The minimum number of steps visible on the escalator at any given time is 150.
Let's assume that the escalator is moving upward at a constant rate, so that the distance traveled by al in one unit of time is equal to three times the distance traveled by bob in one unit of time, which means that al will take three times as many steps as bob does.
Let's say that al walks down 50 steps per unit time, and bob walks up 25 steps per unit time. We know from our earlier assumption about constant speed that al will take three times as many steps as bob does, so if al walks down 50 steps per unit time, then bob walks up 75 steps per unit time—but we also know that there are 150 total visible steps on the escalator at any given point in time.
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what is the improvement in the frequency response of the modified equalizer and what benefits does that bring to the system?
An equalizer is used to adjust or correct the audio signal by boosting or lowering sound frequency. It will affect the sound output for the listener with an altered audio color. In other words, it is used to balance sound in the system.
Audio equalization itself is a process of balancing (boosting or lowering) the sound frequency to make better audio output. For example, tweaking the treble frequency will make the vocal audible, boosting the bass will make the sound heavier, and so many more to tune the sound to your audio taste. In addition, an equalizer can also be used as noise reduction.
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An 80kg woman jumps from a wall and lands stiff-legged in soft sand. The woman's downward speed just as she touches the sand is 6m/s. She is stopped after sinking 0.05m into the sand. Calculate the net force on the woman while she is being stopped by the sand. Round to nearest whole number
The net force on the woman while she was stopped by the sand is 28800 N.
What is force?Force can be defined as the product of the mass of a body and its acceleration.
To calculate the net force on the woman, we use the formula below.
Formula:
F = m(v²-u²)/2s........... Equation 1Where:
m = Mass of the womanF = Force on the womanv = Final velocityu = Initial velocitys = DistanceFrom the question,
Given:
m = 80 kgv = 6 m/su = 0 m/ss = 0.05 mSubstitute these values into equation 1
F = 80(6²-0²)/(2×0.05)F= 80×36/0.1F = 28800 NHence, the net force on the woman is 28800 N.
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what is the potential difference across a 19- m -long, 2.0- mm -diameter copper wire carrying an 7.6 a current?
The potential difference across a 19m long, 2.0mm diameter copper wire carrying a 7.6A current is 676 V.
The resistance of the wire is given by R = ρ L/A
where ρ is the resistivity of copper (ρ = 1.72E-8 Ωm) and L is the length of the wire (19m). So,
R = 1.72E-8 * 2.0E-3/7.6E3
= 912 Ω.
Assuming that no other circuit elements are present, the potential difference across this wire will be equal to the voltage drop across that resistor:
V = IR = 912 * 7.6E3
= 676 V
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2 balls ball 1 and ball 2 are each thrown horizontally from the same height above the ground. ball 2 has a greater initial velocity after leaving the thrower's hand than ball 1. if air resistance is negligible how do the accelerations of each ball and the time it takes each of them to hit the ground compare?
acceleration on both the balls is same
Time to hit the ground is also equal for both the balls.
Here the acceleration is only acceleration due to gravity in vertically downward direction.
No acceleration in horizontal direction as air resistance is neglected.
Both the balls are projected from same height and downward acceleration is same and there is no initial downward velocity ,hence both the balls take same time to hit the the ground.
Time to hit the ground is also equal for both the balls.
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Julie finds a snail on the sidewalk and wants to know whether or not the snail moves throughout the day. She places a single mark on the sidewalk next to the snail.
Julie left a single mark on the sidewalk, and that mark has served as a starting point for me to track the snail's movement. Hence, option D is correct.
What is a snail?In broad terms, a snail is a shelled gastropod. The name is most commonly used in reference to land snails, that are pulmonate gastropod mollusks. However, the majority of the Gastropoda molluscan—which have coiled casings big enough for the animal to completely retract into—are also referred to as snails by their popular name. When used in this broad sense, the word "snail" refers to many different kinds of freshwater and marine snails, as well as land snails.
The distance traveled has been calculated using the reference point represented by the line that has been drawn across the sidewalk. So, choice D is the right one.
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Your question is incomplete, your question probably is :
Julie finds a snail on the sidewalk and wants to know whether or not the snail moves throughout the day. She places a
single mark on the sidewalk next to the snail.
What will Julie use the mark for initially?
determining how fast the snail moves
acting as a standard unit of measure
determining the displacement of the snail
O acting as a reference point for detecting motion
Which formula is used to find the growth rate of a population? O Death rate - Birth rate = Growth rate O Death rate x Birth rate= Growth rate O Birth rate - Death rate= Growth rate O Death rate + Birth rate = Growth rate
The formula used to find the growth rate of a population is Birth rate - Death rate = Growth rate.
Population growth = ( Initial population - Population at time measured ) / Initial population * 100
The population growth rate is also called as rate of natural increase. The average change in population size annually is population growth rate.
Birth rate is the number of births occurring per 1000 population. Death rate is the number of deaths occurring per 1000 population. Since the values are taken per 1000, to find the percentage value the values are divided by 10.
Therefore, the formula used to find the growth rate of a population is Birth rate - Death rate = Growth rate.
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a 1500 kg vehicle is traveling on a curved, icy road. the road is banked at an angle of 10.0 degrees and has a radius of curvature of 400 m. the velocity of the car necessary to travel on the icy road without sliding is .
The vehicle speed required to drive on an icy road without sliding is 28.3 m/s.
The weight of the car is m = 1500 kg
The angle at which the road is inclined is θ = 10
The radius of curvature is r = 400m
The expression for the speed of the car required to travel on the road without sliding is V =[tex]\sqrt{rgtan}[/tex]
V =[tex]\sqrt{400*9.8*tan10}[/tex]
V = 28.3 m/s
Velocity is the rate of change in direction of an object in motion measured by a specific time standard and observed from a specific reference point (for example, 60 km/h north). A key idea in kinematics, the branch of classical mechanics that studies the motion of bodies, is velocity.
The definition of velocity requires both its magnitude and its direction, since it is a physical vector quantity. Velocity is a coherently derived unit that is measured in the SI (metric system) as meters per second (m/s or m/s1). Velocity is a scalar absolute value (magnitude) of speed.
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in this problem, you will use lenz's law to explore what happens when an electromagnet is activated a short distance from a wire loop. you will need to use the right-hand rule to find the direction of the induced current. the switch on the electromagnet, initially open, is closed. what is the direction of the induced current in the wire loop (as seen from the left)?
The magnetic fuse dropped and the field's magnetic direction remained the same when the switch was reopened in this case. following which the loop's current flows in a clockwise direction.
iron filings on paper placed above a bar magnet to represent the direction of magnetic direction. Compass needles point in the direction of the surrounding magnetic field, away from the north pole of a magnetic direction towards its south pole. The movement of electrical charge carriers like electrons is known as current. Positive and negative locations both experience current flow. The ampere is the SI unit for calculating electrical current (A). The movement of electrical charge carriers like electrons is known as current. Positive and negative locations both experience current flow. The ampere (A) is the SI unit used to measure electric current.
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A 3000 W oven is cooking your Sunday roast for 1 hour and
35 minutes. How much did it cost to cook it?
Cost estimated is ₹[19/4]y/-.
Given :- Power=3kW , Time=1hr 35min
Now to convert this time completely into hours following steps can be adopted:- 1 min =1/60 hour, so 35min =35/60 hour
35min= 35/60 =7/12 hour
So total computed time = 1hr + [7/12]hr
computed time =19/12hr
Now since in the question there is no mention about cost , so let the cost be ₹y/unit.
Mathematically , Energy is the product of power and time , i.e.
E= Power x Computed time = 3 x 19/12 = 19/4 units.
Now the energy estimated is 19/4 units whose cost equivalent will be ₹[19/4]y/- , as cost of one unit energy is ₹y/- so cost of 19/4 energy units will be ₹[19/4]y/-.
Once the cost of one unit energy is known to us then just its value in the place of y and we will get the exact amount expended on the total energy consumption.
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Two vehicles r moving in the same direction one has the velocity of 24m/s and another has 18m/s.find their relative velocity & also their relative velocity when they are in opposite direction
When a body is moving in the same direction, its relative speed is 6m/s, while when it is moving in the opposite direction, it is 42 m/s.
Describe relative velocity and its unit.The units used to measure speed and velocity are the same. The meter is the SI unit for measuring both distance and displacement. The second is the second as defined by the International System of Units. Two meters per second divided by two is the SI unit of velocity and speed.
What does Class 11 formula for relative velocity mean?It is calculable using an intermediary reference frame. The velocity vector sum can be used to represent this simply. vAB = vA - vB is the way to express the relative velocity formula.
velocity is the same as the relative velocities of A and B.
A=24,B=18
Vab=24-18=6m/s
In opposite direction
Vab=24-(-18)=42m/s
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The oxidation of copper(I) oxide, Cu 2 O ( s ) , to copper(II) oxide, CuO ( s ) , is an exothermic process. 2 Cu 2 O ( s ) + O 2 ( g ) ⟶ 4 CuO ( s ) The change in enthalpy upon reaction of 98. 93 g Cu 2 O ( s ) is − 100. 9 kJ. Calculate the work, w , and energy change, Δ U rxn , when 98. 93 g Cu 2 O ( s ) is oxidized at a constant pressure of 1. 00 bar and a constant temperature of 25 ∘ C. Note that Δ E rxn is sometimes used as the symbol for energy change instead of Δ U rxn
Copper II oxide is created through the oxidation of copper I oxide, cu2os cu2os. Cuo s An exothermic reaction is Cuo S. The formula is 2cu2o s)+ o2 G 4cuo S.
A simple definition of oxidation is what?Cu2O(s), a copper(I) oxide, is oxidized to copper(II) oxide, CuO, by exothermic processes (s). Cu2O(s), a copper(I) oxide, is oxidized to copper(II) oxide, CuO, by exothermic processes (s).
An oxidation reaction is a chemical process that takes place when an object comes into contact with oxygen or another oxidizing agent (OK-sih-DAY-shun). Oxidation is characterized by the brown hue of sliced apples and rust. In the past, the term "oxidation" was used to describe any chemical reaction that involved oxygen and an element. When magnesium metal and oxygen react, magnesium oxide is produced as a result, which serves as an illustration of this.
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A 1.80-kg block is suspended from a spring with a spring constant of 220.0 N/m. A 0.060-kg bullet is fired into the block from directly below with a speed of 270.0 m/s and is embedded in the block. (A) Find the amplitude of the subsequent motion. (B) What fraction of the original kinetic energy of the bullet appears as mechanical energy in the system of block-spring-bullet?
The fraction of the original kinetic energy of the bullet appears as mechanical energy in the system of block-spring-bullet is 0.72 m.
Amplitude=0.72 m
KE of system=0.5*(1.8+0.06)*8.7^2=70.39 j
Conservation of momentum
0.06*270=(1.8+0.06)*v
v=8.7 m/s
conservation energy
0.5*(1.8+0.06)*8.7^2=0.5*220*x^2+(1.8+0.06)*9.81*x
x=0.72 m
Amplitude=0.72 m
Original KE of bullet = 0.5*0.06*270^2=2187j
KE of system = 0.5*(1.8+0.06)*8.7^2=70.39 j
Amplitude in physics is stated to be the maximum displacement or distance that is moved by a factor on a body that is vibrating or wave measured from its equilibrium role.
As the pendulum swings through its equilibrium point (straight down), it swings to a maximum distance away from the center.
The amplitude of a wave is related to the amount of energy it includes. An excessive amplitude wave consists of a massive amount of power; a low amplitude wave consists of a small quantity of strength. Amplitude and intensity are associated, but not equal.
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a merry-go-round with a radius of 1.5 m is spinning at 2.0 rad/s when a young girl pushes on it for 5.0 revolutions applying an acceleration of 3.0 rad/s2. what is the final angular velocity of the merry-go-round?
The final angular velocity of the merry-go-round is 8 rad/s.
The radius of the Merry-go-round is 1.5 m and it is spinning with a speed of 2rad/s the girl pushes on it for 5 revolutions which applies and acceleration of 3rad/s².
The final angular velocity of the merry-go-round can be given by the equation,
W'² - W² = 2AS
Where,
W' is the final angular velocity,
W is the initial angular velocity,
A is the angular acceleration,
S is the angular displacement which is 10 rad in this case.
Putting values,
W'² - (2)² = 2(10)(3)
W' = 8rad/s.
So, the final angular velocity is 8rad/s.
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find the moment of inertia of a point of mass of 0.005g at a perpendicular distance of 3m from its axis of rotation.
Answer:
Explanation:
Given:
m = 0.005 g = 5·10⁻⁶ kg
R = 3 m
__________
J - ?
J = m·R² = 5·10⁻⁶·3² ≈ 45·10⁻⁶ kg·m²
Answer:
The snapshot of idleness of given point mass still up in the air by,
Where,
- snapshot of idleness
- mass = 0.005 g = ( 0.005/1000 ) = 5 × 10⁻⁶ kg
- opposite distance = 3 m
Put the qualities in the equation,
Hence; the snapshot of idleness of given point mass is 4.5 × 10⁻⁵ kgm².
To find out about snapshot of idleness,
Explanation:
Snapshots of dormancy can be found by adding or coordinating over each 'piece of mass' that makes up an article, increased by the square of the distance of each 'piece of mass' to the hub. In vital structure the snapshot of latency is I=∫r2dm I = ∫ r 2 d m .
For a planar item, the snapshot of idleness about a hub opposite to the plane is the amount of the snapshots of dormancy of two opposite tomahawks through a similar point in the plane of the article. The utility of this hypothesis goes past that of computing snapshots of rigorously planar items.
Picture result for track down the snapshot of idleness of a mark of mass of 0.005g at an opposite distance of 3m from its hub of revolution.
What is snapshot of inactivity of an empty circle about a hub going through its middle ? Arrangement : 'I = (2)/(3) MR^(2)', where 'M' is the mass and 'R' is sweep of the empty circle.
In which situation would the use of a vector quantity be most appropriate? (1 point)
determining the net force that is acting on an object
determining the high and low temperatures on any given day
determining whether it takes more time to melt ice or to melt butter
determining whether a van is moving faster than the speed limit
The situation that would be most appropriate to the use a vector quantity is determining the net force that is acting on an object.
option A is the correct answer.
What is vector quantity?Vector quantities are the physical quantities characterized by the presence of both magnitude as well as direction.
Examples of vector quantities include the following;
Displacement, force, torque, momentum, acceleration, velocity, etcScalar quantities, are those physical quantities that have only magnitude without direction. Example is temperature.
Thus, the situation that would be most appropriate to the use a vector quantity is the situation that needs to be described by both magnitude and direction.
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the graph below shows the position vs. time for a 932 kg cart moving along a horizontal track. To the nearest tenth of a kilojoule, what is the car's kinetic energy at 8.0 seconds?
Answer:use 1/2 x M x V^2
Explanation:
to calculate the kinetic energy, observe the velocity from the graph at 8.0 seconds. and use the formula!
One group approached their investigation by dropping a mass so it fell
vertically downward. They planned to measure the position of the mass as it
descended using a motion detector. They checked whether the motion
detector that they were using was sensitive enough to capture the motion
during the fall, and they were satisfied.
Given that they are measuring the motion (position, velocity, and
acceleration) of the mass, the students can only measure gravitational
potential energy and kinetic energy; any other form of energy is
undetectable. If they hope to see that energy is conserved in this system,
which of the following assumptions must be true (or approximately true)?
Air resistance is negligible. This must be
true.
The initial vertical velocity of the mass is negligible. [Select ]
It's true that air resistance is really low. Energy must not be gained or lost during the experiment if they expect to demonstrate that energy is conserved. In other words, there must be little loss from air resistance.
Describe the mechanism of air resistance.Air is the source of the force known as air resistance. An object travelling through the air experiences the force in the opposite direction. A sports vehicle with a streamlined form will face less air resistance than a lorry with a flat front, enabling the latter to travel faster.
The force of air resistance changes depending on the velocity. This implies that the acceleration is not constant and neither is the force. That is a serious issue.
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A ball is thrown horizontally with a velocity of 12m / s . How long will it take for the ball to hit the ground if it is released 3.5 m from the ground ? Assume no air resistance
A.3.4s
B.1.1s
C.0.85s
D.0.30s
The time taken by the ball is 0.30s.
What is the time taken?We know that the horizontal velocity has to do with the speed of the object has it moves along a horizontal path. In this case, we can see that the ball is thrown horizontally with a velocity of 12m / s. We have also been told in this question as we have it here to assume that there was no air resistance that is involved.
Thus we have;
Horizontal speed of the ball = 12m / s
Distance covered by the ball = 3.5 m
Let us see that;
V = s/t
V = speed
s = distance
t = time
t = s/V
We should now have;
t = 3.5 m/12 m/s
t = 0.30s
We can now see that the time that t would take the ball to hit the ground is 0.30 seconds of time.
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Answer:
Explanation:
Given:
Vₓ = 12 m/s
H = 3.5 m
g = 9.8 m/s²
__________
t - ?
According to the principle of independence of motion, we find the fall time from the formula:
H = g·t²/ 2
t = √ (2·H / g)
t = √ (2·3.5 / 9.8 ) ≈ 0.85 s
Correct answer:
C. 0.85 s
a 3 kg block starts from rest at the top of a 30 degree incline and slides a distance of 2 m down the incline in 1.50 seconds. find the magnitude of the acceleration of the block. find the coefficient of kinetic friction between the block and the ramp.
The magnitude of the acceleration of the block is 1.78m/s².
The coefficient of kinetic friction between the block and the ramp is 0.368.
How can I calculate the coefficient of kinetic friction?The resistive force of friction (Fr), which pushes the objects together, is divided by the normal or perpendicular force (N), which pushes them apart, to produce the coefficient of friction (fr), which is a numerical value. The following formula represents it: fr = Fr/N.
Given,
m=3.00kg, θ=30° ,
x= 2.00m, t=1.50s.
constant rate of acceleration,
[tex]X_{f} = v_{i} t[/tex] + 1/2at²
solving,
a = 2([tex]X_{f}[/tex]-[tex]v_{i} t[/tex])/t²
a = 2(2-0)/(1.5)²
a = 1.78m/s².
We have neither a burrowing-in nor a taking-off action when Newton's law is applied in the y direction, which is perpendicular to the inclination. The y component of acceleration is then equal to zero:
∑ [tex]F_{y}[/tex]=n–mgcosθ=0
Thus n=mgcosθ
Because f=[tex]\mu_{k}[/tex]n
[tex]\mu_{k}[/tex] = f/mgcosθ
[tex]\mu_{k}[/tex] = 9.37/3×9.8×cos30°
[tex]\mu_{k}[/tex] = 0.368.
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Point l is located a distance d2–√ from the midpoint between the two wires. Find the magnitude of the net magnetic field bl created at point l by both wires.
the magnitude of the magnetic field bl created at point l by both wires. is 0.0071 μI / d
since we know the formula we can refer to the magnetic field is
B= μI / 2πR
where I is the current flowing through the wires, R is the distance
Here Using the Pythagoras theorem
R= √d² + (2d)²
R = √d² + 4d²
r = √5d²
r = d√5
substituting the value of R in the formula, we get
= μI / 2π(d√5)
= μI / 2dπ√5
= (1 / 2π√5)(Iμ/d)
=0.0071 μI / d
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Use the information from the graph to answer the
What is the total displacement of the object?
question.
m
Velocity vs. Time
Velocity (m/s)
40
30
20
10
0
Time (s)
0
5
10
15
20
25
Answer:
The total displacement 560 m
Explanation:
Given:
t₀ = 0 s
t = 25 s
V₀ = 10 m/s
V = 35 m/s
___________
D - ?
Acceleration:
a = (V - V₀) / (t - t₀) = (35 - 10) / (25 - 0) = 25 / 25 = 1.0 m/s²
The total displacement:
D = V₀·t + a·t² / 2
D = 10·25 + 1.0·25² / 2 ≈ 560 m
a wheel and axle on a bicycle are designed with an axle radius of 0.125 meters and a wheel radius of 0.5 meters. if a force of 800 newtons is applied to the axle, what is the maximum output force of the bike wheel?(1 point)
The maximum output force of the bike wheel is equal to 40000 newtons.
The maximum output force of the bike wheel is calculated by using the equation:
F = R^2 * P, where F is the force exerted by the wheel on the axle, R is the radius of the axle, and P is the applied force. So we have: 800 N = (0.125 m)^2 * (800 N)
Rearranging gives us: 2 * R^2 = 800 N
Solving for R gives us: 0.5 m = 40000 N/m^2
This means that we must have a radius of 0.5 meters to produce an output force of 40000 newtons.
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Which of the following graphs represent an object at rest? (There could be more than one correct cho 0' 0' 0 0 graph a graph b graph c graph d
Graph A, because distance-time graph is a straight line parallel to the time-axis because the position of the object does not change when it is at rest.
Distance is the length between two points or items, and it is directionless. Since distance is a scalar attribute, it only takes into account the overall magnitude and ignores the start and end locations. Being a scalar attribute, distance may only be positive or zero; it cannot be the opposite.
Although kilometers (km) and centimeters (cm) or millimeters (mm) can also be used to express shorter distances, the meter (m) is the most used unit of measurement for distance (mm). When calculating distance, the letter D is usually used to denote the distance traveled.
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the magnitude of kf depends on the identity of the [ select ] and the magnitude of kb depends on the identity of the
magnitude of kf and the magnitude of kb depends upon the identity of solvent
what is kf and kb?Kf is the depression in freezing point produced by 1 molal solution of a nonvolatile solute while Kb is the elevation in boiling point produced by 1 molal solution of a nonvolatile solute.
Boiling point elevation is the difference in temperature between the boiling point of the pure solvent and that of the solution.
Molality is defined as the total number of moles of solute per kilograms of solvent present in the solution.
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Salem, Sabrina’s magical black cat, gets scared and jumps straight upward with an initial velocity of 20 m/s from a height of 115-meters.
Draw a velocity vs time graph to describe the cat’s motion for the first five seconds of motion.
What is the cat’s velocity and acceleration at it’s maximum height?
What is the cat’s velocity when it hits the ground?
How long does it take for the cat to hit the ground?
PLS HELP!!!!!
Considering a quadratic equation to model the height of the car, we have that:
The graph is given at the end of the answer.At the maximum height, the velocity is of zero and the acceleration is of -9.8 m/s².The velocity when the cat hits the ground is: -51.54 m/s.It takes 7.30 seconds for the cat to hit the ground.What is the quadratic equation for a projectile's height?Considering an acceleration = gravity of -9.8m/s², the equation for the height is given as follows:
h(t) = -4.9t² + v(0)t + h(0).
In which:
v(0) is the initial speed.h(0) is the initial height.Considering the values of these parameters for this problem, of v(0) = 20, h(0) = 115, the equation is:
h(t) = -4.9t² + 20t + 115.
At the maximum height point, we have that:
The velocity is of zero. (standard)The acceleration if of -9.8 m/s². (standard).The velocity function is:
v(t) = v(0) - gt
v(t) = 20 - 9.8t.
Which is the linear function graphed at the end of the answer.
The cat hits the ground at t > 0 for which h(t) = 0, hence:
-4.9t² + 20t + 115 = 0.
Which is a quadratic equation with coefficients given by:
a = -4.9, b = 20, c = 115.
Using a calculator, the positive solution for this equation is:
t = 7.30s.
At this instant, the velocity is:
v(t) = 20 - 9.8(7.3) = -51.54 m/s.
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the hydrogen in a star emits light at 484 nm as observed by an astronomer. which describes the motion of the star if the laboratory value of this spectral line of hydrogen is measured at 486 nm? question 9 options: approaching at 6.17 105 m/s moving away at 6.17 105 m/s approaching at 1.23 106 m/s moving away at 1.23 106 m/s
If the laboratory value of this hydrogen spectral line is detected at 486 nm, the star is moving toward us at a speed of 6.17 105 m/s.
How might Bohr's theory explain the hydrogen spectrum?In less than a year, Niels Bohr had a hydrogen atom model that "explained" the spectral lines. The energy level was a novel idea that Bohr introduced. Sharp spectral lines were released when an electron in hydrogen moved from one of its permitted energy levels, which were defined by the hydrogen atom.The wavelengths, measured from the scale, are 435 nm (purple), 486 nm (blue), and 657 nm (red).Hydrogen has numerous different energy levels while having just one electron. A photon is released when an electron in an object jumps from one energy level to another. Due to the various levels, those photons produce light with various colors and wavelengths.To learn more about Hydrogen atom model refer to:
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Which is an outer planet in our solar system?
A.Earth
B.Jupiter
C.Mars
D.Venus
Question:
Which is an outer planet in our solar system?
Answer:
B. Jupiter
Answer: Jupiter
Explanation: As its situated outside the asteroid belt
Describe the motion of a hockey puck between the instant the puck leaves a player's stick and the instant it hits something. (No "slap shot" allowed, the puck must remain in contact with the ice.)
Answer:
Explanation:
it will have constant friction, or slowing, as it slides along the ice.
a heavy brass ball is used to make a pendulum with a period of 5.5 s. part a how long is the cable that connects the pendulum ball to the ceiling? how long is the cable that connects the pendulum ball to the ceiling? 4.7 m 6.2 m 7.5 m 8.7 m request answer provide feedback
The length of the cable that connects the pendulum ball to the ceiling with a period of 5.5 s is 7.5 m
T = 2 π √ ( L / g )
T = Time period
L = Length of the pendulum
g = Acceleration due to gravity
T = 5.5 s
g = 9.8 m / s²
5.5 = 2 * 3.14 √ ( L / 9.8 )
√ L = 0.88 * √ 9.8
L = 0.77 * 9.8
L = 7.5 m
A simple pendulum consists of a mass suspended in air by a massless and unstretchable string that is fixed to a rigid support on the other end. The time taken to complete on oscillation is the time period of a simple pendulum.
Therefore, the length of the cable is 7.5 m
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What is the fastest speed a tennis ball can cross the net horizontally and still land in the court? from the net to the end line is 12 m, and the height of the net is 1 m. neglect air resistance and spin of the ball.
The maximum velocity of the tennis ball when it cross the net in order to still land in the court is 26.7 m/s
The trajectory of the tennis ball follow a projectile motion. When it cross the net, it can be considered it is at its maximum height.
At this position, the component of the velocity is only in x direction.
Vertical direction:
h = 1/2 . g t²
Where:
h = maximum height
g = acceleration due to gravity = 9.8 m/s²
t = time to land
Substitute h = 1 m
t² = 2/g = 0.204
t = 0.45 seconds
Horizontal direction:
x = v . t
12 = v . 0.45
v = 12 / 0.45 = 26.7 m/s
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