The velocity of the roller coaster at location 4 is 14.14 m/s (approx) using the given values of v₁ = 10 m/s, h₁ = 30 m, and h₂ = 15 m.
Roller coasters are fascinating machines that deliver an exhilarating experience by defying gravity and physics. Roller coaster physics is a significant concept to comprehend before riding a roller coaster or designing one. The laws of physics govern the motion of a roller coaster, including its velocity, acceleration, and potential energy.
A roller coaster moves over a crest at location 1 with a speed of 10 m/s. The question is how fast it's going at location 4, considering the neglect of friction and air resistance. To solve this, we'll need to consider the conservation of energy law.
The total energy of the roller coaster remains constant throughout the ride, and we can convert between potential and kinetic energy.Using the conservation of energy formula, which is: E1 = E2Where E1 is the total energy of the roller coaster at the crest and E2 is the total energy of the roller coaster at location 4.
Both E1 and E2 comprise kinetic energy (KE) and potential energy (PE). So,E1 = KE1 + PE1E2 = KE2 + PE2Since the roller coaster has no friction and air resistance, we can assume that PE1 = PE2 because the height of the roller coaster doesn't change. The energy is converted from potential energy at the crest to kinetic energy at location 4.
We can now use the formula for kinetic energy:KE = (1/2) mv²Where m is the mass of the roller coaster and v is its velocity. Both E1 and E2 can be written in terms of KE, so: E1 = (1/2) mv₁²E2 = (1/2) mv₂².
Substitute the values into the conservation of energy formula: E1 = E2(1/2) mv₁² = (1/2) mv₂²
Simplifying the equation gives:v₂² = v₁²×(h₁ / h₂)
where h₁ is the height of the crest and h₂ is the height of location 4.
To calculate the velocity, we need to take the square root of both sides:v₂ = v₁×√(h₁ / h₂)
Therefore, the velocity of the roller coaster at location 4 is 14.14 m/s (approx) using the given values of v₁ = 10 m/s, h₁ = 30 m, and h₂ = 15 m.
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A 66 kg driver gets into an empty taptap to start the day's work. The springs compress 2.3×10−2 m
. What is the effective spring constant of the spring system in the taptap?
Enter the spring constant numerically in newtons per meter using two significant figures
Explanation:
You want N/m
N = 66 * 9.81
m = 2.3 x 10^-2 m
66* 9.81 / 2.3 x 10^-2 = 28150 = 28 000 N/m to two S D
Question 1
At one section of a long pipe the velocity of the fluid is 1.6 m/s. At another section of the pipe the diameter is three times greater.
What is the velocity of the fluid at this section?
O 0.533 m/s
○ 4.80 m/s
O Not enough information to tell
O 0.178 m/s
Question 2
Three thermometers are placed in a closed, insulated box and are allowed to reach thermal equilibrium. One is calibrated in
Fahrenheit degrees, one in Celsius degrees, and one in Kelvins. If the Celsius thermometer reads -40 °C the Fahrenheit
thermometer would read -40°F.
True
False
Answer:
Answer 1: The answer is O 0.178 m/s.
Answer 2: True: But in this specific case where the Celsius temperature is -40, the Fahrenheit temperature will also be -40.
So, in short, the answer is:
-40 Celsius is equal to -40 Fahrenheit
The work of forensic engineers who investigate fires _____. identifies what started the fire and where it stated identifies what started the fire and where it stated does not consider explosions does not consider explosions is relatively simple is relatively simple is usually done by the firefighting team
The work of forensic engineers who investigate fires involves identifying what started the fire and where it originated, and it does not solely focus on explosions. This process is not relatively simple and is typically conducted by specialized forensic teams rather than firefighting personnel.
Forensic engineers play a crucial role in investigating fires to determine their cause and origin. Their primary objective is to gather evidence and analyze it in order to understand the circumstances surrounding the fire incident.
1. Scene Assessment: Forensic engineers begin by assessing the fire scene. They examine the area to gather initial information about the fire's intensity, pattern, and potential sources.
2. Evidence Collection: Next, the investigators collect physical evidence from the fire scene. This may involve gathering debris, examining burn patterns, and documenting any signs of accelerants or other substances that could have contributed to the fire.
3. Documentation: Forensic engineers meticulously document their findings through photographs, sketches, and written notes. This documentation serves as a crucial reference throughout the investigation process.
4. Laboratory Analysis: Collected evidence is then analyzed in specialized laboratories. Forensic experts employ various techniques such as chemical analysis, microscopy, and other scientific methods to determine the cause of the fire.
5. Report Preparation: Once the analysis is complete, forensic engineers prepare detailed reports outlining their findings. These reports serve as valuable resources for insurance companies, legal proceedings, and future fire prevention efforts.
It is important to note that the work of forensic engineers primarily focuses on identifying the cause and origin of the fire. While they consider various possibilities, including explosions, their investigation is not limited to solely investigating explosions.
Moreover, the process of investigating fires is complex and requires specialized knowledge and expertise. It is typically carried out by dedicated forensic teams rather than the firefighting personnel.
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If you feel pain during weight training, what should you do?
Answer:
Explanation:
Stop. Take a 5-10 minute breather, stretch out like you're doing your pre-workout (warmups). Drink some water, lay down for 3 minutes.
Answer: I hope this helps you
Explanation:
If you experience pain during weight training, it’s important to stop the exercise immediately and assess the source of the pain. If the pain is localized and mild, you can try taking a short break and then continuing with a lighter weight or modified exercise. However, if the pain is severe or spreading, you should stop the workout altogether and seek medical attention as soon as possible. Remember to always listen to your body and use proper form and technique to prevent injury.
Suppose a distant world with surface gravity of 6.32 m/s^2 has an atmospheric pressure of 9.00 ✕ 10^4 Pa at the surface. Answer parts a-c.
The Force ≈ [tex]1.13 * 10^6 N[/tex]
The Weight ≈ [tex]1.66 * 10^5 N[/tex]
Pressure ≈ 6.32 × 10⁴Pa
How to solve for the force(a)
Force = Pressure × Area
Force = (9.00 × 10⁴ Pa) × (π × (2.00 m)²)
Force ≈ [tex]1.13 * 10^6 N[/tex]
(b)
Weight = Density × Volume × g
Weight = (415 kg/m³) × (π × (2.00 m)² × 10.0 m) × (6.32 m/s²)
Weight ≈ 1.66 × 10⁵ N
(c)
Pressure = Pressure at the surface + Density × g × depth
Pressure = [tex](9.00 * 10^4 Pa) + (415 kg/m^3)* (6.32 m/^2)* (10.0 m)[/tex]
Pressure ≈ 6.32 × 10⁴Pa
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What must be your car's average speed in order to travel 225 km in 3.35 h ?
Explanation:
Rate X Time = Distance
Distance / Time = Rate
225 km / 3.35 hr = 67.2 km/hr
The temperature of a aluminum bar rises by 10.0°C when it absorbs 4.73 kJ of energy by heat. The mass of the bar is 525 g. Determine the specific heat of aluminum from these data. Answer is in kJ/kg · °C.
Answer:
Certainly! We can use the formula:
q = mcΔT
where q is the amount of heat absorbed, m is the mass of the aluminum bar, c is the specific heat capacity of aluminum, and ΔT is the change in temperature.
Substituting the given values, we get:
4.73 kJ = (0.525 kg) x c x (10.0°C)
Solving for c, we get:
c = 0.901 kJ/kg · °C
Therefore, the specific heat of aluminum is 0.901 kJ/kg · °C.
Explanation:
27/13 AL + 4/2 He -> ? + 1/On
Please help!!!!!! What’s the missing species???
The missing species of the nuclear reaction obtained is ³⁰₁₅P
How do i determine the missing species?The missing species of the equation can be obtain as follow:
Let the missing species be ʸₓZNow, we can obtain the value of x, y and Z as follow:
²⁷₁₃Al + ⁴₂He -> ʸₓZ + ¹₀n
For x
13 + 2 = x + 0
15 = x
x = 15
For y
27 + 4 = y + 1
31 = y + 1
Collect like terms
y = 31 - 1
y = 30
For Z
ʸₓZ => ³⁰₁₅Z
From the period table, the element with atomic number of 15 is phosphorus, P. Thus, we have
ʸₓZ => ³⁰₁₅Z => ³⁰₁₅P
Therefore, we can write the complete equation as:
²⁷₁₃Al + ⁴₂He -> ³⁰₁₅P + ¹₀n
Thus, the missing species is ³⁰₁₅P
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At time t = 0, a vessel contains a mixture of 14 kg of water and an unknown mass of ice in equilibrium at 0°C. The temperature of the mixture is measured over a period of an hour, with the following results: During the first 45 min, the mixture remains at 0°C; from 45 min to 60 min, the temperature increases steadily from 0°C to 2.0°C. Neglecting the heat capacity of the vessel, determine the mass of ice that was initially placed in the vessel. Assume a constant power input to the container. Answer is in kg.
The mass of ice that was initially placed in the vessel of neglected heat capacity was found to be 1.135 kg.
Given that,
Mass of water = 14 kg
Mass of ice = m kg
P = Power of the burner = dQ/dt
Rate of the heat given by the burner is constant.
In the first 45 min,
dQ/dt = mL/t1 = m x (80 x 4.2 x 10³)/45 min. (1)
From 45 to 60 min,
dQ/dt = (m+14) x δ(Η₂Ο) x Δθ / t2 =(m+14) x (4.2 x 10³) x 2/ 15 min. (2)
From (1) and (2)
m x (80 x 4.2 x 10³)/45 min = (m+14) x (4.2 x 10³) x 2/ 15 min
80m/3 = (m+14) x 2
80m = 6m + 84
m = 1.135 kg
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A satellite weighing 5,400 kg is launched into orbit 3.6400 x 107 m above the center of the earth.
The mass of Earth is 6.0 × 1024 kg. The gravitational constant is 6.673 × 10–11 N•m2/kg2.
The gravitational force of Earth on the satellite is ___
Group of answer choices
9.1 x 10^4
1.6 x 10^3
2.1 x 10^6
Answer:
[tex]\tt F=1.63*10^3 N[/tex]
Explanation:
Gravitational force is defined as the force of attraction between two objects with mass. It is a fundamental force of nature, and it is what keeps us on the ground and what keeps the planets in orbit around the Sun.
The gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers
For the Question:
We can use the following formula to calculate the gravitational force between the Earth and the satellite:
[tex]\boxed{\tt F =\frac{ G * M * m }{ r^2}}[/tex]
Where:
F is the gravitational force
G is the gravitational constant[tex]\tt (6.673 * 10^{-11} Nm^2/kg^2)[/tex]
M is the mass of the Earth [tex]\tt (6.0 * 10^24 kg)[/tex]
m is the mass of the satellite[tex]\tt (5,400 kg)[/tex]
r is the distance between the satellite and the center of the Earth [tex]\tt (3.6400 * 10^7 m)[/tex]
Plugging in these values, we get the following:
[tex]\tt F = \frac{6.673 * 10^{-11} * 6.0 * 10^{24}* 5,400 }{ (3.6400 * 10^7 )^2}[/tex]
[tex]\tt F=1.63*10^3 N[/tex]
Therefore, answer is [tex]\tt F=1.63*10^3 N[/tex]
what impact does liberal arts have on ensuring continued innovation
Answer:
Liberal arts education is important for ensuring continued innovation. It helps students think creatively, solve problems, collaborate effectively, and consider ethical factors. By exploring various subjects and adapting to new situations, liberal arts education equips individuals with the skills needed to generate new ideas and drive progress in different fields.
Chapter 3
#1) State Kepler's three laws in your own words.
#2) Write out Newton's three laws of motion in terms of what happens with the momentum of objects.
3) According to Kepler's second law, where in a planet's orbit would it be moving the fastest?
Where would it be moving the slowest?
#4) The gas pedal, the brakes, and the steering wheel all have the ability to accelerate a car- how?
#5) Explain how a rocket can propel itself using Newton's third law.
#6) A certain material has a mass of 565 g while occupying 50 cm³3 of space. What is this material?
(Hint, Use Table 3.1)
#7) What was the great insight Newton had regarding Earth's gravity that allowed him to develop the
universal law of gravitation?
Kepler's three laws are:
Law 1: Planets move in oval-shaped paths around the Sun, and the Sun is at one of the special points inside this oval shape.Law 2: When a planet gets closer to the Sun, it moves faster. When it gets farther away, it moves slower.Law 3: When a planet takes longer to orbit the Sun, its average distance from the Sun increases.What is Newton's three laws of motionThe Newton's three laws of motion is one that how momentum works.
Law 1: If an object is not moving, it will stay still, and if it is moving, it will keep moving in the same way unless something outside of it makes it stop or change direction.
Law 2: When you push or pull on an object, the object's momentum changes. The faster you push or pull, the more the momentum changes.
Law 3: When you push or pull something, it pushes or pulls back with the same amount of force.
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A liquid ( = 1.65 g/cm^3) flows through a horizontal pipe of varying cross section as in the figure below. In the first section, the cross-sectional area is 10.0 cm^2, the flow speed is 293 cm/s, and the pressure is 1.20 * 10^5 Pa. In the second section, the cross-sectional area is 3.00 cm^2. Answer parts a-b.
Answer:
a) What is the flow speed in the second section? Assume the pressure remains constant.
Given:
Section 1 area = 10.0 cm^2
Section 1 flow speed = 293 cm/s
Section 2 area = 3.00 cm^2
Pressure = 1.20 x 105 Pa (constant)
Since pressure remains constant, by Bernoulli's equation:
P1/ρ + 1/2*v12 = P2/ρ+ 1/2*v22
Since P1 = P2 and ρ (density) is constant:
v22 = 2*(v12 - v22)
v22 = 2*(293^2 - v22)
Solving for v2:
v2 = √(2*293^2) = 846 cm/s
b) What is the kinetic energy loss per second between the two sections?
Kinetic energy = 1/2 * mass * velocity^2
Mass flow rate = density * area * velocity
= 1.65 g/cm^3 * 10.0 cm^2 * 293 cm/s = 485.5 g/s
Kinetic energy loss = 1/2 * (485.5 g/s) * (293^2 - 846^2) cm^2/s^2
= 1/2 * (485.5)*(86124 - 716256)
= 20617 J/s
So the kinetic energy loss per second between the two pipe sections is 20617 J/s.
Explanation:
A simple harmonic oscillator (SHO) has a spring constant of 280 N/m, Total energy of 150 J, and a mass of 4.00 kg. What is its
maximum velocity?
Numerical answer is in units of m/s
The maximum velocity is 8.66 m/s²
As we know, simple harmonic motion refers to a to-and-fro motion in a periodic manner and spring constant refers to the force required to stretch or compress a spring.
The spring constant for a simple harmonic oscillator is given as 280 N/m, the total energy is 150 J and the mass is 4 kgs. We have to find the maximum velocity of the given simple harmonic motion.
We know that Energy = force x perpendicular distance
In an SHM, energy is in the form of Kinetic Energy. Hence, we use the formula for kinetic energy.
To find the maximum velocity, we will apply the formula for kinetic energy.
Since Kinetic Energy = 1/2 mass x velocity²
Therefore, 150 = 1/2 mass x velocity² ; velocity = 8.66 m/s²
Hence, the maximum velocity for the given system of SHM is 8.66 m/s²
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A steam turbine receives steam with a velocity of 28 m/s, specific enthalpy 3000 kJ/kg at a rate of 3500 kg per hour. The steam leaves the turbine with a specific enthalpy of 2200 kJ/kg at 180 m/s. Calculate the turbine output, neglecting losses.
A steam turbine receives steam with a velocity of 28 m/s, specific enthalpy 3000kJ/kg at a rate of 3500 kg per hour. The steam leaves the turbine with a specific enthalpy of 2200kJ/kg at 180 m/s then turbine output is 777.76kW.
To get the turbine output, we must first compute the change in specific enthalpy (h) and mass flow rate ().
Assume that the inlet steam velocity (v1) is 28 m/s.
Specific enthalpy at the inlet (h1) = 3000 kJ/kg
()=3500kg/h mass flow rate
2200 kJ/kg outlet specific enthalpy (h2)
v2 (outlet steam velocity) = 180 m/s
To begin, convert the mass flow rate from kg/h to kg/s as follows: =
[tex]3500 kg/h (1 h/3600 s) = 0.9722 kg/s[/tex]
The change in specific enthalpy (h) can then be calculated:
3000kJ/kg-2200kJ/kg=800kJ/kgh=h1-h2
The following formula can be used to compute the turbine output (P):
[tex]P = ṁ * Δh[/tex]
Substituting P=0.9722kg/s*800kJ/kg=777.76kJ/sork W
As a result, ignoring losses, the turbine output is roughly 777.76kW
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Joe is painting the floor of his basement using a paint roller. The roller has a mass of 2.4 kg and a radius of 3.8 cm. In rolling the roller across the floor, Joe applies a force F = 16 N directed at an angle of 35° as shown. Ignoring the mass of the roller handle, what is the magnitude of the angular acceleration of the roller?
The magnitude of the angular acceleration of the roller is approximately 108.8 rad/s².
To find the magnitude of the angular acceleration of the roller, we can use the rotational analog of Newton's second law: τ = Iα, where τ is the torque, I is the moment of inertia, and α is the angular acceleration.
First, let's calculate the moment of inertia of the roller. The moment of inertia of a solid cylinder rotating about its central axis is given by the formula: I = (1/2)mr², where m is the mass and r is the radius.
Given:
Mass of the roller (m) = 2.4 kg
Radius of the roller (r) = 3.8 cm = 0.038 m
Moment of inertia (I) = (1/2) * 2.4 kg * (0.038 m)² = 0.0021744 kg·m²
Next, we need to calculate the torque (τ) applied to the roller. Torque is given by the formula: τ = rFsin(θ), where r is the distance from the axis of rotation to the point of application of the force, F is the magnitude of the force, and θ is the angle between the force and the line connecting the axis of rotation and the point of application.
Given:
Force applied (F) = 16 N
Angle (θ) = 35°
Distance from the axis of rotation to the point of application (r) is equal to the radius of the roller, so r = 0.038 m.
Torque (τ) = (0.038 m) * (16 N) * sin(35°) = 0.2366 N·m
Now, we can use the equation τ = Iα and solve for the angular acceleration (α):
0.2366 N·m = (0.0021744 kg·m²) * α
α = 0.2366 N·m / 0.0021744 kg·m² ≈ 108.8 rad/s²
Therefore, the magnitude of the angular acceleration of the roller is approximately 108.8 rad/s².
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Is there a difference between shapes when plotting Uniform acceleration towards (+)directtion,Uniform acceleration towards (-)direction, Uniform deceleration towards (+) direction and Uniform deceleration towards (-) direction in displacement time graph.Can you draw the shapes for each type ?
Explanation:
Yes, there are differences in the shapes of position-time graphs for uniform acceleration and uniform deceleration in different directions. Let's consider each case separately:[tex]\hrulefill[/tex]
(1) - Uniform acceleration towards the positive direction:
In this case, the object is moving in the positive direction with a constant acceleration. The displacement-time graph will typically be a curve that starts from an initial position and shows a steady increase in displacement over time. The shape of the graph will depend on the specific acceleration value.
(2) - Uniform acceleration towards the negative direction:
In this case, the object is moving in the negative direction with a constant acceleration. The displacement-time graph will also be a curve, but it will show a steady decrease in displacement over time.
(3) - Uniform deceleration towards the positive direction:
In this case, the object is initially moving in the positive direction but is slowing down with a constant deceleration. The displacement-time graph will be a curve that starts with a positive slope and gradually levels off.
(4) - Uniform deceleration towards the negative direction:
In this case, the object is initially moving in the negative direction but is slowing down with a constant deceleration. The displacement-time graph will be a curve that starts with a negative slope and gradually levels off.
a thin, very light wire is wrapped around a drum that is free to rotate, the free end of the wire is attached to a ball of mass m, the drum is initially a solid disk with a mass M and radius R. you let the mass go at height h above the ground. if you switch out the solid disk and use a hollow disk instead with the same mass and radius, how will the final speed when the mass hits the ground when using a hollow disk compare to the final speed when using a solid disk?
a-greater than the original
b-less than the original
c-cant be determined
d-same as the original
Answer:
a-greater than the original (solid disk)
Explanation:
The hollow drum's lower rotational inertia allows it to rotate faster as the wire unwinds. This absorbs more potential energy, leaving less to translate into the speed of the falling mass. Therefore, the final speed when using a hollow disk will be:
a-greater than the original (solid disk)
Shannon and Chris push on blocks with identical force. SHannon's block is twice as massive as Chris'. After pushing for 5 seconds, who did more work?
. A 0.140 kg baseball is pitched toward home plate at 30.0 m/s.
The batter hits the ball back (opposite direction) to the pitcher at
44.0 m/s. Assume that towards home plate is positive. What is
the change in momentum for the ball?
The change in momentum for the baseball, which is hit back in the opposite direction by the batter, is -10.36 kg·m/s. This change in momentum is obtained by subtracting the initial momentum of 4.2 kg·m/s from the final momentum of -6.16 kg·m/s. The negative sign indicates the opposite direction of the momentum.
To find the change in momentum for the baseball, we can use the formula:
Change in momentum = Final momentum - Initial momentum
Momentum is defined as the product of mass and velocity.
Given data:
Mass of the baseball (m) = 0.140 kg
Initial velocity of the baseball ([tex]v_i_n_i_t_i_a_l)[/tex] = 30.0 m/s
Final velocity of the baseball ([tex]v_f_i_n_a_l_[/tex]) = -44.0 m/s (negative sign indicates opposite direction)
To calculate the initial momentum, we multiply the mass by the initial velocity:
Initial momentum = m * [tex]v_i_n_i_t_i_a_l[/tex] = 0.140 kg * 30.0 m/s = 4.2 kg·m/s
To calculate the final momentum, we multiply the mass by the final velocity:
Final momentum = m * [tex]v_f_i_n_a_l_[/tex] = 0.140 kg * (-44.0 m/s) = -6.16 kg·m/s
Now we can find the change in momentum:
Change in momentum = Final momentum - Initial momentum
Change in momentum = (-6.16 kg·m/s) - (4.2 kg·m/s)
Change in momentum = -10.36 kg·m/s
Therefore, the change in momentum for the baseball is -10.36 kg·m/s. The negative sign indicates a change in direction, as the ball is hit back in the opposite direction.
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What is Moral subjectivism?
Answer:
What Is Moral Subjectivism? Moral subjectivism is based on an individual person's perspective of what is right or wrong. An individual can decide for themselves that they approve or disapprove of a certain behavior, and that is what determines if the behavior is right or wrong.
What is indicated by the following displacement time graph ?
Answer:
The object in motion is deaccelerating in the negative direction.
Explanation:
Interpret the given position-time graph.
Observing the graph we can determine the slope is negative and is gradually flattening out. Thus, we can conclude the object in motion is deaccelerating in the negative direction.
A fish is swimming in the ocean at a depth with 14 atm of absolute pressure. If the fish swims up towards the surface, to a depth
that is now one third where it started, what is the gauge pressure at this depth?
4.67 atm
O 5.67 atm
3.67 atm
1.25 pts
O 4.33 atm
The gauge pressure at the new depth is determined as 3.67 atm.
What is the gauge pressure?The gauge pressure at the new depth is calculated by applying the following formula.
The absolute pressure at the new depth is;
abs P = (1/3) x 14 atm
abs P = 4.67 atm
The gauge pressure at the new depth is calculated as;
Gauge pressure = Absolute pressure at the new depth - Atmospheric pressure
G P = 4.67 atm - 1 atm
G P = 3.67 atm
Therefore, the gauge pressure at the new depth is 3.67 atm.
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workers of 50kg on the left and 40kg on the right on a 40kg plate held by two taut cables.
-The system does not rotate or move. With this in mind make a force diagram: it must have 5 forces labeled
-Write the net force equation
-Write the net torque equation,
Which cable exerts more tension, left or right? Explain why (2pts)
Find the tension of both wires. (3pts)
(a) The force diagram is the image attached.
(b) The net force of the workers is F(net) = (T₁ + T₂) - (W₁ + W₂ + W₃).
(c) The net torque equation of the system is W₁(x/2) - W₂(x/2) = 0
(d) The cable that exerts the most tension is the tension on the left.
(e) The tension in wire 1 is 490 N and the tension in wire 2 is 392 N.
What is the net force of the workers?The net force of the workers is calculated by applying the following equations;
F(net) = (T₁ + T₂) - (W₁ + W₂ + W₃)
The net torque equation of the system is determined as follows;
τ (net) = W₁(x/2) - W₂(x/2) = 0
W₁(x/2) - W₂(x/2) = 0
where;
x is the distance between the two workersThe cable that exerts the most tension is the tension on the left directly above the 50 kg worker because this work has the greatest downward force.
The tension in wire 1 is calculated as;
T₁ = 50 kg x 9.8 m/s²
T₁ = 490 N
The tension in wire 2 is calculated as;
T₂ = 40 kg x 9.8 m/s²
T₂ = 392 N
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The gravitational force exerted on a solid object is 5.05 N as measured when the object is suspended from a spring scale as in Figure a. When the suspended object is submerged in water, the scale reads 3.88 N (Figure b). Find the density of the object. Answer is in kg/m^3.
Answer:
Here are the steps to solve this problem:
Determine the weight of the object in air:
F = ma
Weight (W) = Force (F) x gravitational field strength (g)
W = 5.05 N x 9.8 m/s^2 = 49.5 N
Determine the weight of the object submerged in water:
W' = 3.88 N x 9.8 m/s^2 = 38.0 N
The difference in weight is due to buoyant force:
Fb = Wa - W
Fb = 38.0 N - 49.5 N = 11.5 N
The buoyant force is equal to the weight of the water displaced:
Fb = ρwVg (where ρw is the density of water and V is the volume)
11.5 N = (ρwV)(9.8 m/s^2)
Solve for the volume and density of the object:
V = Fb/( ρwg) = 11.5 N/(1000 kg/m^3)(9.8m/s^2)
= 1.17 x 10^-3 m3
Density of object = mass/volume
ρ = W/V = 49.5 N/(1.17 x 10^-3 m3)
= 4.22 x 104 kg/m3
= 4220 kg/m3
So the density of the object is 4220 kg/m3.
In summary, by using Newton's second law, Archimedes' principle and definitions of weight, buoyant force and density, we were able to determine the density of the object based on measurements in air and water.
Explanation:
A roller coaster, travelling with an initial speed of 15 meters per second, decelerates uniformly at -7.0 meters per second squared to a full stop. Approximately how far does the roller coaster travel during its deceleration
The distance traveled by the rollercoaster during the deceleration is 16.1 m.
What is the distance travelled by the roller coaster?The distance traveled by the rollercoaster during the deceleration is calculated by applying the following formula.
v² = u² + 2as
where;
v is the final velocity of the rollercoasteru is the initial velocity of the rollercoastera is the acceleration of the rollercoasters is the distance traveled by the rollercoasterWhen the rollercoaster stops, the final velocity, v = 0
0 = u² + 2as
-2as = u²
s = u² / -2a
s = (15 m/s) ² / (-2 x - 7 m/s²)
s = 225 / 14
s = 16.1 m
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A 73-g ice cube at 0°C is heated until 65.1 g has become water at 100°C and 7.9 g has become steam at 100°C. How much energy was added to accomplish the transformation? Answer is in kJ.
1.5 A man with a mass of 90,6 kg walks to the back of a train at a velocity of 1m/s while the train moves at a constant velocity of 36 km/h in a easterly direction 1.5.1 The weight of the man 1.5.2 The velocity of the train in m/s 1.5.3 The resultant velocity of the man 1.5.4 The distance the train has travelled in ten (10) minutes (1) (1) (2) (2)
The weight of the man is approximately 888.6 Newtons.
The velocity of the train is approximately 10 m/s.
The resultant velocity of the man is 11 m/s.
The train has traveled a distance of 6000 meters in ten (10) minutes.
To solve this problem1.5.1 The weight of the man can be calculated using the formula:
Weight = mass * acceleration due to gravity
Given:
Mass of the man (m) = 90.6 kg
Acceleration due to gravity (g) ≈ 9.8 m/s²
Weight of the man = 90.6 kg * 9.8 m/s² ≈ 888.6 N
Therefore, the weight of the man is approximately 888.6 Newtons.
1.5.2 The velocity of the train in m/s can be converted from its given velocity in km/h. Since 1 km/h is equal to 1000/3600 m/s, we can calculate:
Velocity of the train (v) = 36 km/h * (1000/3600) m/s ≈ 10 m/s
Therefore, the velocity of the train is approximately 10 m/s.
1.5.3 By taking into account the relative motion of the man and the train, it is possible to determine the man's final velocity. The resultant velocity will equal the vector sum of the man's walking velocity and the train's velocity because the man is traveling toward the rear of the train, which is moving eastward.
Given:
Velocity of the man relative to the train (v_man) = 1 m/s (backwards)
Resultant velocity of the man (v_resultant) = v_man + v_train
v_resultant = 1 m/s + 10 m/s = 11 m/s
Therefore, the resultant velocity of the man is 11 m/s.
1.5.4 The distance the train has traveled in ten (10) minutes can be calculated using the formula:
Distance = velocity * time
Given:
Time (t) = 10 minutes = 10 * 60 seconds = 600 seconds
Velocity of the train (v) = 10 m/s
Distance = 10 m/s * 600 seconds = 6000 meters
Therefore, the train has traveled a distance of 6000 meters in ten (10) minutes.
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A small ferryboat is 4.50 m wide and 6.70 m long. When a loaded truck pulls onto it, the boat sinks an additional 4.70 cm into the river. What is the weight of the truck? Answer is in kN.
Explanation:
Volume of water displaced = 4.5 m x 6.7 m x .047 m = 1.417 m3
mass of displaced water =
1.417 m3 x 1000kg / m3 = 1417 kg = 13900 N = 13.9 kN
The diagram below shows snapshots of an oscillator at different times . What is the frequency of the oscillation ?
In the diagram tha shows snapshots of an oscillator at different times, the frequency of the oscillation is 0.555 Hz.
How to calculate the periodThe period of the oscillation is the time taken for the for the object to return to its original position. (ie. Displacement = 0). From the above snapshot,
Period of oscillation = 1.80s.
From here, finding the frequency is simple as, Frequency = 1/Period. Hence,
Frequency = 1/1.80
= 0.555 Hz (3 sf).
The frequency of the oscillation is indeed 0.555 Hz. The frequency represents the number of oscillations or cycles per second. In this case, the object completes approximately 0.555 oscillations per second.
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