laser

v = 1.5 m/s is the laser's final velocity

M = 59 kg is the mass of the student

V denotes the student's final velocity

Solving this for V, we can determine the student's speed:

$V=-\frac{mv}{M}=-\frac{(42)(1.5)}{59}=-1.07 m/s$

Thus, the student's final speed calculates to 1.07 m/s.

Here, both the laser and the student have a combined speed of 3.1 m/s prior to the student's jump; thus, the initial momentum isn't zero.

<pSo, we formulate the equation of momentum conservation as:

$(m+M)u=mv+MV$

where:

m = 42 kg denotes the mass of the laser

M = 59 kg is the student’s mass

u = 3.1 m/s is their starting velocity

V = -2.1 m/s indicates the student's speed post-jump (she jumps backward)

v signifies the laser's final speed

When we resolve for v, we have:

$v=\frac{(m+M)u-MV}{m}=\frac{(42+59)(3.1)-(59)(-2.1)}{42}=10.4 m/s$

Learn more about momentum:

3 0

2 months ago

Read 2 more answers

A student observes that for the same net force heavier objects accelerate less which statement describes the correct conclusion?

inna [3103]

Answer: Reduced acceleration leads to an increase in mass.

Explanation:

We can rephrase this as:

"When a constant force F is applied, heavier objects experience less acceleration"

As a result, when mass rises, the object's acceleration diminishes.

This is referred to as an inverse correlation between acceleration and mass.

According to Newton's second law, we find that:

F = m*a

Force equals mass multiplied by acceleration.

So, if the force remains constant, we can express it as:

a = F/m.

In this equation, we observe that if acceleration decreases and F stays constant, then the mass m must also rise (as it is found in the denominator)

Therefore, the accurate statement is:

A decrease in acceleration causes the mass to increase.

4 0

1 month ago

Read 2 more answers