So, this is the diagram of the described situation, the strings are attached to a rigid support at their one end and the other end is connected to the particle.
Let, the string making an angle of 45 with the horizontal has a tension of T 1 and
the one making an angle of 30 has a tension of T2.
Now,
what we have done is that we have taken the vertical and
horizontal components of the tension in the two strings.
Now,considering the system to be in equilibrium,
see the diagram,the vertical component of the strings i.e
(T 1 sin 45 & T 2 sin 30) together will act to balance the weight of
the particle(mg)
So,we can say, T 1 sin 45 + T 2 sin 30 = mg. ...(1)
From horizontal equilibrium,we can say, T 1 cos 45 must balance T 2 cos 30 ,
as no other force is present in horizontal direction.
So,T 1 cos 45 = T 2 cos 30. ...(2)
Given,
mg = 10 ⋅ 10 = 100N
So, solving equation 1 & 2 we get,
T 1 = 89.65N and, T 2 = 73.20N
A 7500 kg truck traveling at 5.0 m/s east collides with a 1500 kg car moving
at 20 m/s in a direction 30 o
south of west. After collision, the two vehicles
remain tangled together. Find the speed and state the direction of car.
Since the collision is inelastic, both vehicle will move with a common velocity of 2.5 m/s in south east direction after collision.
Conservation of Linear MomentumIt states that, the sum of the momentum before collision is equal to the sum of the momentum after collision.
Given that a 7500 kg truck traveling at 5.0 m/s east collides with a 1500 kg car moving at 20 m/s in a direction 30° south of west. After collision, the two vehicles remain tangled together.
The given parameters are;
M1 = 7500 kgU1 = 5 m/sM2 = 1500U2 = 20 sin 30 = 10 m/sV = ?The formula to find the speed will be
M1U1 - M2U2 = (M1 + M2)V
7500 × 5 - 1500 × 10 = (7500 + 1500)V
37500 - 15000 = 9000V
22500 = 9000V
V = 22500/9000
V = 2.5 m/s
Therefore, the common speed will be 2.5 m/s and the direction of the car will be toward the south east.
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You are the commander of an exploratory mission
to a black hole. You launch a robotic probe on
a trajectory that will take it into the black hole.
The probe has an internal clock and sends a radio pulse back to your ship at a fixed interval, in
the reference frame of the probe. What effects do
you observe in the signals from the probe as it approaches the black hole? What might you observe
if the hole is rotating?
With increasingly long delays due mostly due to the increasing gravitationally time dilation affecting the probe when a trajectory that will take it into the black hole.
A black hole is a celestial object with a gravitational pull so powerful that nothing, not even light, can escape. A black hole can develop as a result of the death of a massive star. When its internal thermonuclear fuels run out at the end of its life, the center of such a star gravitationally collapses inward into itself, obliterating the star's outer layers.
The crushing weight of component matter crashing in from all directions causes the dying star to be crushed to a point with zero volume and infinite density known as the singularity. Black holes are often hard to observe directly due to their small size and the lack of any visible light from them.
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A rescue helicopter is lifting two people upwords as shown in the diagram below. The tension in the cable is 1205.4 N while the helicopter ascends at a Constant Speed ignore are resistance.
Explanation:
Let
T
be the tension of the cable and m
g
be the force of gravity. If the upward direction is positive, then Newton’s second law is T−mg=ma, where a is the acceleration. Thus, the tension is T=m(g+a). We use constant acceleration kinematics (Table 2-1) to find the acceleration (where v=0 is the final velocity, v
0
=−12m/s is the initial velocity, and y=−42m is the coordinate at the stopping point). Consequently, v
2
=v
0
2
+2ay leads to
a=−
2y
v
0
2
=−
2(−42m)
−12m/s
=1.71m/s
2
We now return to calculate the tension:
T=m(g+a)
=(1600kg)(9.8m/s
2
+171m/s
2
)
=1.8×10
4
N
If a runner maintains a constant speed of 12 km/h, how long will it take to complete a marathon race of 26.2 miles?
Answer:
below
Explanation:
First, convert 26.2 mi to km = 42.16 km
then 42.16 km / 12 km/ hr = 3.51 hr = 3 hr 30.8 m
The helicopter now starts to accelerate upwords at 2,25m.s-2. calculate the tension in the cable if the tension of the cable is 1205,4 N
Answer:
1205.4N
Explanation:
given. "if the tension of the cable is 1205.4N)
Question 12 of 34
A water faucet has a circular handle with radius 2.5 cm attached to a central
shaft with radius 0.50 cm. What is the mechanical advantage of the faucet
handle?
OA. 0.20
OB. 1.3
OC. 5.0
OD. 2.0
Answer:
C: 5
Explanation:
MA = radius of wheel/ radius of axle
MA =2.5/0.5
MA = 5.0
Water flows over a waterfall 16 m high, at the rate of 3,000 × 104 kg/s. If this water powers an electric generator with a 35% efficiency, how much electric power can be supplied? Present your answer in megawatts.
The amount of electric power supplied by the water that flows over a waterfall 16 m high at the rate of 3.00×10⁴ kg/s is 1646400 W.
What is electric power?Electric power is the rate at which electric energy is consumed in an electric circuit or system.
To calculate the electric power supplied by the water, we use the formula below.
Formula:
P = 0.35M'gh.............................. Equation 1Where:
P = Electric powerM' = Falling rate of the waterg = Acceleration due to gravityh = HeightFrom the question,
Given:
M' = 3.00×10⁴ kg/sh = 16 mg = 9.8 m/s²Substitute these values into equation 1
P = 0.35×16×9.8×30000P = 1646400 WHence, the amount of electric power supplied is 1646400 W.
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Two styrofoam balls are placed so their centers are 3.2 cm apart. The mass of one ball is twice the
mass of the other ball. The larger ball exerts a gravitational force of 2.63 X 10-12 N on the smaller ball.
Calculate the mass of each ball. (Use GUESS method.) Answer 4.49 X 10-3 kg, 8.99 X 10-3 kg
I was given the answers, I just want to know the working equation
Answer:
See below
Explanation:
Fg = G m1 m2 / r^2 Fg = force of gravity and
G, the gravitational constant = 6.6743x10^-11 m^3/(kg s^2)
m2 = 2 m1 is given, then sub in the values:
2.63 x 10^-12 = 6.6743 x 10^-11 ( m1)(2 m1) / ( .032)^2
results in 2 m1^2 = .00004035059
then m1 = .004491 kg and m2 is twice this much
mass 1 = 4.49 x 10^-3 kg as you stated
a person kicks a ball into the air with a force f0. the figure shows the position of the ball at various times. what is the net force on the ball and its acceleration at the highest point shown?
Answer:
force=mg+Fo
acceleration=0
Explanation:
A car accelerates from rest to 28 m/s in 3.5 seconds. What’s the acceleration
positive charge Q and a particle with a negative charge -Q. What will be the direction of the electric field at point P?
The direction of the electric field at a given point is determined by the relative magnitudes and positions of the charges involved. The electric field lines always point away from positive charges and towards negative charges. The strength of the electric field is greater when the charges are closer together.
At point P, the direction of the electric field created by a positive charge Q and a particle with a negative charge -Q will depend on the relative positions of the charges. Let's consider two scenarios:
1. If the positive charge Q is closer to point P than the negative charge -Q:
In this case, the positive charge Q will exert a stronger electric field compared to the negative charge -Q at point P. The electric field vectors will point away from the positive charge Q and towards the negative charge -Q. Therefore, the overall direction of the electric field at point P will be towards the negative charge -Q.
2. If the negative charge -Q is closer to point P than the positive charge Q:
In this scenario, the negative charge -Q will exert a stronger electric field compared to the positive charge Q at point P. The electric field vectors will point away from the negative charge -Q and towards the positive charge Q. Consequently, the overall direction of the electric field at point P will be towards the positive charge Q.
It's important to note that the direction of the electric field is independent of the charge of the test particle at point P. The electric field exists irrespective of the presence of a test charge, and its direction is determined solely by the configuration and positions of the charges creating the field.
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How long does it take a ball to fall 75.0m? (g = -9.81 m/s²)
O 15.3 m/s²
O 3.91 s
O 15.3 s
O 3.90 m/s²
Answer:
3.91 s
Explanation:
d = -75
a = -9.81
d = 1/2 at^2
-75 = 1/2 ( -9.81) (t^2)
75 = 1/2 ( 9.81) t^2 shows t = 3.91 s
Monkey Joe is trying to prove how strong he is by pulling a 5000 kg truck. He applies a force of 6000N at an angle of 30 below the horizontal. The coefficient of kinetic friction is 0.01.
Then I need help with all the parts to the question seen in the picture.
(h) The net force equation for y-direction is F(net)_y = F sinθ
(i) The normal force acting on the truck is 490,000 N.
(j) The force of friction acting on the truck is 490 N.
(k) The net force equation for the x - direction is F(net)_x = Fcosθ - Ff.
(l) The acceleration of the truck is 0.94 m/s².
What is free body diagram?A free body diagram (FBD) is a sketch of all the forces acting on object, indicating the direction of the applied force.
↑ N
Ff → Ф ← F
↓W
where;
N is the normal force on the blockW is the weight of the blockFf is the force of frictionF is the applied forceThe net force equation for y-direction is calculated as follows;
F(net)_y = F sinθ
The normal force acting on the truck is calculated as follows;
Fn = mg
where;
Fn is the normal force on the truck acting upwardsm is mass of the truckg is acceleration due to gravityFn = 5000 x 9.8
Fn = 49,000 N
The force of friction acting on the truck is calculated as follows;
Ff = μFn
where;
μ is coefficient of frictionFn is normal forceFf = 0.01 x 49,000 N
Ff = 490 N
The net force equation for the x - direction is written as;
F(net)_x = Fcosθ - Ff
where;
F cosθ is the force applied along the x-directionFf is force of frictionF(net) = 6000 x cos(30) - 490
F(net) = 4,706.15 N
The acceleration of the truck in the sleeping bag is calculated as follows;
a = F(net) / m
a = (4,706.15) / (5000)
a = 0.94 m/s²
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when a roller coaster gets to the bottom of a descent, describe the energy transfers and changes to energy stores that happen if:
a) the brakes are applied
b) it goes up and over a second hill
a) At the application of the brakes, there is a conversion of kinetic to potential energy.
b) When it climbs the second hill, the kinetic energy of the roller coaster is now converted to potential energy.
What is the conservation of energy?Let us recall that according to the principle of the conservation of energy, energy can neither be created nor destroyed but it can be transformed from one form to another. In the roller coaster, we can see the principle of energy transformation at work. This is one of the easiest ways that we could use to be able to describe the conservation of energy.
When a break has been applied in the roller coaster, there is a consversion of energy from kinetic energy to potential energy. Recall that the kinetic energy has to do with the energy that is in motion. This is converted to the potential energy of a stationary roller coaster.
Again when the roller coaster goes up a second hill, there is a change from kinetic to potential energy that the roller coaster would possess at the top of the hill.
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A body is thrown downwards with a velocity of 10ms. Assuming the acceleration due to gravity
is 10ms calculate its displacement after 2s?
s(displacement) = 40m , when a body is thrown towards with a velocity of 10ms.
What is velocity?It can be defined as the distance covered by an object in unit time.
What is displacement?Displacement is defined to be the change in position of an object.
What is acceleration?Rate at which velocity changes with time, in terms of both speed and direction.
How to calculate displacement after 2s when initial velocity is 10ms?S = ut + 1/2 at²
where, S = displacement (m)
u = initial velocity (ms)
a = acceleration (g=10m/s²)
t = time (s)
S = 10×2 + 1/2 × 10(2)²
S = 40m
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A 500 kg roller coaster car pauses at the top of a 40 m hill before rolling without friction to the bottom. Determine the speed of the car at the bottom of the hill
Answer:
v = 28 m/s
Explanation:
Since energy is conserved:
Eg = Ek
mgh = 1/2mv^2
masses cancel
gh = 1/2v^2
(9.8)(40) = 1/2v^2
(2)(40)(9.8) = v^2
v = sqrt(784)
v = 28 m/s
Should the air temperature be less or greater than the temperature in the pool to avoid condensation in an indoor swimming pool?
The temperature in the pool to avoid condensation in an indoor swimming pool is cooler than air temperature.
Temperature :
Temperature is the degree to which an object is hot or cold.Its SI unit is kelvin (K).Humidity:
The amount of water vapour in the air is known as humidity.
The humidity will be high if there is a lot of water vapour in the atmosphere. It feels wetter outside as the humidity
In indoor pools, the relative humidity should be kept between 50 and 55 percent at a temperature of around 26 degrees in the winter and 23 degrees in the summer.
The temperature in the pool to avoid condensation in an indoor swimming pool is cooler than air temperature.
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when 2cm tall object is placed in front of converging lens,0.5 cm long real image is formed 11cm away from object find its focal length
The focal length of the lens is 14.67 cm.
The focal length of an optical device is a measure of how strongly the machine converges or diverges mildly; it's miles the inverse of the system's optical electricity. A wonderful focal length suggests that a system converges mildly, while a negative focal duration shows that the system diverges mildly.
Calculation:-
himage/h object = f-v/f
0.5/2 = f - 11/f
0.25f = f - 11
11 = f - 0.25f
11 = 0.75f
f = 11/0.75
f = 14.67 cm
The focal length ( f ) is the gap from a lens or reflects the point of interest ( F ). this is the distance from a lens or replicates at which parallel mild rays will meet. The focal period of (left) a concave lens (with a negative focal length), (middle) a convex lens and. (right) a concave replicate.
The distance from the center of the lens to the photo focal factor (=image sensor floor) is referred to as the focal period. Its miles are expressed in millimeter (mm) gadgets. A lens with a brief focal duration is an extensive-perspective lens and one with a protracted focal length is a telephoto lens.
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Two microscopic bags each contain two protons. When separated by distance d, electric force on one due to the other is F. When you transfer a proton from one to another without changing anything else. The electric force now is
Two microscopic bags each contain two protons. When separated by distance d, electric force on one due to the other is F. When you transfer a proton from one to another without changing anything else. The electric force now is ¾F.
What is electric force?Electric force is described as the repulsive or attractive interaction between any two charged bodies.
The electric force is one of the various forces that act on objects and has its impact and effects on the given body which is described by Newton’s laws of motion.
The electric force between two electrons is equal to the electric force between two protons when placed at equal distances and this describes that the electric force is not based on the mass of the object, but depends on the quantity known as the electric charge.
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The maximum force that wire A can withstand without breaking is 2000 N. Wire B is made of the same material as wire A but has twice the diameter.
What is the maximum force that wire B can withstand?
The maximum force that wire B can withstand is same as A.
What is force?A force is an effect that can alter an object's motion according to physics. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to describe force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.
The gravitational constant, denoted by the capital letter G, is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's theory of general relativity.
For wire diameter do not effect the force it can withhold so, A and B and have same force 2000 N.
The maximum force that wire B can withstand is same as A.
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A scientist is measuring the height of water hyacinths on 30 ponds. How important is the degree of accuracy of the measurements he gathers? Explain your answers
The degree of accuracy is very important in the measurement of various heights of water hyacinths on ponds to limit errors from its true value.
What is the importance of degree of accuracy for measuring height of water hyacinths?The water hyacinths are a type of aquatic plants that grows in shallow ponds, marshes, small streams, lakes and rivers.
The water hyacinths are very useful to the environment as they reduce water pollution and process as animal feed, compost, and bioenergy.
During measurements in experiment, the accuracy of such measurements should be out under consideration to avoid occurrence of errors.
Although the measurement of the water hyacinth would be gotten from 30 ponds, it's necessary to prevent errors by maintaining accurate heights gotten from each pond as it would act as final value at the end of the experiment.
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A 1275 kg car travels 10 meters in 40 seconds. What is the car’s power?
Using velocity we will get the car’s power is 46.48 m/s.
What is velocity?
velocity is directional speed of a object in motion as an induction of it's rate of change in position observed from a particular frame of reference and as measured by a particular standard of time.
Sol- The linear momentum of a body is defined as the product of its mass and its velocity given by-
P = mv
According to the question the momentum of the truck is-
Pr=2250×25 kgm /s
Pr=56250 kgm/s
Now we can see the momentum of the car and the truck must be same that is Pc=Pr
1210×v =56250 kgm/s
v= 56250/1210
v= 46.48 m/s
Thus the velocity of the car is 46.48m/s .
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(8.6) A space station in deep space is spun like a giant wheel to produce centrifugal force so the occupants experience artificial gravity of one g. How does a clock at the rim of the space station compare with one residing at the hub? What does this say about the behavior of a clock sitting on the surface of a planet with a surface gravity of one g?
The way that the clock at the rim of the space station compare with one residing at the hub is that Rim clock will always runs slower.
The behavior of a clock sitting on the surface of a planet with a surface gravity of one g is the same.
Is there a timepiece on the ISS?For instance, timekeeping on the International Space Station (ISS) is slightly slower than that of reference clocks on Earth. This explains why astronauts on the International Space Station (ISS) mature more slowly, lagging by 0.007 seconds every six months.
Ground-based atomic clocks have served as the industry standard for timekeeping since the 1950s. These clocks use the extremely steady and accurate frequencies of light emitted by particular atoms to keep time.
Therefore, Satellite clocks run slower due to more velocity but faster due to reduced gravity. Clocks move more slowly at the ISS orbital height because velocity dominates. At GPS altitude, clocks move more quickly due to the influence of gravity.
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A car has a weight of 8000 N. The car is supported by four tyres.
The weight on each tyre is equal.
The area of one tyre in contact with the ground is 150 cm².
Calculate the pressure that one tyre exerts on the ground.
Show your working and give your answer in N/cm².
Answer: A
Explanation:
A 2.0 kg block is pushed 2.0 m at a constant
velocity up a vertical wall by a constant force
applied at an angle of 30.0
◦ with the horizontal, as shown in the figure.
The acceleration of gravity is 9.81 m/s
2
.
For a 2.0 kg block is pushed 2.0 m at a constant velocity up a vertical wall by a constant force applied at an angle of 30.0, the work done is 8.3 J
What is Work Done?This refers to the term that shows the product of the displacement of an applied force in a given direction.
Hence, the calculations are:
The work done by a force pushing an object is given by:
W= Fdcos[tex]\alpha[/tex]
where
F is the magnitude of the forced is the displacement of the object[tex]\alpha[/tex] is the angle between the direction of the force and of the displacementd= 1m
[tex]\alpha[/tex] = 63 degrees
W= (18.3)(1)(cos 63 degrees)
=8.3J
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A 2.0 kg block is pushed 1.0 m at a constant
velocity up a vertical wall by a constant force
applied at an angle of 27.0
◦ with the horizontal, as shown in the figure.
The acceleration of gravity is 9.81 m/s
2.
If the coefficient of kinetic friction between
the block and the wall is 0.40, find
a) the work done by the force on the block.
Moving electric charges, or currents, give rise to?
A. Magnetic fields
B. Stored energy
C. Decreases in temperature
D. Potential energy
Answer:
A =Magnetic fields
Explanation:
Jason Bourne drives his stolen Audi A6 at 25 m/s across the roof of a parking garage and off the edge. The lower parking deck is 18.6 m below.
A. How far out from the edge will he land?
B. With what speed will he hit (magnitude and direction)?
A. The distance from the edge that the car will lad is 48.75 m.
B. The velocity it hit the ground with, v is 19.1 m/s in the forward direction.
What distance from the edge will the car travel at a velocity of 25 m/s?The distance from the edge will the car traveling at a velocity of 25 m/s is calculated as follows:
Distance = velocity * timeTime taken = √(2h/g)
where h is the height = 18.6 m
g is the acceleration due to gravity = 9.8 m/s²
t = √(2 * 18.6/9.8)
t = 1.95 seconds
Distance = 25 * 1.95
Distance = 48.75 m
The velocity it hit the ground with, v is calculated as follows:
v²= u² + 2gh
where;
u is initial vertical velocity = 0
g = 9.8 m/s²
h = 18.6 m
v = √2gh
v = √(2 * 9.8 * 18.6)
v = 19.1 m/s in the forward direction.
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Which of the following choices is an example of gathering evidence? OA. Forming opinions. OB. Taking measurements OC. Asking questions. OD. Drawing conclusions. SUB
The following choice is an example of gathering evidence in Taking measurements. Option B.
The scientific method is the process of objectively establishing facts through testing and experimentation. The basic process is to make observations, form hypotheses make predictions conduct experiments and finally analyze the results. Accurate readings are evidence-based.
Without evidence the author just states his opinion. So writing an essay begins with gathering evidence long before writing it. The advantage of naturalistic observation is that the researcher can directly observe the subject in its natural environment. This method gives scientists direct insight into social behavior and helps them realize things they might not have encountered in a laboratory setting.
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A ladder with mass, m= 10.8 kg and length, L= 10.5 m is leaning against a frictionless wall. If the ladder makes an angle of 72 degrees with the ground, what is the horizontal force exerted by the ladder on the wall? Give the answer in newtons (N) and rounded to three significant figures.
430.9 N is the horizontal force exerted by the ladder on the wall
Torque=FLsinθ
m=10.8kg
L=10.5m
g=9.8 ms²
θ=72
Torque=FLsinθ
Torque=1111.32×sin 72
Torque=430.9 N
In mechanics, a force is any action that seeks to preserve, modify, or deform a body's motion. Isaac Newton's three principles of motion, which are outlined in his Principia Mathematica, are frequently used to illustrate the idea of force (1687).
Newton's first law states that unless a force is applied to a body, it will stay in either its resting or uniformly moving condition along a straight path. According to the second law, when an external force applies on a body, the body accelerates (changes velocity) in the force's direction.
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An airplane is taking off from the runway. The airplane accelerates from its initial velocity of 48 m/s and needs to be going 84 m/s in order to be able to take off. They have to take off before they reach the end of the 2965 m. Include known-unknown tables as part of your answer
A. What is the acceleration of the airplane as it heads down the runway?
B. How long does it take for the airplane to reach the end of the runway?
Answer:
A. The acceleration of the airplane is 36 m/s2.
B. It takes the airplane 82.5 seconds to reach the end of the runway.
C. The final velocity of the airplane is 84 m/s.