The magnitude of the starting acceleration to the stopping acceleration of the sports car is closest to 0.937. Amy is approximately 2.7 meters away from the fence.
To find the magnitude of the starting acceleration to the stopping acceleration of the sports car, we can use the equations of motion. The initial velocity (u) is 0 m/s, the final velocity (v) is 40.0 m/s, and the time taken (t) is 2.88 s. Using the equation v = u + at, we can rearrange it to solve for acceleration (a). Substituting the given values, we find that the starting acceleration is approximately 13.89 m/s^2. Similarly, for the stopping acceleration, we use the same equation with v = 0 m/s and t = 3.14 s, finding that the stopping acceleration is approximately -12.74 m/s^2. Taking the ratio of the magnitudes of these accelerations, we get 0.937.
For Amy throwing the ball over the fence, we can analyze the projectile motion. The vertical component of the initial velocity (v_y) is 8.0 m/s * sin(40°), and the time it takes for the ball to reach its maximum height can be calculated using the equation v_y = u_y + gt, where g is the acceleration due to gravity. Solving for t, we find it to be approximately 0.511 s. During this time, the ball reaches its maximum height, which is 1.0 m above the ground. Since the fence is 2.0 m high, the total height the ball reaches is 3.0 m. Using the equation for vertical displacement, h = u_yt + (1/2)gt^2, we can solve for the horizontal displacement (x) using the equation x = u_xt, where u_x is the horizontal component of the initial velocity. Substituting the given values, we find that Amy is approximately 2.7 meters away from the fence.
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does cool air have more or less air pressure than warm air
Answer:
cold
Explanation:
cold air is more dense than warm air, therefore it has a higher pressure
Now let's apply this to Trial 2. In this instance, Hailey (who is on the cart with Christine) has a mass of 69 kg. Conner is on the other cart.
1. Determine Conner's mass. Describe your process and results below.______
Here, Conner's mass is represented by m2.u2 is the velocity of Conner before the collision. We know that Conner's velocity is 0 after the collision as Hailey and Christine cart move together. So the final velocity, v1 and v2 will be 0 after the collision. Therefore, Conner's mass is 61 kg.
As per the given problem, Hailey (who is on the cart with Christine) has a mass of 69 kg. Conner is on the other cart. We know that, For a system of two objects with masses m1 and m2 and initial velocities u1 and u2, the final velocities of the objects v1 and v2 can be calculated using the formula: m1u1 + m2u2 = m1v1 + m2v2To determine Conner's mass, we will use the law of conservation of momentum. The total momentum of a system before a collision is equal to the total momentum of the system after the collision. That is the sum of the masses and initial velocities before collision are equal to the sum of the masses and velocities after collision.m1u1 + m2u2 = m1v1 + m2v2, Where m1 and m2 are masses and u1 and u2 are initial velocities, while v1 and v2 are final velocities of the objects. Consider the velocity of Hailey, who is on the cart with Christine, to be 0.Initial momentum = m1u1 + m2u2 = m2u2.
Therefore, m1u1 + m2u2 = m1v1 + m2v2 becomes m2u2 = m1v1 + m2v2. Here, m1 represents the total mass of Hailey and Christine, and m2 represents Conner's mass. Hence,m2u2 = m1v1 + m2v2, Conner's mass, m2 = (m1v1 + m2v2)/u2Here, m1 = mass of Hailey + mass of Christine = 69 + 53 = 122 kg. After the collision, Hailey and Christine move together. Hence, their final velocity, v1 = 3.8 m/s. Conner and his cart are at rest. Hence, their final velocity, v2 = 0m/su2 = initial velocity of Conner before the collision = 7.6 m/s. Now, we can determine Conner's mass using the above formula.m2 = (m1v1 + m2v2)/u2 = (122*3.8 + m2*0)/7.6 = 0.5*122m2 = 61 kg.
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What are some questions engineers should ask when researching a problem?
Who will this help?
How long will it take to get it right?
What a materials can be used to solve the problem?
How much will the project cost?
Answer:
is this a check all that apply or a single answer?
Arrange the following in order of increasing radius: O2-, F- , Ne ,Rb+ ,Br- Rb+ < F- < Br- < O2- < Ne Br- < Rb+ < Ne < F- < O2- Ne < F- < O2- < Rb+ < Br- O2- < F- < Ne < Rb+ < Br- O2- < Br- < F- < Ne < Rb + Br- < F- < O2- < Ne < Rb+ F- < O2- < Ne < Br- < Rb + Rb+ < F- < Br- < Ne
Radii is a vital feature of the elements, and it can be useful in determining the characteristics of elements in various chemical and physical processes. The radii of atoms and ions of the same element differ due to their various charge and mass characteristics.
Atomic and ionic radii increase as you move down a group on the periodic table, and decrease as you move across a period from left to right due to increased nuclear charge, making the electrons closer to the nucleus. The size of an atom and ion also changes due to the number of electrons charge, and electronic configuration.In order of increasing radius, the arrangement of \(Ne, F-, O2-, Br-, Rb\) is given as follows:
\(Ne < F- < O2- < Br- < Rb+\)
Rb+ has the smallest radius due to its large nuclear charge and fewer electrons in the valence shell.
As a result, they are larger than Rb+. O2- has more electrons than Ne and is the largest among the given ions and atoms. It is important to note that in certain conditions, the trends in radii may not be valid because of hybridization and other factors. Nonetheless, this arrangement is valid for the given ions and atoms.
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Warm 12 grams of water from 98 degrees Celsius to 99 degrees Celsius
Answer:
E=mc△T
E=0.012(4200)(99-98)
E=50.4J
50.4 joules of heat is used
If you increase the pressure on a gas sample by decreasing the volume, the
particles will speed up. True False
Answer: True
If you increase the pressure on a gas sample by decreasing the volume, the particles will speed up.
arge-scale structure in the universe has probably been shaped primarily by the gravity of cluster matter.
T/F
Arge-scale structure in the universe has probably been shaped primarily by the gravity of cluster matter is true.
The large-scale structure of the universe, such as the formation of galaxy clusters, superclusters, and cosmic filaments, is primarily shaped by the gravitational interactions of matter. Gravity acts as the dominant force in pulling matter together over cosmic scales, leading to the formation of structures on the largest observable scales in the universe. The gravitational attraction between matter, including dark matter, drives the clustering of galaxies into groups and clusters, which in turn contributes to the overall structure of the universe. Other factors, such as the expansion of the universe and the influence of dark energy, also play a role but gravity remains the primary force shaping the large-scale structure of the universe.
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rank the light intensity, from largest to smallest, at the point p in the figures.
The light intensity from largest to smallest ranking will be :B > D > A=C > E. where the area is measured on the plane perpendicular to the direction .
In physics, the intensity is the amount of energy that is transmitted per unit area, and the area is measured on a plane perpendicular to the direction that the energy equation will propagate. I = P/ 4(d2), with P denoting power. Let power of 1 bulb equal = P where I = intensity, d = distance at which the intensity must be determined.
case A = I = P / (1) (1) 1 = P case with 2 = P In the situation B = I = 2P/(0.5)2 = 8P C = I = 4P / (2) (2) ^2 = P case Case (1)2 = 3P: D = I = 3P E = I = 2P /(1.5) (1.5) ^2 = 0.8 P
B > D > A=C > E will be the order of light intensity, from greatest to least.
rank the light intensity, from largest to smallest, at the point p in the figures?
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the projectile launcher uses a spring to launch the ball from the top of the lab table. describe the energy transformations
The energy transformations in a projectile launcher involve the conversion of potential energy stored in the spring into kinetic energy of the ball, which is then transformed into other forms of energy as the ball moves through the air and interacts with other objects.
When a projectile launcher uses a spring to launch a ball, there are several energy transformations that occur:
1.Potential energy is stored in the spring as it is compressed. The amount of potential energy stored is given by the equation PE = (1/2) k x², where k is the spring constant and x is the distance that the spring is compressed.
2.When the spring is released, the potential energy is transformed into kinetic energy as the spring expands and pushes the ball forward. The kinetic energy of the ball is given by the equation KE = (1/2) m v², where m is the mass of the ball and v is its velocity.
3.As the ball travels through the air, it loses some of its kinetic energy due to air resistance, which is a form of non-conservative force. This energy is transformed into heat and sound energy.
4.When the ball hits a surface, some of its kinetic energy is transferred to the surface, causing it to deform or move. The remaining kinetic energy of the ball is transformed into other forms of energy, such as heat and sound energy.
Overall, the energy transformations in a projectile launcher involve the conversion of potential energy stored in the spring into kinetic energy of the ball, which is then transformed into other forms of energy as the ball moves through the air and interacts with other objects.
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Q.7. For a system with a transfer function of G(s)=- co² s² +2a+w² if the natural frequency is 0.5 and the damping ratio is 1.3, which of the following statements is correct regarding the unit step response of the system?
O A) Damped
O B) Undamped
O C) Underdamped
O D) Crittically Damped
O E) Overdamped
The system described by the transfer function G(s) = -co² s² + 2a + w², with a damping ratio of 1.3 and a natural frequency of 0.5, has an overdamped unit step response. So, the correct option is (E)
The transfer function of the system is given as G(s) = -co² s² + 2a + w², where co represents the damping ratio, a represents an arbitrary constant, and w represents the natural frequency of the system. We are given that the natural frequency is 0.5 and the damping ratio is 1.3.
To determine the type of unit step response, we need to analyze the damping ratio (co) in relation to the critical damping value (co_critical).
The critical damping ratio (co_critical) is defined as the value where the system is on the threshold between being overdamped and underdamped. It is given by the formula co_critical = 2 * sqrt(a * w²).
In our case, the natural frequency (w) is 0.5, so we can calculate co_critical as follows: co_critical = 2 * sqrt(a * 0.5²).
Since the damping ratio (co) is given as 1.3, we can compare it with co_critical to determine the type of unit step response.
If co > co_critical, the system is considered overdamped (Option E).
If co = co_critical, the system is considered critically damped (Option D).
If co < co_critical, the system is considered underdamped (Option C).
Based on the given values, we can determine that the system is overdamped (Option E) because the damping ratio (1.3) is greater than the critical damping ratio.
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what is a hydraulic system
Explanation:
Hydraulic systems use the pump to push hydraulic fluid through the system to create fluid power. The fluid passes through the valves and flows to the cylinder where the hydraulic energy converts back into mechanical energy. The valves help to direct the flow of the liquid and relieve pressure when needed
If the force of friction opposing the motion is 21 n, what force f (in newtons) is the person exerting on the mower?
The force exerted by the person on the mower is 21 N (assuming the force of friction opposing the motion is equal to the force exerted by the person).
When an object is in motion, there is often a force of friction acting against the direction of motion. In this case, the force of friction opposing the motion is given as 21 N.
According to Newton's third law of motion, the force of friction is equal in magnitude and opposite in direction to the force exerted by the person on the mower.
Therefore, if the force of friction opposing the motion is 21 N, it means that the person is exerting an equal but opposite force of 21 N on the mower.
This force helps to overcome the frictional force and propel the mower forward. It is important for the person to exert a force greater than or equal to the force of friction to ensure smooth movement of the mower.
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an automobile has a mass of 2000 kg and is traveling at 30m/s. what is the kinetic energy of the automobile?
The kinetic energy of the automobile is 900,000 joules.
Kinetic energy is a property of a moving object or particle and depends not only on its motion but also on its mass.
The kinetic energy (KE) of an object can be calculated using the formula KE = (1/2)mv^2, where m is the mass of the object and v is its velocity.
Given that the mass of the automobile is 2000 kg and its velocity is 30 m/s, we can substitute these values into the formula:
KE = (1/2)mv^2 = (1/2) x 2000 kg x (30 m/s)^2
= 900,000 J
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A space shuttle is flying north at 6,510 m/s. It
then begins accelerating at 28.4 m/s² directly
northeast to properly align its path towards
orbit around the Earth. After 60.0 s, what is
the magnitude of its velocity?
Vf = [?] m/s
a
Vf
Answer:
7808 m/s
Explanation:
Find NE velocity after 60 s of acceleration in that direction:
= a t = 28.4 m/s^2 * 60 s = 1704 m/s
Vertical component = 1704 sin 45 = 1204.9 m/s
Horiz component = 1704 cos 45 = 1204.9 m/s
Add the two vertical components
6510 + 1204.9 = 7714.9 m/s = vertical velocity
Pythagorean theorem to find resultant of vertical and horiz v's
Vf ^2 = 1204.9^2 + 7714.9^2 0
Vf = 7808. m/s
Answer: 81.1 for the direction of its velocity and 7808 for the magnitude of its velocity
Explanation:
Consider the six hypothetical electron states listed in the table. i Which, if any, of these states are not possible? Enter the letters of the states that are not possible in alphabetical order. For example, if you think that only states C and D are not possible, then enter CD. This part will be visible after you complete previous item(s). This part will be visible after you complete previous item(s).
The Pauli exclusion principle, which states that no two electrons in an atom can have the same set of quantum numbers.
What is the Pauli exclusion principle?In order to determine which electron states are not possible, we need to consider the Pauli exclusion principle, which states that no two electrons in an atom can have the same set of quantum numbers.
The quantum numbers include the principal quantum number (n), the azimuthal quantum number (l), the magnetic quantum number (m), and the spin quantum number (s).
If any of the quantum numbers are the same for two electron states, they cannot exist simultaneously in an atom. Therefore, we need to examine the six hypothetical states listed in the table and check if any of them have the same set of quantum numbers.
Without the specific details of the table and the quantum numbers associated with each state, it is not possible to provide a definitive answer within the 100-word limit.
However, by comparing the quantum numbers of each state, it would be possible to determine which states violate the Pauli exclusion principle and are therefore not possible.
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a string is wrapped around a pulley with a radius of 2.0 cm and no appreciable friction in its axle. the pulley is initially not turning. a constant force of 42.5 n is applied to the string, which does not slip, causing the pulley to rotate and the string to unwind. if the string unwinds 1.2 m in , what is the moment of inertia of the pulley?
The pulley's moment of inertia is 0.2 kg/m2.
Calculation:Equation of motion suggests:
s = ½ at^2
a = 2s/t^2
a = (2 × 1.2)/4.9^2 = 0.09996 m/s^2
Following are the linear and angular accelerations:
a =rα
a/r = 0.09996/0.02 = 4.9979 rad/s2
Torque = T = rF = (0.02)(50) = 1 N
Now, Moment of inertia = I = T/ α = 1/(4.9979) = 0.2 kg.m^2
What is a pulley's motion?We can see that the translational component of the rolling action is carried out by string and attached blocks, while the rotating component of the rolling motion is carried out by a pulley. Pulley and string motions are hence the same as rolling motions. Pulley Rolling is performed by a fixed pulley and rope.
What is the ring pulley's moment of inertia?A solid disc has a moment of inertia of 0.5*MR2, but a ring (which has mass solely on the circumference) has a moment of inertia of MR2. A pulley may have spokes to support it or it may have mass centered around the circumference in the shape of a solid disc.
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If a ball is dropped from the top of a
building and it takes 11 seconds to hit the
ground, how tall is the building? travel?
why does it hurt more to kick a bowling ball than a soccer ball
The combination of higher mass and lower elasticity in a bowling ball results in a more painful experience when compared to kicking a soccer ball.
Kicking a bowling ball is more painful than kicking a soccer ball because of the differences in their masses and elasticity. The pain experienced when kicking an object is determined by the transfer of kinetic energy and the interaction between the object and the body.
A bowling ball is much heavier and has a higher mass compared to a soccer ball. When you kick a bowling ball, it has a greater amount of momentum, which is the product of mass and velocity. The higher momentum results in a greater force being exerted on your foot upon impact, leading to a higher level of discomfort or pain.
In addition, the elasticity of the objects plays a role. Soccer balls are designed to be more elastic, allowing them to absorb and distribute the impact force more effectively. This elasticity helps to reduce the amount of force transmitted back to your foot, resulting in less pain. On the other hand, bowling balls are typically less elastic, leading to a greater transfer of force and more discomfort when kicked.
Overall, the combination of higher mass and lower elasticity in a bowling ball results in a more painful experience when compared to kicking a soccer ball.
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What is the area of space around a magnet called?
Answer:
These acts of attraction and repulsion are called “magnetism”, and the magnetic space around a magnet is called the “magnetic field”
Explanation:
if peter expends 2,000 calories running a mile in one hour and samantha burns 1000 calories riding a bike in thirty minutes. who spent the greatest amount of energy during their exercise
Peter expended the greatest amount of energy during his exercise. He burned 2,000 calories running a mile in one hour, while Samantha burned 1,000 calories riding a bike in thirty minutes.
Peter spent the greatest amount of energy during his exercise compared to Samantha. While Samantha burned 1,000 calories riding a bike in thirty minutes, Peter burned 2,000 calories running a mile in one hour. Calories burned during exercise depend on various factors such as intensity, duration, and individual differences. In this case, Peter's exercise had a higher energy expenditure because he ran for a longer duration and covered a greater distance. Running typically requires more energy expenditure compared to biking due to the higher impact and engagement of larger muscle groups. Hence, Peter expended a greater amount of energy during his exercise session.
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a boy looks at the reflection of his digital watch in a plane mirror and thinks the time is 10:11. what is the correct time?
Answer:
11:10 will be the time. reflection causes the object to be flipped when you see its image at the mirror
When a parachutist jumps from an airplane, he eventually reaches a constant speed, called the terminal velocity. This means thatSelect one:a. the force of air resistance is equal to zero. b. the effect of gravity has died down.c. the effect of gravity increases as he becomes closer to the ground.d the acceleration is equal to g.e. the force of air resistance is equal to the weight of the parachutist.
When an object moves at constant speed, the net force acting on that object is equal to 0:
\(\Sigma\vec{F}=0\)Two forces act over a parachutist while falling: the force of gravity (weight) and the air resistance. Those two forces have opposite directions, we can consider that the air resistance is positive because it points upwards, and the weight is negative because it points downwards:
\(\begin{gathered} \Sigma F=F_{\text{air}}-F_{\text{gravity}}=0 \\ \Rightarrow F_{air}=F_{gravity} \end{gathered}\)Then, when the parachutist reaches the terminal velocity, the force of air resistance is equal to the weight of the parachutist.
Therefore, the answer is option e:
\(\begin{gathered} e) \\ \text{The force of air resistance is equal} \\ \text{to the weight of the parachutist.} \end{gathered}\)What happens to the molecules when the solid changes phase?
they begin to move quickly and can break away from other molecules
Answer:
When solid changes atoms/molecules begin to speed up and move around. Compared to when they are in the solid phase, where they barely move and are slow and are compacted.
PLS HELP ME Which object has the greatest kinetic energy?
A: a truck with a mass of 3,500 kg moving at 30 m/s
B: a person with a mass of 73 kg running 6 m/s
C: a locomotive engine with a mass of 205,000 kg moving 5 m/s
D: a fast pitched baseball with a mass of .5 kg moving at 46.9 m/s
A locomotive engine with a mad of 205000kg moving with 5m/s
Explanation:
\(from \: the \: options \: substitute \: the \: formulars \: for \: kinetic \: energy \\ for \: opton \: a \: ke = \frac{1}{2} mv {}^{2} = \frac{1}{2} \times 3500 \times 30 {}^{2} = 1575000 \\ for \: option \: b \: ke = \frac{1}{2} mv {}^{2} = \frac{1}{2} \times 73 \times 6 {}^{2} = 1314 \\ for \: option \: \: c = \frac{1}{2}mv {}^{2} = \frac{1}{2} \times 205000 \times 5 {}^{2} = 2562500 \\ for \: option \: d \: = \frac{1}{2}mv {}^{2} = \frac{1}{2} \times 0.5 \times(46.9) {}^{2} = 549.9025 \\ from \: the \: analysis \: above \: the \: options \: that \: has \: the \: highest \: kinetic \: energy \: is \: a \: locomotive \: engine \: with \: a \: mass \: of \: 205000kg \: moving \: with \: a \: velocity \: of \: 5 \frac{m}{s} \)
A spring has a spring constant of 100 N/m. When the spring is compressed by 5 mm (such that \Delta xΔx is negative), determine the restoring spring force.
Given that spring constant, k = 100 N/m and displacement, x = - 5mm = - 0.005 m
The formula of restoring force according to Hooke's law,
\(F=-kx\)Substituting the values, we get
\(\begin{gathered} F=-100(-0.005) \\ =\text{ 0.5 N} \end{gathered}\)Thus, the force is 0.5 N
Exercise 17.69 - Enhanced - with Feedback and Hints MISSED THIS? Read Section 17.6 (Pages 745-753); Watch KCV - Part A 17.6. IWE 17.8. A 0.190M solution of a weak acid (HA) has a pH of 2.93. Calculate the acid ionization constant (K
a
) for the acid. Express your answer using two significant figures
The acid ionization constant (\(K_{a}\)) for the weak acid HA in the given question for the shared values will be around 0.
We must use the pH and concentration of the acid solution to determine the acid ionization constant (Ka) for the weak acid HA.
The amount to which the weak acid dissociates in water is indicated by the acid ionization constant.
Assumed: pH = 2.93.
HA concentration: 0.190 M.
We will use the following relationship between pH and the number of hydronium ions ( \(H_{3} 0^{+}\) ) to address this issue:
pH equals -log \(H_{3} 0^{+}\)
First, using the provided pH, we must determine the hydronium ion concentration:
\(H_{3} O^{+}\) = \(10^{-pH}\)
\(H_{3} O^{+}\)= \(10^{-2.93}\)
\(H_{3} 0^{+}\) = 7.33 × \(10^{-3}\) M
As we know that HA is a weak acid, it dissociates into its conjugate base
(\(A^{-}\)) and hydronium ions like the following reaction:
\(HA\) ⇄ \(A^{-}\) + \(H_{3} 0^{+}\)
Expression for equilibrium to the above reaction:
\(K_{a\)= (concentration of conjugate base x concentration of hydronium ions)/ concentration of HA
We don't know the concentration of the conjugate base.
But we do know that the solution is very dilute so we can say that the dissociation of the given acid is very less compared to the concentration.
So we can take its value to be 0.
\(K_{a}\) = (0 × \(H_{3} 0^{+}\)) / HA
\(K_{a}\) = 0
So, the acid ionization constant for the given acid will be zero.
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The acid ionization constant (Ka) for the weak acid is \(1.7 * 10^{-3}\).
To calculate the acid ionization constant (Ka), we need to use the pH value and concentration of the weak acid solution. The pH of the solution indicates the concentration of H+ ions, which is related to the concentration of the weak acid and its dissociation.
The pH can be converted to the concentration of H+ ions using the formula: \([H+] = 10^{(-pH).\)
In this case,\([H+] = 10^{(-2.93).\)
Since the weak acid is not completely dissociated, the concentration of the weak acid ([HA]) can be approximated as its initial concentration, which is given as 0.190M.
The dissociation of the weak acid can be represented as follows:
HA ⇌ H+ + A-
The equilibrium expression for the dissociation is \(K_a = [H+][A-] / [HA]\).
Substituting the values into the equation:
\(Ka = (10^{(-2.93)})(10^{(-2.93)}) / 0.190.\)
Calculating the value gives us:
\(Ka = 1.7 * 10^{-3.\)
Therefore, the acid ionization constant (Ka) for the weak acid is approximately \(1.7 * 10^{-3}\).
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What is true about most of the mass in the universe?
A. It was created in the last 30,000 years. B. It is invisible to astronomers.
C. It has already decayed into pure energy.
D. It is made of nitrogen atoms.
Answer:
B. It is invisible to astronomers.
Explanation:
Most of the mass in the universe exists in the form of dark matter, which is invisible to astronomers.
Which is the preserved evidence of the activity of an organism?
Answer:
Fossils are the remains of an ancient organism or the traces of activity of such an organism. There are two types of fossils: body fossils and trace fossils. Body fossils include preserved remains of an organism (i.e. freezing, drying, petrification, permineralization, bacteria and algea).
a cylinder with , and a diameter is being pulled by a string with a force . the cylinder rolls on a surface with a coefficient of friction of horizontally: a cable reel on a flat surface is pulled by a force at its center. friction exists between the reel and the surface. determine r, and the acceleration. is the cylinder slipping?
The radius of the cylinder is approximately 2.19 m, and the cylinder is experiencing a deceleration of approximately 1.86 m/s². Since the cylinder is decelerating and the force applied is less than the friction force, it is not slipping.
From the given information:
Mass of the cylinder, m = 5 kg
Moment of inertia of the cylinder, I = 12 kg·m²
Diameter of the cylinder, D = 0.5 m
Force applied, F = 25 N
Coefficient of friction, μ = 0.7
Radius of the cylinder, r = ?
To determine the radius (r) of the cylinder, we can use the relationship between moment of inertia (I) and mass (m) for a solid cylinder:
I = (1/2) * m * r²
Given I = 12 kg·m² and m = 5 kg, we can solve for r:
12 = (1/2) * 5 * r²
r² = 12 / (1/2) * 5
r² = 12 / 2.5
r² = 4.8
r ≈ √4.8
r ≈ 2.19 m
So, the radius of the cylinder is approximately 2.19 m.
Now, let's determine the acceleration of the cylinder. The force applied is given as F = 25 N. The friction force can be calculated using the equation:
Friction force = μ * Normal force
Since the cylinder is being pulled by the string, the normal force is equal to the weight of the cylinder, which is given by:
Weight = mass * acceleration due to gravity
Weight = m * g
Assuming a standard acceleration due to gravity of 9.8 m/s²:
Weight = 5 kg * 9.8 m/s² = 49 N
Friction force = μ * Normal force = μ * Weight = 0.7 * 49 N = 34.3 N
Now, we can calculate the net force acting on the cylinder:
Net force = Force applied - Friction force
Net force = 25 N - 34.3 N
Net force = -9.3 N
Since the net force is negative, indicating that the force applied is less than the friction force, the cylinder will experience a deceleration rather than acceleration. The magnitude of the deceleration can be calculated using Newton's second law:
Net force = mass * acceleration
-9.3 N = 5 kg * acceleration
acceleration = -9.3 N / 5 kg
acceleration = -1.86 m/s²
The negative sign indicates that the deceleration is in the opposite direction to the force applied, which means the cylinder is moving in the direction opposite to the applied force.
Hence, the radius of the cylinder is approximately 2.19 m, and the cylinder is experiencing a deceleration of approximately 1.86 m/s². Since the cylinder is decelerating and the force applied is less than the friction force, it is not slipping.
Learn more about Friction force from the link given below.
https://brainly.com/question/30280206
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Find the work done by a weightlifter lifting a 20kg barbell 2.2 m upward at a constant speed.
Answer:
440J
Explanation:
First, let us find the weight of the barbell.
The formula to find the weight is :
W = m × g
Here,
m ⇒ mass ⇒ 20 kg
g ⇒ acceleration of gravity
Let us find it now.
W = m × g
W = 20 kg × 10 ms⁻²
W = 200N
And now let us find the work done by this weight lifter.
Work = Force × Displacement
Let us find it now.
Work = Force × Displacement
= 200N × 2.2m
= 440J