The average force exerted on the ball by the glove will be 129 N.
What is force?Force is defined as the push or pulls applied to the body. Sometimes it is used to change the shape, size, and direction of the body. Force is defined as the product of mass and acceleration. Its unit is Newton.
Given data;
Mass,(m)=0.15-kilogram
Initial speed,u=43 meters per second
Time period,t= 0.050 seconds
Average force exerted,F=?
The average force exerted on the ball by the glove is;
[tex]\rm F = m\frac{v-u}{t} \\\\ F=0.15( \frac{43-0}{0.050} )\\\\ F=129 N[/tex]
Hence, the average force exerted on the ball by the glove will be 129 N.
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A car is traveling along a straight road at a velocity of 30m/s when its engine cuts off. For the next ten seconds, the car slows down, and its average acceleration is a₁. For the next five seconds, the car slows down further, and its average acceleration is a₂. The ratio of the average acceleration values is a₁/a₂=1.5. Find the velocity of the car at the end of the initial ten-second interval.
The velocity of the car at the end of the initial ten-second interval is 15a₂ + 30.
Initial velocity of the carv = u + at
after 10 seconds;
v = 30 + 10a₁ --(1)
after 5 seconds
v₂ = v + 5a₂ ---- (2)
solve (1) and (2) together
v₂ = 30 + 10a₁ + 5a₂
but a₁/a₂=1.5
a₁ = 1.5a₂
v₂ = 30 + 10(1.5a₂) + 5a₂
v₂ = 30 + 15a₂ + 5a₂
v₂ = 30 + 20a₂
from equation (2), v₂ = v + 5a₂
v + 5a₂ = 30 + 20a₂
v = 15a₂ + 30
Thus, the velocity of the car at the end of the initial ten-second interval is 15a₂ + 30.
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How to magnetic stripes provide evidence of seafloor spreading
Magnetic stripes provide evidence of seafloor spreading due to their occurrence in the region of sea floor.
How to magnetic stripes provide evidence of seafloor spreading?When the Earth's magnetic field reverses, a new stripe starts to form. Such magnetic patterns enable the scientist to recognize the occurrence of sea-floor spreading and provides strongest evidence for the theory of plate tectonics.
So we can conclude that magnetic stripes provide evidence of seafloor spreading due to their occurrence in the region of sea floor.
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A ball is projected with initial velocity 50m/s at an angle of elevation of 37 degrees from the top of a cliff 55 m high. Calculate the total time the ball is in the air and the maximum horizontal distance covered.
The total time the ball is in the air is 1.47 s and the maximum horizontal distance covered is 58.7 m.
Time of motion of the ball
The time of motion of the ball is calculated as follows;
h = vt + ¹/₂gt²
55 = (50sin37)t + ¹/₂(9.8)t²
55 = 30.1t + 4.9t²
4.9t² + 30.1t - 55 = 0
Solve using formula method;
t = 1.47 s
Horizontal distance of the ballX = vxt
where;
vx is the horizontal velocityt is time of motionX = (50 x cos37) x 1.47
X = 58.7 m
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A stone is dropped from the top of a tower which touches the ground after 2 seconds. Calculate the speed of the stone hitting the ground surface. (g = 9.8 m/s²)
Answer:
19.6 m/s
Explanation:
The velocity is the product of acceleration and time.
__
Here, the acceleration is due to gravity.
v = at
v = (9.8 m/s²)(2 s) = 19.6 m/s
The stone hits the ground with a speed of 19.6 m/s.
A stone is dropped from the top of a tower which touches the ground after 2 seconds.
Calculate the speed of the stone hitting the ground surface. (g = 9.8 m/s²).[tex] \mathbb{SOLUTION:} [/tex][tex]v = u + at[/tex][tex]v = 9.8 m/s² x 2sec[/tex][tex]v = 19.6 \: m/ {s}^{2} [/tex]••••••••••••••••••••••••••••••••••••••••••••Hence, The stone hit the ground with the velocity speed of 19m/s².
- When you're solving velocity, you're determining how fast an object moves from its original position, with respect to a frame of reference, and a function of time.
- That means an object's velocity will be equal to the object's speed and direction of motion.
"Problem has been solve"
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A solenoid with 465 turns has a length of 8.00 cm and a cross-sectional area of 3.10 ✕ 10−9 m2. Find the solenoid's inductance and the average emf around the solenoid if the current changes from +3.50 A to −3.50 A in 7.83 ✕ 10−3 s
The solenoid's inductance and the average emf around the solenoid if the current changes from +3.50 A to −3.50 A in 7.83 ✕ 10−3 s will be 1.01 ×10⁻⁸ H and 9.02 × 10⁻² V.
What is a solenoid?A coil of wire that carries an electric current is a solenoid. A solenoid is an electromagnet formed by a helical coil of wire.
Which generates a magnetic field when an electric current is passed through the coil.
A solenoid is a form of coil that produces a magnetic field when the electric current is passed through it. A solenoid is created when a conductive wire is used to make a loop.
Given data;
Turns ,N = 465
Length,L= 8.00 cm
Cross-sectional area,A = 3.10 ✕ 10−9 m2.
Solenoid's inductance, L=?
The average emf around the solenoid, E=?
Time of flow,t= 7.83 ✕ 10−3 s
Current changes from +3.50 A to −3.50 A
The inductance of the solenoid is found as;
[tex]\rm L = \frac{\mu_0 AN^2}{L} \\\\ \rm L = \frac{4 \times \pi \times 10^{-7}\times 3.0 \times 10^{-9} \times (465)^2 }{8.00 \times 10^{-2}} \\\\ L= 1.01 \times 10^{-8} \ H[/tex]
The average emf around the solenoid is found as;
[tex]\rm e = L \frac{I_2-I_1}{t} \\\\ \rm e = 1.01 \times 10^{-8} \times \frac{3.50-(-3.50)}{7.83 \times 10^{-3}} \\\\ e =9.02 \times 10^{-12} \ V[/tex]
Hence, the solenoid's inductance will be 1.01× 10⁻⁸ H.
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3. Sarah is a world-class diver in the women's 3-m springboard competition. Her height
h (in metres), above the water t seconds after she leaves the board is given by
h = -4.9t2 + 8.8t + 3. How long is Sarah in the air before she reaches the water?
Make sure to round your answer to the nearest tenth.
Answer:
2011, 2013, 2016 Alberta Education
Answer:
1.163 seconds
Explanation:
see the attached. solve the quadratic equation.
A skier (m=55.0 kg) starts sliding down from the top of a ski jump with negligible friction and takes off horizontally.
a. If h = 6.50 m and D = 11.4 m, find H.
b. Find her total kinetic energy as she reaches the ground.
a. The value of H is 11.51 m
b. The total kinetic energy as she reaches the ground is 6.21 kJ.
The mechanical energy is the sum of kinetic energy and the potential energy of an object at any instant of time.
M.E = KE +PE
Given is a skier (m=55.0 kg) starts sliding down from the top of a ski jump with negligible friction and takes off horizontally. Value of h = 6.50 m and D = 11.4 m.
Time taken to reach the ground after take off is
t = √2h/g
t = √(2x6.50) /9.81
t =1.15 s
The speed at that time is
speed = distance /time
v = 11.4 /1.15
v = 9.913 m/s
a. From energy conservation principle,
v = √2g(H-h)
Plug the values, we get
9.913 = √(2 x 9.81 (H - 6.5)
Squaring both sides and solving, we have
H = 11.51 m
Thus, the value of H is 11.51 m.
b. The energy at the ground will be only potential energy
Total kinetic energy at the ground = mgH
T.K.E = 55 x 9.81 x 11.51
T.K.E =6.21 kJ
Thus, the total kinetic energy is 6.21 kJ.
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what is the energy of a photon with a frequency of 8.34 x 10^14 hz, in joules?
Answer:
E = 5.52 x 10⁻¹⁹ J
Explanation:
The formula for energy of a photon, E, is:
[tex]E = hf[/tex]
where h is Plank's constant = 6.62 x 10 ⁻³⁴ .
Using the formula:
E = 6.62 x 10⁻³⁴ x 8.34 x 10¹⁴
= 5.52 x 10⁻¹⁹ J
Two particles P and Q each moves towards ther along Straight Line (M)(N), 51m long. P starts from M with velocity 5m/s and constant acceleration Of 1m/s². Q Starts from N at the Same time with velocity 6m/s and at a Constant acceleration of 3m/s². find the time when the
a) Particles are 30m apart, 13
b) Particles meet
c) velocity of P is ¾ of the velocity of Q
The time required by the particles are as follows:
a. t = 1.5 seconds
b. t = 3 seconds
c. t = 0.4 seconds
What is the time required?The time required for the particles to be at several distances apart is calculated using the equation of motion given below:
[tex]S = ut + \frac{1}{2}at^{2}[/tex]
a) Time required to be 30 m apart:
Assuming the distance covered by P is S1 and distance covered by Q is S2.
S1 + S2 = 51 - 30
S1 + S2 = 21
Substituting the values of velocity and acceleration in the equation of motion above:
5t + 1/2t^2 + 6t + 3t^2 = 21
2t^2 + 11t - 21 = 0
Solving for time, t by factorization, t = 1.5 seconds
b) Time required to meet:
Assuming the distance covered by P is S1 and distance covered by Q is S2.
S1 + S2 = 51
Substituting the values of velocity and acceleration in the equation of motion above:
5t + 1/2t^2 + 6t + 3t^2 = 51
2t^2 + 11t - 51 = 0
Solving for time, t by factorization, t = 3 seconds
c) Time required for velocity of P is ¾ of the velocity of Q:
Using the equation of motion: V = u + at
Vp = 3/4 Vq
4Vp= 3Vq
Substituting the values:
4(5 + t) = 3(6 + 3t)
5t = 2
t = 0.4 seconds
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In a small village in southern Italy, childbirth is considered?
Answer:
a community event
Explanation:
How do we solve questions C and D? I already did A and B and I am confused on how to continue
(a) The work done in moving the unit charge from point C to A is 7.62 x 10⁻³ J.
(b) The work done in moving the unit charge from point D to B is 7.62 x 10⁻³ J.
Work done in moving the charge from C to A
W = Fd
W = Kq²/d
from 0 origin to C, d = √(5² + 5²) = 7.07 mfrom 0 origin to A, d = 5 mW(C to A) = W(0 to C) + W(0 to A)
[tex]W(C \ to \ A) = - \frac{Kq^2}{7.07} + \frac{Kq^2}{5} \\\\ W(C \ to \ A) = 0.0586 \ Kq^2\\\\W(C \ to \ A) = 0.0586 \times 9 \times 10^9 \times (3.8\times 10^{-6})^2\\\\W(C \ to \ A) = 7.62 \times 10^{-3} \ J[/tex]
Work done in moving the charge from D to Bfrom 0 origin to D, d = √(5² + 5²) = 7.07 mfrom 0 origin to B, d = 5 mW(D to B) = W(0 to D) + W(0 to B)
W(D to B) = 7.62 x 10⁻³ J
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Which statement is a true catalyst in a reaction
Answer:
it alters the rate of chemical reaction
hope it is useful
A ball A of mass 0.5 kg moving with a Velacity of 10 m/s a head on Collision with a ball B of mass 2kg moving with a Velocity of 1ms in the oppoite direction. If A and B stick together after Collision, Calculate the Common Velocity in the direction of A
Answer:
The common velocity v after collision is 2.8m/s²
Explanation:
look at the attachment above ☝️
a highway curve has a radius of 300 m. at what angle should it be banked for a traffic speed of 100 km/h
The angle at which it should be banked for a traffic speed of 100 km/h is
14.57°.
How do find the angle of Banking of road?Banking of roads is the practice of raising the outer borders of curving roads over the inner edge in order to give vehicles the necessary centripetal force to make a turn safely.Skidding can be prevented by banking.The banking of roadways aids in preventing toppling or overturning.To find the angle of banking following formula can be used,
[tex]tan \alpha = v^{2} /rg[/tex]
Given v = 100km/h or
= 100 x 1000 / 3600
= 27.7 m/s
Hence,
[tex]tan \alpha = (27.7)^{2} / 300 * 9.81[/tex]
[tex]tan\alpha = 0.26[/tex]
[tex]\alpha = tan^{-1} 0.26[/tex]
[tex]\alpha = 14.57[/tex]°
Hence, the angle of banking of the road will be 14.57°
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A skateboarder starts from rest and maintains a constant acceleration of 0.50 m/s² for 8.4 s. What is the rider's displacement during this time
meters
Answer:
4.2m/s
Explanation:
0.50x8.4=4.2m/s
Which sentence uses the subjunctive mood correctly?
A. Americans take fewer vacations than people in many other
nations.
OB. It's best that Marci learns how to do her own laundry.
C. It is important that she apologize to her sister for what she said.
D. Be sure to put your dirty clothes in the hamper, not next to it.
The sentence that uses the subjunctive mood correctly is as follows:
Be sure to put your dirty clothes in the hamper, not next to it.Thus, the correct option is D.
What is Subjunctive mood?Subjunctive mood may be defined as statements or actions that are in the probable situation of doubt and suspicion.
Except for the sentence fourth, the rest all indicates the factual concept with the appropriate condition.
Therefore, the correct option for this question is D.
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Answer:
C. it is important that she apologize to her sister for what she said
Explanation:
test approved
In infrared satellite images, land appears _________ and clouds appear _________. A. red, yellow B. white, black C. black, white D. yellow, red
In infrared satellite images, land appears black and clouds appear white. C
What are infrared satellite images?Infrared satellite images are images produced as a result of electromagnetic radiations reflected or emitted from a target surface in the infrared position of the electromagnetic spectrum.
On infrared images, the clouds emit very bright white color because of the low temperature and the land appears to be black because of the hot temperature.
Therefore, in infrared satellite images, land appears black and clouds appear white. C
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The practice of science can answer only scientific questions. And scientific
questions guide the design of investigations. What must be true of the
possible answers to a scientific question?
OA. They could be shown to be false by evidence.
B. They are at odds with established scientific theories.
C. They support an established scientific theory.
OD. They do not require the use of physical measurements.
SUBMIT
Evidence might be used to demonstrate their falsity. must apply to all potential solutions to a scientific topic.Option A is correct.
What is a Scientific hypothesis?A scientific hypothesis is the main element in the scientific method and experiment.
It is said that a hypothesis is a scientific hypothesis. The majority must agree on it, or it must be done after thorough experimentation.
Only scientific inquiries can have their answers provided by scientific endeavor. Scientific concerns have an impact on the research's design as well.
Evidence might be used to demonstrate their falsity. must apply to all potential solutions to a scientific question.
Hence option A is correct.
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A rocket is fired with an initial Velocity OF 100m/s at an angle OF 55 above the horizontal, It explodes on the mountain Side 12s after its Firing What is x-and y-coordinates of the rocket relative to its Firing point?
Answer:
( 688.29 , 276.66 ) meters
Explanation:
Break into horizontal and vertical components
x = 100 cos 55 = 57.36 m/s
the x coordinate is then 12 seconds * 57.36 m/s = 688.29 meters
y coordinate is a bit more complex because of the curved path due to gravity
Original y velocity = 100 sin 55
y = vo t - 1/2 (9.81)(t^2)
y = 100 sin 55 (12) - 1/2 (9.81) (12)^2
yf = 276.66 meters
A uniform, 255 N rod that is 1.80 m long carries a 225 N weight at its right end and an unknown weight W toward the left end. When W is placed 60.0 cm from the left end of the rod, the system just balances horizontally when the fulcrum is located 75.0 cm from the right end.
Part a) Find W.
Part b) If W is now moved 20.0 cm to the right, how far must the fulcrum be moved to restore balance? Δx = ?
Part c) If W is now moved 20.0 cm to the right, in what direction must the fulcrum be moved to restore balance?
(a)The value of W for the given condition will be 237.3 N.
(b)The distance must the fulcrum be moved to restore balance will be 0.070 m.
What is the center of mass?A location is established in relation to an object or set of objects in the center of mass. It is the system's average position across all of its components.
Given data;
Weight is applied to the right end of the rod, W₁= 225 N
Rod's weight,W₂ = 255
W₃ is the Weight at "x" distance from the left end.
x1 is the location of W₁ with respect to the left end, where L = 1.80 m
m is the location of the rod's center of mass from the left end.
The position of W from the left end; x₃ = 50 cm = 0.50 m
Xcm is the position of the center of gravity of the rod at the fulcrum from the left end;
Given that the fulcrum is balanced in this situation, the rod's center of gravity will be there.
Xcm= L - 75 cm
Xcm=1.80 m - 0.75 m
Xcm= 1.05 m
The value of x₂
x₂= 1.80 m/2 = 0.90 m
Currently, the horizontal center of gravity is determined by
[tex]\rm X_{cm} =\frac{ (W_1x_1 + W_2x_2 + W_3*x_3)}{(W_1 + W_2 + W_3)}[/tex]
Substitute the values we get;
[tex]\rm 1.05 = \fraca{ (225 \times 1.80 + 255\times 0.90 + W\times 0.50)}{(225 + 255 + W)}\\\\ W = \frac{ (225\times 1.80 + 255\times 0.90 - 480 \times 1.05)}{(1.05 - 0.50)}\\\\ W = 237.3 \ N[/tex]
After moving the fulcrum 20.0 cm to the right,
The location of the W from the left end;
x₃ = .50 cm + 20 cm
x₃ = 70 cm
x₃ = 0.70 m
W₁, W₂, W, x₁, and x₂ have fixed values. Therefore, based on these values, the new center of gravity will be:
[tex]\rm X_{cm} =\frac{ (W_1x_1 + W_2x_2 + W_3*x_3)}{(W_1 + W_2 + W_3)}[/tex]
[tex]\rm X_{cm} = \frac{(225\times 1.80 + 255\times 0.90 + 237.3\times 0.70)}{(225 + 255 + 237.3)}\\\\ X_{cm} = 1.12 m[/tex]
Fulcrum must be shifted by;
Y = (1.12 - 1.05)
Y= 0.070 meters.
W has been moved in the appropriate direction, thus the fulcrum should likewise be moved in the appropriate direction.
Hence, the value of W for the given condition will be 237.3 N. and the distance must the fulcrum be moved to restore balance will be 0.070 m.
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pleaseeeeeee I need HELP in 20 mins,Asap!!!
A 6.00 -kg clay ball is thrown directly against a perpendicular brick wall at a velocity of 22m/s^2 and shatters into three pieces, which all fly backward. The wall exerts a force of 2640N on the ball of for 0.1s. One piece of mass 2kg travels backward at a velocity of 10m/s and an angle of 32° above the horizontal. A second piece of mass 1kg travels at a velocity of 8m/s and an angle of 28° below the horizontal. What is the velocity of the third piece?
The velocity of the third piece is 124.02 m/s at 1.05⁰ below the horizontal.
Velocity of the third piece
The velocity of the third piece is calculated from the principle of conservation of linear momentum.
mu = m₁u₁ + m₂u₂ + m₃u₃
where;
m is mass of the clayu is velocity of the clayu₁ is velocity of first pieceu₂ is velocity of second pieceu₃ is velocity of third piecem₃ is mass of the third piece = 6 kg - (2 kg + 1 kg) = 3 kgMomentum in y - direction6(22)sin(0) = 2(10)sin32 - 1(8)sin(28) + 3u₃y
0 = 6.84 + 3u₃y
u₃y = -6.84/3
u₃y = -2.28 m/s
Change in momentumΔP = Pf - Pi = J
where;
Pf is final momentumPi is the initial momentumJ is impulse2640(0.1) = 2(10)cos32 + 1(8)cos(28) + 3u₃x - 6(22)
264 = -108 + 3u₃x
3u₃x = 372
u₃x = 372/3
u₃x = 124 m/s
Resultant velocityu₃ = √(124² + 2.28²)
u₃ = 124.02 m/s
Direction of the velocitytanθ = u₃y/u₃x
tanθ = 2.28/124
tanθ = 0.018
θ = 1.05⁰ (below the horizontal)
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what are risk factors of an autoimmune disease
Explanation:
Your Sex. Overall, 78% of people affected by autoimmune disease are female (1). ...Genetics. Certain disorders, such as lupus and multiple sclerosis, tend to run in families (3, 4). ...Having an autoimmune disease. ...Obesity. ...Smoking and Exposure to Toxic Agents. ...Certain Medications. ...Infections.Question 2 of 10
Which two types of energy does a book have as it falls to the floor?
A long thin solid rod lies along the positive x-axis. One end is at x = 1.80 m and the other at x = 3.40 m. The linear mass density is λ = a[tex]x^{3}[/tex] + bx, where λ is measured in kg/m, and the constants have the following values: a = 1.70 kg/[tex]m^{4}[/tex] and b = 2.20 kg/[tex]m^{2}[/tex].
1. Determine the total mass of the rod.
2. Calculate the x-coordinate of the center of the mass for this rod.
1. The total mass of the rod is 61.48 kg.
2. The x-coordinate of the center of the mass for this rod is 172.6021 m.
What is density?The density is the ratio of the mass and the volume of the object. It is denoted by ρ.
ρ = mass/Volume = m/V
Given a long thin solid rod lies along the positive x-axis. One end is at x = 1.80 m and the other at x = 3.40 m. The linear mass density is
λ = ax³ + bx,
where λ is measured in kg/m, and the constants have the following values: a = 1.70 kg/m⁴ and b = 2.20 kg/m²
So, λ = 1.70x³ + 2.20x
1. The total mass of the rod is
m =₁.₈³⁴ ∫ [1.70x³ + 2.20x] dx
m = [ 1.70x⁴/4 + 2.20x² /2 ]₁.₈³⁴
Putting the limits, we have
m = 69.51 - 8.02548
m = 61.48 kg
Thus, the total mass of the rod is 61.48 kg
2. The x-coordinate of the center of the mass for this rod
Xcm =∫ xλdx/m
Xcm =∫[ x ( 1.70x³ + 2.20x) /m ]dx
Xcm =∫[( 1.70x⁴ + 2.20x²) /m ]dx
On integrating and putting the limits x = 1.80 m to x = 3.40 m
Xcm = = [ {1.70(3.4)⁵/5 + 2.20(3.4)³ /3} - {1.70(1.8)⁵/5 + 2.20(1.8)³ /3} ]
Xcm = 183.3034 - 10.70133
Xcm = 172.6021 m
Thus, the x-coordinate of the center of the mass for this rod is 172.6021 m.
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Imagine that you're doing an experiment to determine how the running speed of a hamster depends on the weight of the hamster when plotting your data what variable should be on the y-axis
The variable on the y-axis should be the running speed of hamsters since it is the dependent variable.
What is the dependent variable?The dependent variable is the variable whose value fluctuates depending on other variables in an experiment.
In this case, the running speed is the dependent variable because it depends on the weight of the hamster.
The dependent variable is generally graphed on the Y axes, whereas the independent variable is graphed on the X-axes.
In conclusion, the variable on the y-axis should be the running speed of hamsters since it is the dependent variable.
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what is the output voltage of a transformer if the input is 240volts, and the number of turns on the primary coil is 1200 and on the secondary coil is 200.
The output voltage of a transformer is 40V.
What is an output voltage?An output voltage is the voltage released by a device, such as a voltage regulator or a generator.
The formula to calculate Output voltage of transformer is:
[tex]\frac{V_{s} }{V_{p} } = \frac{N_{s} }{N_{p} }[/tex]
here, [tex]V_{s}[/tex] is the secondary voltage, [tex]V_{p}[/tex] is the primary voltage, [tex]N_{s}[/tex] is the number of secondary windings and [tex]N_{p}[/tex] is the number of primary windings.
According to the question.
[tex]N_{p}[/tex] =1200 , [tex]N_{s}[/tex]=200 , [tex]V_{p}[/tex]=240V ,[tex]V_{s}[/tex]= ?
By using the formula of Output voltage,
[tex]{V_{s} } = \frac{V_{p}N_{s} }{N_{p} }[/tex]
=[tex]\frac{240*200}{1200}[/tex]
[tex]=40V[/tex]
Therefore, 40V is the output voltage of a transformer.
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An m = 6.11 g bullet is fired into a 365 g block that is initially at rest at the edge of a table of h = 1.08 m height as shown in the figure.
1. The bullet remains in the block, and after the impact the block lands d = 1.84 m from the bottom of the table. How much time does it take the block to reach the ground once it flies off the edge of the table?
2. What is the initial horizontal velocity of the block as it flies off the table?
3. Determine the initial speed of the bullet.
(a) The time taken the block to reach the ground once it flies off the edge of the table is 0.47 s.
(b) The initial horizontal velocity of the block as it flies off the table is 3.91 m/s.
(c) The initial speed of the bullet is 237.5 m/s.
Time of motion of the blockThe time of motion of the block is calculated as follows;
h = ¹/₂gt²
where;
h is height of the tablet is time of motiont = √(2h/g)
t = √( (2 x 1.08) / 9.8)
t = 0.47 s
Initial horizontal velocity of the blockx = vt
v = x/t
v = (1.84)/(0.47)
v = 3.91 m/s
Initial speed of the bulletm1u1 + m2u2 = v(m1 + m2)
where;
m1 is mass of bulletm2 is mass of blocku1 is initial velocity of the bulletu2 is the initial velocity of the blockv is initial horizontal velocity of the block as it flies off the table0.00611(u1) + 0.365(0) = 3.91(0.00611 + 0.365)
0.00611u1 = 1.451
u1 = 1.451/0.00611
u1 = 237.5 m/s
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2. A man pushes on a piano with mass 180 kg; it slides at constant velocity down a ramp that is inclined at 19.0° above the horizontal floor. Neglect any friction acting on the piano. Calculate the magnitude of the force applied by the man if he pushes (a) parallel to the incline and (b) parallel to the floor.
Answer: See below
Explanation:
Part (a):
As the velocity of the piano is constant, the net force on the piano is zero. The friction is also zero.
Here, F is the force applied by the man towards the inclined plane, mg is the weight of the piano and N is the normal force.
Applying Newton's law we get,
[tex]F = mg\sin \theta[/tex]
Substituting we get,
[tex]F &= \left( {180\;{\rm{kg}}} \right) \times \left( {9.8\;{\rm{m/}}{{\rm{s}}^{\rm{2}}}} \right) \times \sin 19.0^\circ \\ &= 574.3\;{\rm{N}}[/tex]
Therefore, the force is 574.3 N
Part (b)
Here, the force F is applied parallel to the floor.
The friction is zero.
Applying Newton's law we get,
[tex]F\cos \theta &= mg\sin \theta \\ F &= mg\tan \theta[/tex]
Substituting we get,
[tex]F &= \left( {180\;{\rm{kg}}} \right) \times \left( {9.8\;{\rm{m/}}{{\rm{s}}^{\rm{2}}}} \right) \times \tan 19.0^\circ \\ &= 607.4\;{\rm{N}}[/tex]
Therefore, the force is 607.4 N
A cup of water is warmed from 21 °C to 85 °C. What is the difference between these two temperatures, in kelvins?
Answer:
337k
Explanation:
First, let us find the difference between the given two temperatures.
Difference = 85°C - 21°C
= 64°C
And now we have to write the temperature in kelvins.
To convert Celcius to Kelvins you can add 273 to the temperature in Celcius.
Let us find it now.
64°C + 273 = 337k
Therefore,
64°C ⇒ 337k
Suppose a piano tuner stretches a steel piano wire 7.5 mm. The wire was originally 0.975 mm in diameter, 1.45 m long, and has a Young's modulus of 2.10 × 1011 N/m2. Calculate the force a piano tuner applies to stretch the steel piano wire in Newtons.
The forces a piano tuner applies to stretch the steel piano wire willl be 1.4 × 10¹¹ N.
What is force?Force is defined as the push or pulls applied to the body. Sometimes it is used to change the shape, size, and direction of the body. Force is defined as the product of mass and acceleration. Its unit is Newton.
The application of a force may be used to describe the steel as an elastic element within a certain range of applied force.
Given data;
Young modulus, E=2.10 × 10¹¹ N/m²
Cross-sectional area,A
Final length,[tex]\rm L_f = 1.45 m = 1450 \ mm[/tex]
Initial length,[tex]\rm L_i = 7.5 mm[/tex]
[tex]\rm F = \frac{(L_f-L_i)(E)(A)}{L_1} \\\\ \rm F = \frac{(1450 - 7.5)(2.0 \times 0^{11})(0.746)}{1450} \\\\ F = 1.4 \times 10^{11} \ N[/tex]
Hence, the force a piano tuner applies to stretch the steel piano wire willl be 1.4 × 10¹¹ N.
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