Answer: Positive Talk
Explanation:
At its maximum speed, a typical snail moves about 4.0 m in 5.0 min.
What is the average speed of the snail?
Answer:
Explanation:
Given
Distance = 4.0m
Time = 5.0 mins = 300secs
Required
Average speed
Average speed = Distance/Time
Average speed = 4.0/300
Average speed = 0.01333m/secs
Hence the average speed of the snail is 0.01333m/s
An object of mass 2kg moves in circles at radius 8m at uniform speed of 30m/s calculate. A_angular velocity B_ceritripetal force
The angular velocity is 3.75 m/s and the centripetal force is 225 N respectively.
The angular velocity of an object with respect to some extent is a degree of the way rapid that item actions through the point's view, within the feel of the way speedy the angular function of the item modifications. An instance of angular pace is a ceiling fan. One blade will whole a complete round in a certain amount of time T, so its angular speed with respect to the middle of the ceiling fan is twoπ/T.
Calculation:-
A. angular velocity ω = v/r
= 30 /8
= 3.75 m/s
B. Centripetal force = mv²/r
= 2×30²/8
= 225 N
There are 3 formulations we will use to find the angular velocity. the primary comes instantly from the definition. The angular pace is the rate of alternate of the position attitude of an object with respect to time, so w = theta / t, in which w = angular pace, theta = position attitude, and t = time.
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A 150 N crate is being pulled up a perfectly smooth ramp that slopes upward at 15 degrees by a pull that is directly at 30 degrees above the surface of the ramp. What is the magnitude of the pull required to make the crate move up the ramp at a constant velocity of 1.75 m/s?
The magnitude of the pull required to make the crate move up the ramp at a constant velocity of 1.75 m/s is 44.83 N.
What is the magnitude of the force required?
The magnitude of the force pull required to make the crate move up the ramp at a constant velocity of 1.75 m/s is calculated by applying Newton's second law of motion.
F(net) = ma
where;
F(net) is the net force on the cratem is the mass of the cratea is the acceleration of the crateat constant velocity, the acceleration of the crate = 0
F(net) = 0
Fx - Fgx = 0
where;
Fx is the horizontal component of the applied forceFgx is the horizontal component of the weight of the crateFcos(30) - 150sin(15) = 0
F = 150 sin(15) / cos30
F = 44.83 N
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Suppose that the stone is launched with a speed of 3 m/s and travels 40 m before coming to rest. What is the approximate magnitude of the friction force on the stone?.
The relationship between velocity, acceleration, and displacement is given by v2 = vo2 + 2as, which is derived from Newton's law of motion. Where a, and s are the acceleration and displacement, and v and vo are the final and starting velocities, respectively. Using the second law of Newton,
The problem mentions the stone's initial speed as 3 m/s. Moreover, the stone will stop after 40m. This indicates that the displacement is 40m, and the final speed is 0 m/s. Calculations for rock acceleration are as follows:
(0 m/s)^2 = (3 m/s)^2 + 2a (40m).
9 m^2/s^2 = -2a(40m) (40m)
0.1 m/s2 is equal to a=-9m2/s2/80m.
This implies that the stone will slow down and come to a stop as a result.
F = 20 kg * -0.1 m/s2. To continue,
F = 2N = 20 kg * 0.1 m/s2. Thus, the frictional force is 2N in magnitude.
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4. Interpret Data The graph below shows the
motion of an elevator. Explain its motion.
Answer:
Below
Explanation:
0-1 sec descends at constant rate from 10 to 6 m
1-2 sec stops at 6m
2-3 sec descends at constant rate to 2 m
3-4 sec stops at 2 m
4-5 sec descends at another constant rate to 0 m
A bike accelerates from 0 m/s to 15 m/s over the span of 5 seconds. How fast is the bike
traveling after 2.5 seconds?
The bike is travelling at 22.5 m/s after 2.5 s
What is acceleration?This is defined as the rate of change of velocity which time. It is expressed as
a = (v – u) / t
Where
a is the acceleration v is the final velocity u is the initial velocity t is the time How to determine the acceleration Initial velocity (u) = 0 m/sFinal velocity (v) = 15 m/sTime (t) = 5 sAcceleration (a) =?a = (v – u) / t
a = (15 – 0) / 5
a = 3 m/s²
How to determine the final velocity in the first 2.5 s Initial velocity (u) = 15 m/sAcceleration (a) = 3 m/s²Time (t) = 2.5 s Final velocity (v) = ?a = (v – u) / t
3 = (v – 15) / 2.5
Cross multiply
v – 15 = 3 × 2.5
v – 15 = 7.5
Collect like terms
v = 7.5 + 15
v = 22.5 m/s
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A helpful association method like remembering the Allies during World War II as BAR
(Britain, America, and Russia) is called
O an acronym
O the DAP flashcard method
O a visual image
O a mind map
Answer:
an acronym because it is shorted to remember like mvemjsun it's the planet
What research method allows us to isolate cause and effect, as for example, in
determining if a type of educational intervention increases student's knowledge
of sexuality?
Scientific investigation using experimental methods is the good way to isolate the cause and effect in a study.
What is experimental methods ?The only study methodology that can quantify cause and effect connections between variables is the experimental approach. To prove cause and effect, three requirements must be accomplished.
These conditions can be met by using experimental designs: Starting with a sample , a basic experimental design involves randomly placing individuals in either the experimental group or the control group.
The control group will serve as a benchmark for comparison and will go through the same thing as the experimental group, but it won't be subjected to the independent variable.
This addresses the placebo effect, which is the tendency for a group to anticipate changes simply from participation. The two groups are measured once more to see whether a change has taken place after the experimental group was exposed to the independent variable.
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Electromagnetic waves transport energy.
a. True
b. Fasle
Answer:
a
Explanation:
energy is transferred in electromagnetic waves
In 2012, NASA sent the 900kg Curiosity robot to Mars to study the planet. a) Recall the relationship between the weight P and the mass m. Specify the units. b) What is the weight of Curiosty on Mars? c) Compare the weight of Curiosity on Earth and on Mars. Why is it more important on Earth
(a)The units for weight are typically expressed in Newtons (N), while mass is measured in kilograms (kg).
(b)The weight of Curiosity on Earth is approximately 8820 Newtons.
a) The relationship between weight (P) and mass (m) is given by the formula P = m * g, where g represents the acceleration due to gravity. The units for weight are typically expressed in Newtons (N), while mass is measured in kilograms (kg).
b) To calculate the weight of Curiosity on Mars, we need to determine the acceleration due to gravity on Mars. The acceleration due to gravity on Mars is approximately 3.71 m/s². Using the weight formula, we have P = m * g = 900 kg * 3.71 m/s² = 3339 N. Therefore, the weight of Curiosity on Mars is approximately 3339 Newtons.
c) The weight of Curiosity on Earth is significantly greater compared to its weight on Mars. On Earth, the acceleration due to gravity is approximately 9.8 m/s². Using the weight formula, we have P = m * g = 900 kg * 9.8 m/s² = 8820 N. Therefore, the weight of Curiosity on Earth is approximately 8820 Newtons.
The difference in weight between Earth and Mars is important because weight is directly related to the force of gravity. The greater weight on Earth indicates a stronger gravitational force, which affects the overall dynamics and requirements for missions like Curiosity.
It affects the launch and landing processes, the structural integrity of the spacecraft, the fuel and energy requirements, and the ability to conduct experiments and operate the robotic systems effectively. Understanding these differences is crucial for mission planning, spacecraft design, and mission success.
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❧ What is Thermal expansion and contraction of solids?
In physics, the term "thermal expansion" refers to the expansion that takes place when heat is applied to a body. Each molecule in a body has an increased kinetic energy when it is heated. Molecular collisions between molecules happen more frequently as a result of the increase in kinetic energy. Now, when collisions happen, objects with greater kinetic energy than before will create a larger space around them. Practically, this results in growth.
Now, relating it to equation part:
Depending on the force of attraction acting between molecules, each substance has a specific arrangement and packaging. Therefore, the object with less attraction will occupy more space around it while using less kinetic energy than the object with more attraction. Therefore, for various metals, the coefficient of thermal expansion has been established experimentally.
for example: coefficient of thermal expansion of copper is 16.6∗10−6m/mK.
16.6∗10−6m/mK. That means if you apply 1 kelvin of heat on a copper rod of length 1 m, it will expand 16.6∗10−6 m more.
Expansion ∞ Length Lo (i) Note: ∞ is for proportionality sign.
Suppose an iron rod of 10 m and other of 1 m, obviously the larger one will expand more. (other functions remain same)
Expansion ∞ Change in Temperature - Δ (ii)
The more the temperature the higher kinetic energy the molecules posses. Therefore more expansion.
Therefore, on combining Expansion = α L0 ΔT Here α is the thermal expansion of the material.
Now adding L0 on both sides and taking L0 common on the right side (to get the new length of the rod)
L= L0(1+αΔT)
This is for linear expansion, similarly you can relate for superficial and cubical expansion.
The molecules slow down when solids cool. The solids shrink as a result of the molecules being able to move closer together. When heated, solids expand. Additionally, they undergo a process known as thermal contraction when they are cooled.
Thank you,
Eddie
Question 1 of 10
When thermal conduction is occurring within a solid, what happens to its
particles?
A. They begin to move more slowly.
B. They move in the same direction.
C. They vibrate faster.
O O
D. They move past each other.
SUBMIT
Answer is C
When thermal conduction is occurring within a solid, the particles vibrate faster. (option C)
When thermal conduction occurs within a solid, the particles of the solid undergo certain changes. Here is a step-by-step explanation:
Thermal conduction:
Thermal conduction is the transfer of heat energy within a solid material due to the movement of its particles. It occurs when there is a temperature gradient within the solid, where one end is at a higher temperature and the other end is at a lower temperature.
Particle motion:
In a solid material, the particles are closely packed and held in a fixed position by intermolecular forces. However, when thermal energy is supplied to the solid, the particles gain kinetic energy and begin to vibrate.
Increased kinetic energy:
The transfer of heat energy causes the particles to gain kinetic energy, which results in increased vibrational motion. The particles oscillate around their equilibrium positions more vigorously.
Vibrational motion:
As the particles vibrate faster, their amplitude of vibration increases. This increased vibrational motion allows the particles to pass on their kinetic energy to neighboring particles through collisions.
Transfer of heat:
The faster vibration of particles enables the transfer of heat energy from higher temperature regions to lower temperature regions within the solid. The particles with higher kinetic energy collide with neighboring particles, transferring the thermal energy.
In summary, during thermal conduction within a solid, the particles do not move in the same direction, move past each other, or slow down. Instead, they vibrate faster around their equilibrium positions, enabling the transfer of heat energy through the solid material.
Therefore, the correct answer is C. They vibrate faster.
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The velocity time graph of an object mass 50 g is shown in figure study graph and answer
1)calculate force acting on object in time interval 0-3 seconds
2)calculate the force acting on the object in the time interval 6-10 seconds
3)Is there any time interval in which no force acts on object.Justify
1) The force acting on the object during the time interval 0-3 seconds is 1/3 N.
2) The force acting on the object during the time interval 6-10 seconds is -0.5 N.
3) There is no time interval in which no force acts on the object.
(i) Force acting on the object in time interval 0-3 seconds. Force acting on the object is equal to the product of its mass and acceleration, i.e.,F = ma.
In the given velocity-time graph, the acceleration of the object can be determined by determining the slope of the velocity-time graph from 0 to 3 seconds.
Slope = (change in velocity) / (change in time)= (20-0) / (3-0) = 20/3 m/s^2
Acceleration, a = slope= 20/3 m/s^2
Mass of the object, m = 50 g = 0.05 kg
∴ Force acting on the object, F = ma= 0.05 × 20/3= 1/3 N.
Therefore, the force acting on the object during the time interval 0-3 seconds is 1/3 N.
(ii) Force acting on the object in time interval 6-10 seconds. Similar to the first question, the force acting on the object in time interval 6-10 seconds can be determined by determining the acceleration of the object during this time interval.
The slope of the velocity-time graph from 6 seconds to 10 seconds can be determined as follows:
Slope = (change in velocity) / (change in time)= (-20-20) / (10-6) = -40/4= -10 m/s^2 (negative sign indicates that the object is decelerating)
Mass of the object, m = 50 g = 0.05 kg
∴ Force acting on the object, F = ma= 0.05 × (-10)= -0.5 N.
Therefore, the force acting on the object during the time interval 6-10 seconds is -0.5 N.
(iii) Time interval in which no force acts on the object. There is no time interval in which no force acts on the object. This is because, as per Newton's first law of motion, an object will continue to remain in a state of rest or uniform motion along a straight line unless acted upon by an external unbalanced force.In other words, if the object is moving with a constant velocity, there must be a force acting on the object to maintain its motion.
Therefore, there is no time interval in which no force acts on the object.
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How to travel in the speed of light?
Answer:
Explanation:
1. eectromagnetic Fields. Most of the processes that accelerate particles to relativistic speeds work with electromagnetic fields to the same force that keeps magnets on your fridge!
Magnetic Explosions
Wave-Particle Interaction's
The units of Work, Energy and power are________ ________units.
Answer:
the units of work and energy is joule and unit of power is Watt
what is the most effortless walking speed for a person with 90cm long legs if the length of each step is 90cm
Answer:
75 cm/second.
Explanation:
Formula:
Walking speed = stride length / time per step
Walking speed = 90cm/time per step
= 90cm/1.2 seconds (a common estimate time per step)
= 75cm/second.
How is the plot of output of dc generator different from the plot of output for an ac generator
The key difference between the two types of generators is that DC generators produce a constant and unidirectional output while AC generators produce a varying and alternating output.
How does the AC and DC generator works ?The output of a DC generator produces a steady, unidirectional current that flows in one direction. The plot of its output voltage versus time would be a straight line with no fluctuations or changes in direction.
On the other hand, an AC generator produces an alternating current that changes direction periodically, usually at a fixed frequency. The plot of its output voltage versus time would be a sinusoidal waveform with a repeating pattern of positive and negative values.
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Calculate the force of gravity between planet X and planet y if both planets are 3.75 X 10^11 m apart, planet X has a mass of 1.55 X 10^22 kg and planet
Y has a mass of 3.95 X 10^28 kg.
(The radius of planet X is 6.0 X 10^6 m, the radius of planet Y is 1.50 X 10^6 m, and G = 6.67 X 10^-11 Nm2/kg2)
So, the force of gravity that the asteroid and the planet have on each other approximately \( \boxed{\sf{2.9 \times 10^{17} \: N}} \)
IntroductionHi ! Now, I will help to discuss about the gravitational force between two objects. The force of gravity is not affected by the radius of an object, but radius between two object. Moreover, if the object is a planet, the radius of the planet is only to calculate the "gravitational acceleration" on the planet itself,does not determine the gravitational force between the two planets. For the gravitational force between two objects, it can be calculated using the following formula :
\( \boxed{\sf{\bold{F = G \times \frac{m_1 \times m_2}{r^2}}}} \)
With the following condition :
F = gravitational force (N)G = gravity constant ≈ \( \sf{6.67 \times 10^{-11}} \) N.m²/kg²\( \sf{m_1} \) = mass of the first object (kg)\( \sf{m_2} \) = mass of the second object (kg)r = distance between two objects (m)Problem SolvingWe know that :
G = gravity constant ≈ \( \sf{6.67 \times 10^{-11}} \) N.m²/kg²\( \sf{m_X} \) = mass of the planet X = \( \sf{1.55 \times 10^{22}} \) kg.\( \sf{m_Y} \) = mass of the planet Y = \( \sf{3.95 \times 10^{28}} \) kg.r = distance between two objects = \( \sf{3.75 \times 10^{11}} \) m.What was asked :
F = gravitational force = ... NStep by step :
\( \sf{F = G \times \frac{m_X \times m_Y}{r^2}} \)
\( \sf{F = 6.67 \cdot 10^{-11} \times \frac{1.55 \cdot 10^{22} \cdot 3.95 \times 10^{28}}{(3.75 \times 10^{11})^2}} \)
\( \sf{F \approx \frac{40.84 \times 10^{-11 + 22 + 28}}{14.0625 \times 10^{22}}} \)
\( \sf{F \approx 2.9 \times 10^{39 - 22}} \)
\( \sf{F \approx 2.9 \times 10^{17} \: N} \)
ConclusionSo, the force of gravity that the asteroid and the planet have on each other approximately
\( \boxed{\sf{2.9 \times 10^{17} \: N}} \)
See MoreGravity is a thing has depends on ... https://brainly.com/question/26485200Compound interest is a method of calculating interest for which interest is computed on the initial investment amount as well as on any previous interest.
The starting principal sum is multiplied by both of these variables, and the annual interest rate is increased to the number of compound periods minus one.
The full original amount of the loan is then reduced by the resulting value. Compound interest is the term for interest that is earned on interest. This may be shown using simple math: if you start with $100 and it earns 5% interest every year, you will have $105 at the end of the first year. At the end of the second year, you will have $110.25. On the initial principal sum, simple interest is calculated each time. Compound interest is calculated using the sum of the principal and interest. It is equal every year on a particular principal.
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What is the difference between chronic and acute stress?
Acute stress is long-term, while chronic stress is short in duration.
Acute stress is short-term, while chronic stress endures over time.
Chronic stress varies by geographic location, while acute stress is universal.
Chronic stress is not harmful, while acute stress has negative consequences.
Answer:
The correct difference between chronic and acute stress is:
Acute stress is short-term, while chronic stress endures over time.
Explanation:
Acute stress refers to the immediate and temporary response of the body to a specific stressful event or situation. It is often characterized by a rapid increase in heart rate, heightened alertness, and the release of stress hormones like adrenaline. Acute stress is a normal and natural response to perceived threats or challenges, and once the stressor is removed or resolved, the body returns to its normal state.
On the other hand, chronic stress is long-term and persists over an extended period. It is typically caused by ongoing or recurring stressors, such as work pressures, financial difficulties, relationship problems, or chronic health conditions. Chronic stress can have a cumulative and prolonged impact on physical and mental well-being. It may lead to a range of health issues, including cardiovascular problems, weakened immune system, digestive disorders, anxiety, depression, and burnout.
Chronic stress is considered detrimental to overall health, while acute stress, when experienced in moderation, can actually be beneficial as it can enhance performance and help individuals deal with immediate challenges. It is important to manage chronic stress effectively through stress-reducing techniques, self-care practices, and seeking support when needed to prevent its negative consequences on health and well-being.
2. A 70.0-kg man and a 55.0-kg woman holding a 2.50-kg purse on ice skates stand facing eac other. (a) If the woman pushes the man backwards so that his final speed is 1.50 m/s, with what average force did she push him, assuming they were in contact for 0.500 s? (b) What i the woman's recoil speed? (c) If she now throws her 2.50-kg purse at him at a 20.0° angle ac
a) The average force with which the woman pushed the man is 210 N.
b. the woman's recoil speed is still 3.68 m/s
c. If she now throws her 2.50-kg purse at him at a 20.0° angle, the speed is 0.
How do we calculate?We first calculate the Momentum = (70.0 kg)(-1.50 m/s) + (55.0 kg)(v) + (2.50 kg)(-1.50 m/s)
0 = (70.0 kg)(0 m/s) + (55.0 kg)(v) + (2.50 kg)(-1.50 m/s) - (70.0 kg)(-1.50 m/s)
v = 3.68 m/s
Δp = (70.0 kg)(1.50 m/s) - (70.0 kg)(0 m/s) = 105 kg·m/s
The average force exerted on the man by the woman is:
Average force = Δp / Δt
Average force = 105 kg·m/s / 0.500 s
Average force = 210 N
b) The woman's recoil speed is :
0 = (70.0 kg)(-1.50 m/s) + (55.0 kg)(v) + (2.50 kg)(-1.50 m/s)
v = 3.68 m/s
c) If the woman throws her 2.50-kg purse at the man at a 20.0° angle, we apply the conservation of momentum equation in two dimensions and get the speed as 0.
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How can you describe the motion of an object in a race?
an effort force 40n is applied to a screwdriver to pry the lid off of a can of pain. the screwdriver applies 100n of force to the lid. what is the MA of the screwdriver?
Answer:
MA = 2.5
Explanation:
Given that,
Effort force applied to a screwdriver to pry the lid off of a can= 40 N
The screwdriver applies 100n of force to the lid = 100 N
We need to find the mechanical advantage of the screwdriver. Mechanical advantage of a machine is given by the ratio of load to the effort.
m = load/effort
= 100/40
= 2.5
Hence, the MA of the screwdriver is 2.5
economy?
A
Supply decreases
Price decreases
B.
Pnce increases
Scaroty decreases
c.
Demand increases
Pace increases
DO
Demand increases
Price decreases
Answer:
I. don't. get. this. question
C. Demand increases
Pace increases
what is the full meaning of D.D.T
which particles are elctrically neutral
Explanation:i think its nuetrons
which of the following are responsible for the repulsive force between two identically charged atoms?
B: Electrostatic force is responsible for the repulsive force between two atoms charged identically.
The electrostatic force is an attractive force as well as a repulsive force induced by the electric charge particles. The electrostatic force is also called Columb's force. The Columb attraction would be named after Charles-Augustin de Coulomb, a French scientist. One of nature's four basic forces however is electrostatic force.
Between two charges placed at a distance, there exists the electrostatic force. The magnitude of the electrostatic force relies on the magnitude of each charge and the distance between them. When two identically charged objects (both with positive charges or both with two negative charges) are brought together, then the same charges repel each other.
"
Complete question
which of the following are responsible for the repulsive force between two identically charged atoms?
A: force of attraction
B: electrostatic force
"
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A 60.0 kg person jumps onto the floor from a height of 3.0m. Find
the KE of the jumper when she hits the ground.
Answer:
1800 J
Explanation:
GPE= mgh
60*3*10
=1800 J
Complete the sentence with the word "element" or "compound." O is a(n) and H2O2 is a(n)
Answer:
O is an element whilst H2O2 is a compound.
Explanation:
O is an element. You can find it on the periodic table. H2O2 is composed of both H and O. Thus, H2O2 is a compound.
The O is a(n) element and \(H_{2} O_{2}\) is a(n) compound.
What is element?All facets of a species of atoms with a specific count of protons in its nuclei are referred to as chemical elements, such as the pure substance made exclusively of the that species.
What is compound?A compound comprises a substance created by the chemical fusion of two or more components.
Therefore, the O is a(n) element and \(H_{2} O_{2}\) is a(n) compound.
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34. [8 Marks] A spring is compressed with a 5.0 kg mass by 20.0 cm from its equilibrium position. When the spring is released, the 5.0 kg mass travels along a smooth horizontal surface and then up a frictionless plane at 30° to the horizontal. Calculate the distance it would travel up the inclined plane before coming back down again.
Answer and Explaination:
To solve this problem, we can analyze the forces acting on the mass as it travels up the inclined plane. We'll consider the gravitational force and the force exerted by the spring.
1. Gravitational force:
The force due to gravity can be broken down into two components: one perpendicular to the inclined plane (mg * cosθ) and one parallel to the inclined plane (mg * sinθ), where m is the mass and θ is the angle of the inclined plane.
2. Force exerted by the spring:
The force exerted by the spring can be calculated using Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position. The force can be written as F = -kx, where F is the force exerted by the spring, k is the spring constant, and x is the displacement from the equilibrium position.
Given:
Mass (m) = 5.0 kg
Compression of the spring (x) = 20.0 cm = 0.20 m
Angle of the inclined plane (θ) = 30°
First, let's find the force exerted by the spring (F_spring):
F_spring = -kx
To find k, we need the spring constant. Let's assume that the spring is ideal and obeys Hooke's Law linearly.
Next, let's calculate the gravitational force components:
Gravitational force parallel to the inclined plane (F_parallel) = mg * sinθ
Gravitational force perpendicular to the inclined plane (F_perpendicular) = mg * cosθ
Since the inclined plane is frictionless, the force parallel to the inclined plane (F_parallel) will be canceled out by the force exerted by the spring (F_spring) when the mass reaches its highest point.
At the highest point, the gravitational force perpendicular to the inclined plane (F_perpendicular) will be equal to the force exerted by the spring (F_spring).
Therefore, we have:
F_perpendicular = F_spring
mg * cosθ = -kx
Now, let's substitute the known values and solve for k:
(5.0 kg * 9.8 m/s^2) * cos(30°) = -k * 0.20 m
49.0 N * 0.866 = -k * 0.20 m
42.426 N = -0.20 k
k = -42.426 N / (-0.20 m)
k = 212.13 N/m
Now that we know the spring constant, we can calculate the maximum potential energy stored in the spring (PE_spring) when the mass reaches its highest point:
PE_spring = (1/2) * k * x^2
PE_spring = (1/2) * 212.13 N/m * (0.20 m)^2
PE_spring = 4.243 J
The maximum potential energy (PE_spring) is equal to the maximum kinetic energy (KE_max) at the highest point, which is also the energy the mass has gained from the spring.
KE_max = PE_spring = 4.243 J
Next, we can calculate the height (h) the mass reaches on the inclined plane:
KE_max = m * g * h
4.243 J = 5.0 kg * 9.8 m/s^2 * h
h = 4.243 J / (5.0 kg * 9.8 m/s^2)
h = 0.086 m
The height the mass reaches on the inclined plane is 0.086 m.
Now, we can calculate the distance traveled.
A 5.0 kg object compresses a spring by 0.20 m with a spring constant of 25 N/m. It climbs an incline, reaching a maximum height of 0.0102 m before coming back down, traveling a total distance of 0.0428 m.
Given data: Mass of the object, m = 5.0 kg, Displacement of the spring, x = 20.0 cm = 0.20 mAngle of the inclined plane, θ = 30°Calculating the spring constant, k. Using Hooke’s Law; F = -kx Where F is the restoring force required to bring the spring back to its equilibrium position.From the equation, F = ma For the object attached to the spring,m * a = -kx. On integrating,∫ma dt = -∫kx dt .On integrating the left side with limits from 0 to t and right side with limits from 0 to x, where the limits on the left are for acceleration and the right are for the displacement of the spring; mv - mu = -½ kx²At maximum compression, the velocity of the mass is zero, i.e., v = 0 and the initial velocity is also zero. Therefore, mv - mu = -½ kx²0 - 0 = -½ k (0.20)²∴ k = 25 N/mWork done on the spring in compressing it, W = ½ kx² = 0.5 * 25 * (0.20)² = 0.5 JSince the inclined plane is frictionless, the only force acting on the object will be the component of its weight acting along the plane. Hence, it will move up the incline with an acceleration of, a = g sin θ = 9.8 * sin 30° = 4.9 m/s²When the object has reached its maximum height, its velocity will be zero. Using the equation of motion; v² - u² = 2as0 - u² = 2as∴ s = u² / 2a. Now, the initial velocity of the object up the incline is,u = √(2gH)Where H is the height to which it climbs, and is given by, H = W / m g Where W is the work done on the object in lifting it to height H, and m is the mass of the object. W = 0.5 J, m = 5 kg. So, H = 0.5 / (5 * 9.8) = 0.0102 m∴ u = √(2gH) = √(2 * 9.8 * 0.0102) = 0.4525 m/sNow, the distance traveled by the object up the incline is,s = u² / 2a = (0.4525)² / (2 * 4.9) = 0.0214 m. When the object comes back down, it will travel the same distance down the incline, before coming to rest. Therefore, the total distance travelled up and down the incline is,2s = 2 * 0.0214 = 0.0428 m.For more questions on the spring constant
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