A metal ball of mass 2 kg is supported by a massless inextensible string, 12 cm long. A horizontal force displaces the ball by 30oto the vertical so that the string remains taut. Find:a) the horizontal force.b) the tension in the thread.

Explanation:

Given that,

The dummy is thrown forward with a force of 130 N, [tex]F_1=130\ N[/tex]

Side force acting on the dummy, [tex]F_2=4500\ N[/tex]

We need to find the force acting on the sensor report. It can be calculated using Pythagoras theorem as :

[tex]F_{net}=\sqrt{F_1^2+F_2^2}[/tex]

[tex]F_{net}=\sqrt{130^2+4500^2}[/tex]

[tex]F_{net}=4501.87\ N[/tex]

So, the net force acting on the sensor report is 4501.87 N. Hence, this is the required solution.

The net force acting on the dummy is 4502 N.

Force is a vector, the resultant force (net force) is that single force that has the same effect in magnitude and direction as two or more forces acting together. The resultant of a vector must take into cognizance, the geometry of the problem.

The dummy is thrown forward with a force of 130.0N while simultaneously being hit from the side with a force of 4500.0N. The net force must now be obtained by Pythagoras theorem.

Fnet^2 = F1^2 + F2^2

F1 = 130.0N

F2 = 4500.0N

Fnet = √(130.0N)^2 + (4500.0N)^2

Fnet = 4502 N

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Mass x SH x °C (or K) ΔT

= 75g x 0.45J/g/K x 6.0 ΔT

= 202.5 Joules of heat absorbed.

(202.5J / 4.184J/cal = 48.4 calories).

I guess that is the answer

The amount of heat would be absorbed by 75.20 g of iron when from 22°C to 28°C is equal to 8834.5 J.

Specific heat capacity for any substance is the amount of heat energy required to raise the temperature by 1°C of a unit mass of that substance. The mathematically Specific heat capacity can be expressed as:

Q= m C ΔT

where Q is the amount of heat energy, ΔT is the change in temperature, and C is the specific heat capacity of the system.

Specific heat capacity is an intensive property as it is independent of the size or quantity of the matter.

Given, the Specific heat capacity of the iron, C = 0.44 J/gK

The mass of the iron, m = 75.20 g

The change in the temperature = ΔT = 28 - 22 = 6°C = 273-6 = 267 K

The heat absorbed by iron, Q = mCΔT = 75.20 × 0.44 × 267

Q = 8834.5 J

Therefore, the heat would be absorbed by 75.20 g of iron is 8834.5 Joules.

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Answer:

true

Explanation:

That is true, i think.

Answer:

True

Explanation:

length of the vector is proportional to the magnitude of the vector

so length of vector will be in the proportional to the magnitude of the vector here

initial length of the vector is 3 cm which represent the velocity vector as 100 m/s

now it means 3 cm length is proportional to speed which is 100 m/s

now if we draw another vector of length 6 cm then here we can see that if length of vector is doubled then initial length

so here the magnitude of velocity will also be doubled

so here final speed must be double of initial speed

[tex]v_f = 2* v_i[/tex]

[tex]v_f = 2*100 = 200 m/s[/tex]

Focal distance of an ellipse is given by the formula

[tex]f = ae[/tex]

here a = length of semi major axis

e = eccentricity of the path

now here we know that

length of major axis for the path of planet is given as 32 units

so here we can say

[tex]2a = 32 units[/tex]

[tex]a = 16 units[/tex]

so length of semi major axis is 16 units

focal distance for the planet path is given as 8 units

now from the above formula we can write

[tex]f = a*e[/tex]

[tex]8 = 16*e[/tex]

[tex]e = \frac{8}{16}[/tex]

[tex]e = \frac{1}{2} = 0.5[/tex]

so eccentricity for the path of planet will be 0.5

Answer: C) velocity is a vector and requires a direction.

Explanation:

In physics, there are two types of quantities:

- scalars: these are quantities that have only a magnitude

- vectors: there are quantities that have both magnitude and direction

As an example, speed is a scalar while velocity is a vector. Therefore, speed has only a magnitude, while velocity has both magnitude and direction: therefore, the difference between the two quantities is that velocity is a vector and requires a direction, as stated in option C.

Answer:

velocity is a vector and requires a direction.

Explanation:

Speed is defined as the total distance covered per unit time and the velocity is defined as the total displacement per unit time.

Speed is a scalar quantity and velocity is a vector quantity. The quantities that have both magnitude and direction are vector quantity and the quantity that have only magnitude are scalar quantity.The SI unit of both velocity and speed is m/s.

So, the correct option is (c) "  velocity is a vector and requires a direction ".

initial height of the boy when he jump or dive is 5 meter

[tex]h_1 = 5 m[/tex]

now his final position is 2 yards above the surface

[tex]h_2 = 2 yards[/tex]

as we know that

[tex]1 yard = 0.9144 m[/tex]

[tex]2 yards = 1.83 m[/tex]

now by energy conservation we can say

change in potential energy = gain in kinetic energy

[tex]mg(h_1 - h_2) = \frac{1}{2} mv^2[/tex]

divide both sides by mass "m"

[tex]g*(5 - 1.83) = \frac{1}{2}*v^2[/tex]

[tex]v^2 = 2*9.8*(5 - 1.83)[/tex]

Now kinetic energy will be given as

[tex]KE = \frac{1}{2} mv^2[/tex]

[tex]KE = \frac{1}{2}*70 * 2*9.8*( 5 - 1.83)[/tex]

[tex]KE = 2175 J[/tex]

so his kinetic energy will be 2175 J

Resistance of our body is given as

[tex]R = 30,000 ohm[/tex]

voltage applied across the body is

[tex]V = 120 V[/tex]

now by ohm's law current pass through our body is given by

[tex]i = \frac{V}{R}[/tex]

[tex]i = \frac{120}{30,000}[\tex]

[tex]i = 4 * 10^{-3} A[/tex]

So current from our body will be 4 * 10^-3 A

Answer:

It take the bullet 0.64 seconds to hit the ground.

Explanation;

 We have equation of motion , [tex]s= ut+\frac{1}{2} at^2[/tex], s is the displacement, u is the initial velocity, a is the acceleration and t is the time.

Here we need to consider only vertical motion of bullet.

Initial velocity = 0 m/s, Displacement = 1.98 m, acceleration = acceleration due to gravity = [tex]9.8m/s^2[/tex], we need to find time taken

Substituting

   [tex]1.98= 0*t+\frac{1}{2} *9.8*t^2\\ \\ 4.9t^2=1.98\\ \\ t^2=0.404\\ \\ t=0.64 seconds[/tex]

   It take the bullet 0.64 seconds to hit the ground.

A scalar quantity is one in which there is no direction given.

30 Lbs would be the answer, since there is no indicator of direction.

the answer is c another magnet can be attracted or repelled because they have north and south sides

Answer: Option (C) is the correct answer.

Explanation:

A magnet will only be attracted by another magnet as each magnet contains opposite poles. These poles are north pole and south pole.

Hence, like poles are repel each other whereas opposite poles are attracted towards each other.

Therefore, when a magnet comes in contact with a copper wire then there will be attraction between them.

On the other hand, if south pole of a magnet comes in contact with the north pole of another magnet then a force of attraction will occur between them.

Due to this both the magnets get attracted towards each other. But when south pole of a magnet comes in contact with the south pole of another magnet then force of repulsion will occur.

Thus, we can conclude that another magnet will be attracted to or repelled by a magnet.

1 h 13 min and 50 s it will take.

To answer this question, we must use the equation for the volumetric expansion of gases at constant pressure. This equation is given by:

[tex]V=V_{0}(1 + \alpha(T_{2}-T_{1}))[/tex]

We know:

[tex]V_{0}[/tex] is the initial volume [tex]= 0.5 m ^ 3[/tex]

ΔT is the temperature change = 45 ° -20 ° = 25 °

[tex]\alpha[/tex] is the coefficient of gas expansion and is equal to 1/273

Then the final volume of the gas is:

[tex]V=0.5*(1+\frac{1}{273}*25)[/tex]

[tex]V=0.546m^ 3[/tex]

We need to find the average speed of the ball during the motion of 1 m

In order to find that we took several reading and found following times to cover the distance of 1 m

t1 = 2.26 s

t2 = 2.38 s

t3 = 3.02 s

t4 = 2.26 s

t5 = 2.31 s

Now in order to find the average time we can write

[tex]T_{mean} = \frac{t_1 + t_2 + t_3 + t_4 + t_5}{5}[/tex]

[tex]T_{mean} = \frac{2.26 + 2.38 + 3.02 + 2.26 + 2.31}{5}[/tex]

[tex]T_{mean} = 2.45 s[/tex]

So average time to cover the distance of 1 m by ball will be 2.45 s

here 3.02 s is not the average time but we can say it is the median of the readings of all possible values which we can not use in our calculation as average time

Intially, we have:

Pressure P1 = 400KPa

Temperature T1= 110Kelvin

When,

Temperature T2= 235 Kelvin

Pressure P2= ?

We have gas equation:

PV= nRT

P/T= nR/V

Considering nR/T as constant, we have:

P1/T1 = P2/T2

400/110= P2/235

P2= 854.5 KPa

So the new temperature will be 854.5 KPa

The question is unclear regarding the boat's velocity. Is it 20 m/s south relative to the water, or relative to the earth? (It is a river, after all...)

There's also the possibility that the boat's velocity relative to the river is 0. Take the south direction to be negative and north to be positive, and denote by [tex]v_{A/B}[/tex] the velocity of a body A relative to a body B. Under these conditions,

[tex]v_{B/E}=v_{B/W}+v_{W/E}\iff-20\,\dfrac{\mathrm m}{\mathrm s}=0+-20\,\dfrac{\mathrm m}{\mathrm s}[/tex]

(B for boat, E for earth, W for water) so that the passenger's velocity relative to the earth is

[tex]v_{P/E}=v_{P/B}+v_{B/W}+v_{W/E}[/tex]

(P for passenger)

[tex]v_{P/E}=10\,\dfrac{\mathrm m}{\mathrm s}+0-20\,\dfrac{\mathrm m}{\mathrm s}=-10\,\dfrac{\mathrm m}{\mathrm s}[/tex]

or 10 m/s south.

Given:

Time taken: 3.5 hrs

Speed: 120mi/HR

Now we know that

distance = speed x time

Substituting the given values in the above formula we get

Distance= 120mi/hr x 3 hrs

Distance = 360 mi= 579.36 Km

The speed is the distance covered by an object at a particular time. The distance between the Platform 9 and Hogwarts is 360 miles.

The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.

Speed = Distance Covered / Time taken

Given that it takes 3.5 hours for the Hogwarts Express, moving at a speed of 120 mi/hr, to make it from Platform 9 to Hogwarts. Therefore, we can write the given quantities as,

Speed of the Hogwarts Express = 120 miles per hour

Time taken = 3 hours

Now, the distance between the Platform 9 and Hogwarts can be written as,

Speed = Distance / Time

120 miles per hour = Distance / 3 hours

Distance = 120 miles per hour × 3 hours

Distance = 360 miles

Hence, the distance between the Platform 9 and Hogwarts is 360 miles.

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The lava flowed through low-lying valleys and over the smaller Cascade Mountain Range. As it reached the ocean shore, it sank down into the soft sediments, cooling and hardening into thick black basalt.

Hope I Helped

The volume of a cube is given by s^3. So the volume of this block is 3cm x 3cm x3 cm = 27 cm^3.

density = mass/volume =27 g / 27 cm^3 = 1 g/cm^3.

the answer is 1 g/cm^3. I hope this helps!

If we assume the acceleration that the sled undergoes is constant throughout its motion, then we have the average velocity [tex]\bar v[/tex] of the sled to be

[tex]\bar v=\dfrac{v_i+v_f}2=\dfrac{\Delta x}{23\,\mathrm s}[/tex]

where [tex]\Delta x[/tex] is the total displacement of the sled, and [tex]v_i[/tex] and [tex]v_f[/tex] are the sled's initial and final velocities, respectively. The sled eventually stops, so we take [tex]v_f=0[/tex] and solve for [tex]v_i[/tex]:

[tex]\dfrac{v_i}2=\dfrac{15\,\mathrm m}{23\,\mathrm s}\implies v_i=1.3\,\dfrac{\mathrm m}{\mathrm s}[/tex]

Now, take the sled's starting position to be the origin. The sled moves in one direction, which we take to be the positive direction. Then because it's slowing down, we expect its acceleration to be in the negative direction (and hence with negative sign). In particular, the sled's position [tex]x[/tex] at time [tex]t[/tex] is

[tex]x=x_i+v_it+\dfrac12at^2[/tex]

We have [tex]\Delta x=x-x_i=15\,\mathrm m[/tex], [tex]v_i=1.3\,\frac{\mathrm m}{\mathrm s}[/tex], and [tex]t=23\,\mathrm s[/tex], so we can solve for acceleration [tex]a[/tex]:

[tex]15\,\mathrm m=\left(1.3\,\dfrac{\mathrm m}{\mathrm s}\right)(23\,\mathrm s)+\dfrac12a(23\,\mathrm s)^2[/tex]

[tex]\implies a=-0.056\,\dfrac{\mathrm m}{\mathrm s^2}[/tex]

With a mass of [tex]m=52.5\,\mathrm{kg}[/tex], we find that the stopping force is

[tex]F=ma=-2.9\,\mathrm N[/tex]

which means the stopping force has magnitude [tex]2.4\,\mathrm N[/tex] in the negative direction (opposite the direction of the sled's initial velocity).

Let the directions are defined by vectors as following

East = + x direction

West = - x direction

North = + y direction

South = - y direction

upwards = + z direction

downwards = - z direction

So here we are given that it moves

1). 10 m East

2). 9 m South

3). 3 m North

4). 2 m down

So we can write it as

[tex]d_1 = 10 \hat i[/tex]

[tex]d_2 = 9 (-\hat j)[/tex]

[tex]d_3 = 3 \hat j[/tex]

[tex]d_4 = 2 (-\hat k)[/tex]

Now total displacement will be given as

[tex]d = d_1 + d_2 + d_3 +d_4[/tex]

[tex]d = 10 \hat i - 9 \hat j + 3 \hat j - 2 \hat k[/tex]

[tex]d = 10 \hat i - 6 \hat j - 2 \hat k[/tex]

now the magnitude of the displacement will be

[tex]d = \sqrt{10^2 + 6^2 + 2^2}[/tex]

[tex]d = 11.8 m[/tex]

so the magnitude of displacement will be 11.8 m

The magnitude of the mole's displacement from its original position is approximately 11.83 meters.

To find the magnitude of the mole's displacement, you can break down the motion into its components and use vector addition. Here's the step-by-step calculation:

1. The mole runs 10 meters due East, which we'll represent as +10 meters in the horizontal (X) direction.

2. Then, the mole runs 9 meters due South, which we'll represent as -9 meters in the vertical (Y) direction. This is because it's in the opposite direction of the positive Y-axis.

3. After that, the mole runs 3 meters due North, which we'll represent as +3 meters in the vertical (Y) direction.

4. Finally, the mole burrows 2 meters down a hole, which we'll represent as -2 meters in the depth (Z) direction. This is because it's in the opposite direction of the positive Z-axis.

Now, we can calculate the total displacement vector by adding the individual components:

Displacement in the X direction: 10 meters (East)

Displacement in the Y direction: (3 meters - 9 meters) = -6 meters (South)

Displacement in the Z direction: -2 meters (Down)

To find the magnitude of the displacement, we can use the Pythagorean theorem in three dimensions:

[tex]\[|D| = \sqrt{(Dx^2 + Dy^2 + Dz^2)}\][/tex]

[tex]\[|D| = \sqrt{(10^2 + (-6)^2 + (-2)^2)}\][/tex]

[tex]\[|D| = \sqrt{(100 + 36 + 4)}\][/tex]

[tex]\[|D| = \sqrt{140}\][/tex]

The magnitude of the mole's displacement from its original position is approximately 11.83 meters.

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m = mass of the bullet = 10 g = 10 x 10⁻³ kg = 0.01 kg       (since 1 g = 10⁻³ kg)

M = mass of pendulum = 2 kg

h = height to which pendulum rises = 12 cm = 0.12 m

V = velocity of the pendulum-bullet combination after collision = ?

Using conservation of energy

kinetic energy of the combination just after collision = Potential energy gained due to raise in height of the center of mass

(0.5) (m + M) V² = (m + M) gh

V = sqrt(2gh)

inserting the values

V = sqrt(2 x 9.8 x 0.12)

V = 1.5 m/s

v = velocity of the bullet before the collision

using conservation of momentum

momentum of bullet before collision = momentum of bullet-pendulum combination after collision

m v = (m + M) V

(0.01) v = (0.01 + 2) (1.5)

v = 301.5 m/s

hence initial speed of the bullet is 301.5 m/s

The initial speed of the bullet is calculated using the conservation of momentum and conservation of mechanical energy by equating the kinetic energy after collision with the potential energy at the pendulum's highest point and then using the momentum conservation to get the bullet's initial velocity.

To calculate the bullet's initial speed when it strikes a ballistic pendulum, we can use the principles of conservation of momentum and conservation of mechanical energy. First, we find the velocity of the bullet-pendulum system just after the collision using energy considerations. Since the bullet becomes embedded in the pendulum, this is an inelastic collision, and mechanical energy is not conserved during the collision. However, the system's mechanical energy is conserved as it swings upwards to its highest point.

As the pendulum rises to a height of 12 cm, all the kinetic energy of the system is converted into potential energy. The potential energy (PE) gained by the pendulum can be calculated using PE = mgh, where m is the total mass of the system (bullet plus pendulum), g is the acceleration due to gravity (9.81 m/s2), and h is the height (12 cm or 0.12 m). The kinetic energy (KE) just after the collision can be equated to this PE.

The total mass m after the bullet is embedded in the pendulum is (10 g + 2000 g). To find the velocity of the system after the collision, we can use the equation KE = 1/2 m v2 and solve for v. Then, by using the conservation of momentum, the initial velocity of the bullet u can be determined, since momentum before collision (bullet's momentum) is equal to the momentum after collision (system's momentum). The bullet's initial speed is found through the equation mu = (m + M)v, where M is the mass of the pendulum.

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Average velocity differs from average speed in that it considers displacement over elapsed time and has direction, while average speed is total distance over time without direction.

Average velocity is different than average speed because calculating average velocity involves taking into consideration not just the total distance traveled but the displacement (the change in position) of an object, and it is a vector quantity which means it has both magnitude and direction. On the other hand, average speed is simply the total distance traveled divided by the elapsed time and is a scalar quantity, which means it does not have a direction associated with it.

For example, if you were to drive to a store, then turn around and drive back home, making the starting and ending points the same, your displacement would be zero, therefore your average velocity would be zero. However, your average speed would be the total distance for the trip divided by the time taken to travel that distance. This illustrates that average speed can be greater than the magnitude of average velocity due to changes in direction.

To calculate average speed, one would use the formula: total distance traveled ÷ elapsed time. Meanwhile, average velocity is calculated using the formula: displacement ÷ travel time. Therefore, if you are only interested in how fast you are going regardless of the direction, you would look at average speed. But if you need to know your speed in a particular direction, you would consider average velocity.

D. Gravitational force.

Answer:

Gravitational force

Explanation:

When ball is placed on the slope and slightly disturbed then ball will roll down the slope with increasing speed.

This increasing speed or acceleration of ball is due to the component of weight of ball which is along the inclined plane.

As shown in the FBD the component of weight perpendicular to inclined plane is used to counterbalance the normal force while other component of weight parallel to the inclined plane is accelerating the ball down the plane

So here we can write

[tex]mgsin\theta = ma[/tex]

so here

[tex]a = gsin\theta[/tex]

so ball is accelerating due to gravitational force

The atomic emission spectra of a sodium atom on earth and of a sodium atom in the sun would be the same.

When atoms of sodium get excited they move to a higher level and when they move back to the ground level, they emit photons.

Thus the emitted energy of photon depends only on the atom of the sodium (element) and is independent of the atmosphere where it is .Since we are comparing the emission spectra of the same element sodium it is the same on both earth and sun.

v₀ = initial velocity of the car before brakes are applied

v = final velocity of the car after it comes to a stop = 0 mph

d = stopping distance

a = acceleration caused due to braking force

Using the kinematics equation

v² = v²₀ - 2 a d

0² =  v²₀ - 2 a d

d = v²₀ /(2a)

Since the acceleration is same , the stopping distance is directly proportional to the square of the initial speed of car before brakes are applied

hence

d₁/d₂ = v²₀₁/v²₀₂

Given that : v₀₁ = 60 mph   and v₀₂ = 15 mph

inserting the values

d₁/d₂ = (60)²/(15)²

d₁ = 16 d₂

hence distance increases by a factor of 16 times.

A car skidding from 60 mph will skid 16 times farther than a car from 15 mph because the kinetic energy is proportional to the square of the velocity, and the work done by friction to stop the car is equal to its initial kinetic energy.

The question asks how much farther a car will skid if it locks its brakes at 60 mph compared to a skid from 15 mph. When a car locks its brakes, the distance it skids before coming to a stop is directly related to the kinetic energy it had when the brakes were applied. Kinetic energy is given by the formula [tex]KE = \frac{1}{2}mv^2[/tex]. Because the kinetic energy depends on the square of the velocity, a car moving at 60 mph (which is four times faster than 15 mph) will have 16 times the kinetic energy ([tex]4^2[/tex]).

Assuming that the frictional force acting on the car is the same in both situations, we know that the work done by the frictional force to stop the car is equal to the car's initial kinetic energy. Hence, the car skidding from 60 mph will skid 16 times farther than the car skidding from 15 mph, because work is directly proportional to distance when force is constant (Work = Force × Distance). Therefore, the distance increases by a factor of 16 times.

The blank should be filled with the word 'technicians,' reflecting the need for specialized workers who possess practical technical skills to maintain and repair equipment as technology evolves.

Maintenance technicians are needed in great numbers to service all sorts of technical equipment. Technicians are those individuals who have the practical and technical knowledge to build, operate, maintain, and repair various kinds of equipment and machinery. This demand for technicians is a reflection of the growing complexity and proliferation of technology in contemporary society. As new technologies emerge, they often require different skills than those needed for older technologies, creating a need for continuous training and updating of skills among workers.

Moreover, significant infrastructure projects, such as the expansion of electrical transmission systems, will necessitate an increase in specialized workers, including technicians, to maintain and repair these systems efficiently. Preventive maintenance schedules and activities further highlight the essential role that technicians play in ensuring the smooth operation of various systems and equipment in industries as diverse as manufacturing, transportation, and housing.

If Voq doubles, abN gets multiplied by 16 .

If Voq=3, abN=81 .

If the value of VOq doubles, the magnitude of the restoring force doubles.

The formula for the restoring force of an abductin pad is:

F = k * x

where:

F is the restoring force

k is the spring constant

x is the distance the spring is compressed or stretched

In this case, we are told that VOq doubles. VOq is the spring constant. So, if VOq doubles, k doubles. This means that the restoring force doubles.

The restoring force is the force that pushes the shell open when the muscles relax. If the restoring force doubles, the shell will be pushed open with twice the force. This means that the shell will open more quickly and easily.

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