Is Your weight
determined by
gravity?

As you were holding the block down and in place, the spring exerted an upward force that balanced the downward push by your hand and its own weight. So this restoring force has a magnitude of R such that

R - 50 N - (3 kg) g = 0   =>   R = 79.4 N

As soon as you remove your hand, the block has acceleration a such that, by Newton's second law,

R - (3 kg) g = (3 kg) a   =>   a = (79.4 N - (3 kg) g) / (3 kg) ≈ 16.7 m/s^2

pointing upward.

Answer: Answer is below <3 (The underlined part is the answer)

Explanation: The reason why an object with a smaller mass has a larger acceleration than an object with a larger mass if the same force acts on each is because the acceleration of an object depends on its mass as well as the force exerted on it, and if the mass is smaller than the other object than it is faster.

The reason why a football accelerates faster than a soccer ball when the same amount of force is applied is because of the difference in their masses. The acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass. This means that the smaller the mass of an object, the greater the acceleration it experiences when the same amount of force is applied to it.

A football is typically smaller and lighter than a soccer ball, so when the same amount of force is applied to both balls, the football experiences a greater acceleration due to its lower mass. This is consistent with Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass.

Additionally, the surface area and shape of the balls can also affect their acceleration. A football is typically more aerodynamic with a pointed shape that reduces air resistance, allowing it to move through the air more easily and accelerate faster. In contrast, a soccer ball has a more spherical shape that can create more air resistance, slowing down its acceleration.

Therefore, the mass, shape, and surface area of the ball are all factors that can affect its acceleration when a force is applied.

The orbital speed of an ice cube in the rings of Saturn is 11.2 Km/s. The correct answer is option C

The speed of an object travelling around a circle depends on two quantities namely;

Given that  an ice cube in the rings of Saturn. The mass of Saturn is 5.68 x 10^26 kg, and use an orbital radius of 3.00 x 105 km. (G= 6.67 × 10-11 N·m2/kg2)

The given parameters are:

Let us first calculate the gravitational field strength on the Saturn.

g = GM/r²

Substitute all the necessary parameters and convert km to m

g = (6.67 × \(10^{-11}\) × 5.68 × \(10^{26}\)) ÷ (300000 × 1000)²

g = 3.79 × \(10^{16}\) ÷ 9 × \(10^{16}\)

g = 0.421 m/s²

The  orbital speed will be

V² = gr

V² = 0.4211 × 300000 × 1000

V² = 126333333.3

V = √126333333.3

V = 11239.8 m/s

Convert it to Km/s by dividing the answer by 1000

V = 11239.8/1000

V = 11.2 Km/s

Therefore, the orbital speed of an ice cube in the rings of Saturn is 11.2 Km/s

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Answer:

The apparent depth d = 19.8495 cm

Explanation:

The equation for apparent depth can be expressed as:

\(d = \dfrac{d_1} {\mu_1}+\dfrac {d_2}{\mu_2}\)

here;

\(d_1 = d_2 = 15 \ cm\)

\(\mu_1\) = refractive index in the first liquid = 1.75

\(\mu_2\) = refractive index in the second liqquid= 1.33

∴

\(d = \dfrac{15}{1.75}+\dfrac{15}{1.33}\)

\(d = 15( \dfrac{1}{1.75}+\dfrac{1}{1.33})\)

\(d = 15( 0.5714 +0.7519)\)

d = 15(1.3233 ) cm

d = 19.8495 cm

308.6 m the maximum height reached.

Define velocity

The main determinant of an object's location and rate of motion is its velocity. It can be explained as the distance an object travels in one measure of time. The displacement of the item in a given amount of time is referred to as velocity.

The distance a person travels in a predetermined amount of time is referred to as speed.

Vi is the starting speed.

Vf is final speed

A=acceleration and Y=displacement

When the bag is freed, its Vi equals that of a balloon traveling at 13 m/s upward.

At the moment of release, choose up as positive y=0.

Vf=0 when it is maximum. Using the equation 2Vf=2Vi+2ay,

0=(13m/s)2+2(9.81m/s2)y, and y=8.6m

300 + 8.6 = 308.6 m is the highest point.

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Answer:

1.4m/s

Explanation:

Average velocity is the total distance covered divided by the total time taken.

 Average velocity  = \(\frac{total distance }{time }\)  

 Total time taken  = 5s + 6s  = 11s

The first distance covered  = velocity x time  = 1.4 x 5 = 7m

     second distance covered  = velocity x time  = 1.4 x 6  = 8.4m

So;

  Average velocity  = \(\frac{7 + 8.4}{11}\)    = 1.4m/s

Vehicles need to be serviced for several reasons such as preventing costly repairs and improving fuel economy.

First, regular maintenance can help to prevent costly repairs down the road. Second, maintenance can help to improve fuel economy and emissions. Third, maintenance can help to keep your vehicle safe and reliable.

The servicing requirements for petrol/diesel and electric vehicles differ in a number of ways. Petrol/diesel vehicles require oil changes more frequently than electric vehicles. This is because petrol/diesel engines use oil to lubricate the moving parts, while electric motors do not. Petrol/diesel vehicles also require tune-ups more frequently than electric vehicles.

This is because petrol/diesel engines have more moving parts that need to be synchronized, while electric motors have fewer moving parts.

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A. The average speed you can use to pull the safe is 1.02 m/s

B. The time needed to pull the safe up is 17.65 s

First, we shall obtain the force. This is shown below:

F = mg

F = 60 × 9.8

F = 588 N

Finally, we shall obtain the average speed. Details below:

Power = force × average speed

600 = 588 × average speed

Divide both sides by 588

Average speed = 600 / 588

Average speed = 1.02 m/s

The time needed to pull the safe up can be obtained as follow:

Time = Total distance / average speed

Time = 18 / 1.02

Time = 17.65 s

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Complete question:

You know you can provide 600 W

of power to move large objects. You need to move a 60-kg

safe up to a storage loft, 18 m

above the floor.

Part A

With what average speed can you pull the safe straight up?

Part B

What is the time needed to pull the safe up?

The traffic cop needs 23.3 seconds to pass the automobile.

When your velocity (not speed) changes, you are accelerating. A automobile moving at a steady 100 km/h in a straight line has no acceleration. Average acceleration is equal to (change in velocity) / (duration). The car's acceleration is zero because its change in velocity is also zero.

\(d1 = v1*t1 = 35.0 m/s * 1 s = 35.0 m\)

\(d = d1 = 35.0 m\)

\(d2 = v2*t + (1/2)at^2\)

\(d2 = (1/2)at^2\)

\(v2*t + (1/2)at^2 = (1/2)at^2\)

\(v2*t = (1/2)at^2\)

Solving for t, we get:

\(t = (2v2/a) = (235.0 m/s)/3.0 m/s^2 = 23.3 s\) (rounded to 2 decimal places)

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Answer:

Explanation:

The torque is given by the formula:

τ = F × r × sin(θ)

where τ is the torque, F is the force applied, r is the distance between the force and the pivot point, and θ is the angle between the force and the lever arm.

In this case, the person's weight is the force being applied, and it can be calculated as:

F = m × g

where m is the mass of the person and g is the acceleration due to gravity (9.81 m/s^2).

F = 65 kg × 9.81 m/s^2 = 637.65 N

The distance between the person and the pivot point is 1.5 m, so r = 1.5 m.

The angle between the person's weight and the lever arm is 90 degrees, so sin(θ) = 1.

Therefore, the torque the person is exerting on the board is:

τ = F × r × sin(θ) = 637.65 N × 1.5 m × 1 = 956.475 N·m

So the person is exerting a torque of 956.475 N·m on the diving board with respect to the pivot point.

Alright. It is necessary to identify the variables. Time, grass height, and their connections are separate points. To put it another way, it is both growing and lowering the drop.

From 0 to 1.5 seconds, the object is moving in the positive direction with a constant velocity of 10 m/s with time t. The position graph is a straight line with a positive slope, the velocity graph is a straight line with a constant slope of 10 m/s, and the acceleration graph is a straight line with a slope of 0 m/s^2.

How is it conceivable when spring and summer would be becoming longer in the autumn.

The behavior of these variables will depend on the specific situation and the forces acting upon the object in question. For example, if an object is in free fall, its position "x" will decrease as it falls towards the ground, its velocity "vx" will increase, and its acceleration "ax" will be constant and equal to the acceleration due to gravity.

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The complete question is :

Now, for each time period, look at the graphs of x, vx, and ax. Briefly describe what is happening for each of these variables during your identified time periods. To view any of these graphs in detail, double-click the graph. You’ll be able to view it in the Data Tool window. The graph is attached below

The question examines the interpretation of physics graphs representing displacement (x), velocity (vx), and acceleration (ax). Displacement graphs display object's position changes, velocity graphs show the speed and direction of its movement, and acceleration graphs reflect changes in velocity.

The question is asking you to analyze graphs representing displacement (x), velocity (vx), and acceleration (ax). In general, the displacement graph (x) shows the object's position relative to a particular point over time. A slope in this graph indicates movement, while horizontal lines mean the object is stationary.

The velocity graph (vx) displays how fast and in what direction the object is moving. Positive values indicate movement in one direction, and negative values represent movement in the opposite direction. A horizontal line at zero on the velocity graph means the object is at rest.

Finally, the acceleration graph (ax) reveals how velocity is changing over time. A zero on this graph means a constant velocity, even if it isn't zero.

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Answer:

Explanation:

To find the resultant of two velocity vectors, we can use vector addition. Given two velocity vectors v1 and v2, their resultant vector vR can be found by adding the two vectors:

vR = v1 + v2

The angle that the resultant moves with the first vector can be found using trigonometry. If we let theta be the angle between v1 and vR, then we can use the following formula:

tan(theta) = (vR_y / vR_x)

where vR_x is the x-component of the resultant vector and vR_y is the y-component of the resultant vector.

Alternatively, we can use the dot product to find the angle between the two vectors. The dot product of two vectors is defined as:

v1 . v2 = |v1| |v2| cos(theta)

where |v1| and |v2| are the magnitudes of the vectors and theta is the angle between them. Solving for theta, we get:

theta = acos((v1 . v2) / (|v1| |v2|))

where acos is the inverse cosine function.

To summarize:

Find the resultant vector vR by adding the two velocity vectors v1 and v2: vR = v1 + v2

Find the angle theta between v1 and vR using either the tangent formula or the dot product formula:

a. tan(theta) = (vR_y / vR_x)

b. theta = acos((v1 . v2) / (|v1| |v2|))

Answer:

Torque

Explanation:

Torque is a physical quantity that measures the amount of force that acts on any object, and thereafter causing that object in question to rotate. Also, the torque can represent the amount of load an engine can handle in order to generate a particular amount of power, thereby making the engine to rotate.

.Torque is given mathematically as

T = F * r * sinθ, where

T = Torque in Nm

F = Force applied in N

r = radial distance in m

θ = angle turned as a result if the applied force

Answer:

a) 0.47MW

b) 39.24%

Explanation:

In order to find the power needed for the elevator to operate at its maximum capacity, we can make use of the following formula:

P=Fv

where P is the power, F is the force and v is the velocity.

The force the elevator must carry can be calculated with the following formula:

F=mg

where m is the mass of the elevator and g is the acceleration of gravity, so:

\(F=(8000 kg)(9.81 m/s^{2})\)

F=78 480 N

so now we can make use of the power formula:

P=Fv

P=(78 480N)(6 m/s)

P=470 880W

P=0.47W

b)

In order to find the efficiency, we will suppose that the generator can generate a maximum of 0.47 W so we use the following formula:

\(efficiency = \frac{P_{in}}{P_{out}}*100\%\)

\(efficiency=\frac{0.470880}{1.2}*100\%\)

efficiency=39.24%

When a Cellulose Acetate rod is rubbed with a woolen duster, friction occurs, rubbing loosely held electrons from the rod onto the duster. So, this time, the rod loses electrons. Since the Acetate rod now has fewer electrons than protons it has become positively charged. Hope this helps!

Answer:

The charge becomes positive.

Explanation:

When rubbed with cellulose acetate the charge of the fur/wool will become negative.

The tension of the second cable is  8310N

We are given the information that A weight of 5000 N is suspended by two cables. The object is at rest. The first cable is horizontal and the second makes an angle of 143 with the first cable. To find the value, we use the formula T2 = T1*cos(143°) + √T1^2-T2^2, where T1 is the tension in the first cable and T2 is the tension in the second cable. Since the object is at rest, the sum of the tensions in the two cables must equal the weight of the object, 5000N. Therefore, T1 = 5000N. We then substitute this value into the formula and solve for T2. This results in a value of 8310N for the tension in the second cable.

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Answer:3000

Explanation:

given:u=0v=20m/st= 8sec

thereforea=v-u/t=20-0/8=20/8=5/2 m/som=1200 kg

thereforef=ma=1200*5/2=600*5=3000N

The magnitude of the electric field along the positive z axis is kqz/√(z^2+a^2)^3/2 , the angular frequency of these oscillations is √(kqq0/ma^3)

1. Given that a uniformly charged ring in the xy plane, centered at the origin.

Radius of the ring(r) = a

positive charge distributed evenly along its circumference = q

k= 1/4piepsion

The electric field can be described as, E = kq/r^2

The force exerted on an electric charge by a charge is F = q0E

Any vector can be projected along the z = A(z)=Acosθ

We know that ∑F =ma

Acceleration along z axis = a =d^2z/dt^2

The equation of motion for a simple harmonic oscillation along z is d^2z/dt^2 = -ω^2z

Here,  ω is the cosine function in a right-angled triangle is cosθ = z/√(z^2+a^2)

dE(z)=dEcosθ we know that E = kq/z^2+a^2

To calculate the magnitude of the electric field caused by complete rings, integrate dE(z)=dEcosθ

E(z) = Ecosθ = kq/(z^2+a^2) x  z/√(z^2+a^2)

E(z) = kqz/(z^2+a^2)^3/2

2. We know that F= q0E = kqq0z/(z^2+a^2)^3/2

Given The ball will oscillate along the z axis between z=d and z=-d in simple harmonic motion. Let z =d

F = kqq0d/(d^2+a^2)^3/2 = kqq0d/a^3

Force at any point along z = - kqq0z/a^3

We know F = ma =  

- kqq0z/a^3 = md^2z/dt^2

d^2z/dt^2= - kqq0z/ma^3

This equation of motion can be compared with the equation of motion for simple harmonic motions to find the angular frequency.

ω =√(kqq0/ma^3)

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Answer:

(a) F1 = 7.19N

(b) F2 = 1.01N

Explanation:

You have the following two forces exerted to an object:

F1: larger force

F2: weaker force

When the forces are in the same direction, to the east, the acceleration of the object is 0.919 m/s^2.

You use the Newton second law to write the following equation:

\(F_1+F_2=ma\)           (1)

m: mass of the object = 8.93 kg

When the two forces are in opposite direction, one to the east and the other one to the west, you have the following equation (2):

\(F_1-F_2=ma'\)               (2)

a': acceleration = 0.693 m/s^2

Then, with both equations (1) and (2) you have a 2x2 systems of equation.

You can find the values of F1 and F2 by solving the 2x2 system.

First, you sum equation (1) and (2):

\(F_1+F_1+F_2-F_2=ma+ma'\\\\2F_1=m(a+a')\) (3)

You solve the equation (3) for F1:

\(F_1=\frac{m(a+a')}{2}=\frac{(8.93kg)(0.919m/s^2+0.693m/s^2)}{2}=7.19N\)

Next, you can replace the value of F1 into the equation (1) and you can obtain the value of F2:

\(F_2=ma-F_1\\\\F_2=(8.93kg)(0.919m/s^2)-7.19N=1.01N\)

Finally, you have:

(a) The values of the larger force is 7.19N

(b) The values of the weaker force is 1.01N

Explanation:

a boy walks at 2m/s for 30sec and run at 5m/s for 20sec. what is his average speed

An electromagnet consists of a conductive wire wrapped around a magnetic core, creating a magnetic field when an electrical current is passed through it.

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Answer:

A= v-u/t

= 8m/s - 18m/s ÷ 100s

= - 0.1m/s^2

Hope this helps!

42 times must he repeat this exercise to burn off the energy in one slice of pizza.

What is energy?

Energy is the ability or capability to do tasks, such as the ability to move an item (of a certain mass) by exerting force. Energy can exist in many different forms, including electrical, mechanical, chemical, thermal, or nuclear, and it can change its form.

Energy burn by the weightlifter = potential energy

Potential energy = mgh

Potential energy = 25.(9.8)(0.50)

Potential energy = 122.5 Joule.

Assume 25% of efficiency so energy burn = 122.5*25/100

energy burn = 30.625 joule

Number of times = 1260/30.625

Number of times = 42 times.

42 times must he repeat this exercise to burn off the energy in one slice of pizza.

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Answer:

Explanation:

Because we assume the pendulum is a "mathematical pendulum" (neglecting the moment of inertia of the bob), we can find:

\(T=2\pi\sqrt{\frac{L}{g}} \rightarrow 4=2\pi\sqrt{\frac{L}{9.81}} \rightarrow \frac{4}{\pi^{2}}=\frac{L}{9.81} \rightarrow L \approx 3.97 m\)

By using the \(y=A\sin(\omega t) \rightarrow v = \frac{dy}{dt}=\omega A \cos\omega t = \omega\sqrt{A^{2}-y^{2}}\)

The mean position is the position when y = 0, so:

\(\omega = \frac{2\pi}{T}=\frac{2\pi}{4}=0.5\pi\) rad/s

and \(v = \omega A \rightarrow A=\frac{40}{0.5\pi}=\frac{80}{\pi}\) in centimeters (cm).

A 66.1-kg boy is surfing and catches a wave which gives him an initial speed of 1.60 m/s. He then drops through a height of 1.59 m, and ends with a speed of 8.51 m/s. The nonconservative work done on the boy is approximately -42.7 kilojoules.

To find the nonconservative work done on the boy, we need to consider the change in the boy's mechanical energy during the process. Mechanical energy is the sum of the boy's kinetic energy (KE) and gravitational potential energy (PE).

The initial mechanical energy of the boy is given by the sum of his kinetic energy and potential energy when he catches the wave:

E_initial = KE_initial + PE_initial

The final mechanical energy of the boy is given by the sum of his kinetic energy and potential energy after he drops through the height:

E_final = KE_final + PE_final

The nonconservative work done on the boy is equal to the change in mechanical energy:

Work_nonconservative = E_final - E_initial

Let's calculate each term:

KE_initial = (1/2) * m * v_initial^2

= (1/2) * 66.1 kg * (1.60 m/s)^2

PE_initial = m * g * h_initial

= 66.1 kg * 9.8 m/s^2 * 1.59 m

KE_final = (1/2) * m * v_final^2

= (1/2) * 66.1 kg * (8.51 m/s)^2

PE_final = m * g * h_final

= 66.1 kg * 9.8 m/s^2 * 0

Since the boy ends at ground level, the final potential energy is zero.

Substituting the values into the equation for nonconservative work:

Work_nonconservative = (KE_final + PE_final) - (KE_initial + PE_initial)

Simplifying:

Work_nonconservative = KE_final - KE_initial - PE_initial

Calculating the values:

KE_initial = (1/2) * 66.1 kg * (1.60 m/s)^2

PE_initial = 66.1 kg * 9.8 m/s^2 * 1.59 m

KE_final = (1/2) * 66.1 kg * (8.51 m/s)^2

Substituting the values:

Work_nonconservative = [(1/2) * 66.1 kg * (8.51 m/s)^2] - [(1/2) * 66.1 kg * (1.60 m/s)^2 - 66.1 kg * 9.8 m/s^2 * 1.59 m]

Calculating the result:

Work_nonconservative ≈ -42.7 kJ

Therefore, the nonconservative work done on the boy is approximately -42.7 kilojoules. The negative sign indicates that work is done on the boy, meaning that energy is transferred away from the boy during the process.

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Answer:

potential lines that are perpendicular to the electric field, they must be parallel to the plates

Explanation:

A and C) for this drawing, as the electric field lines go from the positive plate to the negative plate and are horizontal to the potential lines that are perpendicular to the field, they must be parallel to the plates, see attached part a

B) in this case the ground has an energy of zero and the lines are parallel to the ground, see attached part b