A suspended platform of negligible mass is connected to the floor below by a long vertical spring of force constant 1200 N/m. A circus performer of mass 70 kg falls from rest onto the platform from a height of 5.8 m above it. Find the maximum spring compression

Answers

Answer 1

Answer:

The maximum spring compression = 3.21 m

Explanation:

The height of the circus performer above the platform connected to string material = 5.8 m

Let the maximum compression of the spring from the impact of the circus performer be x.

According to the law of conservation of energy, the difference in potential energy of the circus performer between the initial height and the level at which spring is compressed to is equal to the work done on the spring to compress it by x

Workdone on the spring by the circus performer = (1/2)kx²

where k = spring constant = 1200 N/m

Workdone on the spring by the circus performer = (1/2)(1200)x² = 600x²

The change in potential energy of the circus performer = mg (5.8 + x)

m = mass of the circus performer = 70 kg

g = acceleration due to gravity = 9.8 m/s²

The change in potential energy of the circus performer = (70)(9.8)(5.8 + x) = (3978.8 + 686x)

600x² = 3978.8 + 686x

600x² - 686x - 3978.8 = 0

Solving this quadratic equation

x = 3.21 m or - 2.07 m

Since the negative answer doesn't satisfy the laws of physics, our correct answer is 3.21 m

Hope this Helps!!!

Related Questions

When an external magnetic field is applied, what happens to the protons in a sample?A) All protons align with the field.B) All protons align opposite to the field.C) Some protons align with the field and some align opposite to it.D) All protons assume a random orientation.
WILL MARK BRAINLIEST PLS HELPPP -- Which of Newton’s Laws explains why the satellite would collide with the moon if gravity is “turned off?”picture attached
A tuning fork vibrates at 15,660 oscillations every minute. What is the period (in seconds) of one back and forth vibration of the tuning fork?
A student lifts their 75 N backpack 0.50 m onto their chair. How much work is done?
5. The order is to give 600 mg of Ampicillin IM q8h. The directions for dilution on the 2 gm vial reads: Reconstitute with 4.8 mL of sterile water to obtain a concentration of 400 mg per mL. How many mL will you administer per dose?

If a person’s weight is W on the surface of the earth, calculate what it would be, in terms of W, at the surface of (a) the moon;
(b) Mars;
(c) Jupiter.

Answers

Answer:b

Explanation:

A circular coil lies flat on a horizontal surface. A bar magnet is held above the center of the coil with its north pole pointing downward, and is released from rest. What is the direction of the induced current in the coil, as viewed from above, as the magnet approaches the coil in free fall?a. clockwise
b. counterclockwise
c. There is no induced current in the coil.

Answers

Answer:

Option B

Explanation:

As per the Lenz’s law of electromagnetism the current induced in a conductor due to any change has a tendency to oppose the change which is causing this induces current.

Thus, when a constant magnetic field with an electric circuit is varied, it produces and induced current which flow in a direction such that its sets a magnetic field that tries to restore the flux

Hence, option B is correct

The 160-lblb crate is supported by cables ABAB, ACAC, and ADAD. Determine the tension in these wire

Answers

Answer:

$F_(AB) = 172.1356\nF_(AC) = 258.2033\nF_(AD) = 368.8004$

Explanation:

Using the diagram (see attachment) we extract the following position vectors:

$Vector (OA) = 6i + 0j + 0k \nVector (OB) = 0i + 3j + 2k \nVector (OC) = 0i - 2j + 3k$

Next step is to find unit vectors $u_(AB) ,u_(AC), u_(AD), u_(AE)$ as follows:

$u_(AB) = (vector(AB))/(magnitude(AB)) \n= \frac{OB - OA}{magnitude({vector(OB - OA))} }\n=(-6i +3j+2k)/(√(6^2 + 3^2+2^2) ) \n\n=-0.857 i +0.429j+0.286k\n\nu_(AC) = (vector(AC))/(magnitude(AC)) \n= \frac{OC - OA}{magnitude({vector(OC - OA))} }\n=(-6i -2j-3k)/(√(6^2 + 2^2+3^2) ) \n\n=-0.857 i -0.286j+0.429k\n\nu_(AD) = +1i\nu_(AC) = -1k$

Using the diagram we find the corresponding vectors Forces:

$F_(AB) = F_(AB) i + F_(AB)j +F_(AB)k\nF_(AC) = F_(AC) i + F_(AC)j +F_(AC)k\nF_(AD) = F_(AD) i + F_(AD)j +F_(AD)k\nW = -160 k$

Equation of Equilibrium:

$Sum of forces = 0\nF_(AB). u_(AB) + F_(AC).u_(AC) + F_(AD).u_(AD) + W = 0\n(-0.857F_(AB)i + 0.429F_(AB)j +0.286F_(AB)k) + (-0.857F_(AC)i - 0.286F_(AC)j +0.429F_(AC)k) + (+1F_(AD) i) + (-160k) = 0$

Comparing i , j and k components as follows:

$-0.857F_(AB) -0.857F_(AC) +1F_(AD) = 0\n+ 0.429F_(AB) - 0.286F_(AC) = 0\n+0.286F_(AB) +0.429F_(AC) = 160$

Solving Above equation simultaneously we get:

$F_(AB) = 172.1356\nF_(AC) = 258.2033\nF_(AD) = 368.8004$

A small grinding wheel is attached to the shaft of an electric motor which has a rated speed of 3600 rpm. When the power is turned on, the unit reaches its rated speed in 5 s, and when the power is turned off, the unit coasts to rest in 70 s. Assuming uniformly accelerated motion, determine the number of revolutions that the motor executes (a) in reaching its rated speed, (b) in coasting to rest.

Answers

Answer:

(a) θ1 = 942.5rad, (b) θ2 = 13195 rad

Explanation:

(a) Given

ωo = 0 rad/s

ω = 3600rev/min = 3600×2(pi)/60 rad/s

ω = 377rad/s

t1 = 5s

θ1 = (ω + ωo)t/2

θ1 = (377 +0)×5/2

θ1 = 942.5 rads

(b) ωo = 377rad/s

ω = 0 rad/s

t2 = 70s

θ2 = (ω + ωo)t/2

θ2 = (377 +0)×70/2

θ2 = 13195 rad

The height h (in feet) of an object shot into the air from a tall building is given by the function h(t) = 650 + 80t − 16t2, where t is the time elapsed in seconds. (a) Write a formula for the velocity of the object as a function of time t.

Answers

Answer:

80 - 32t

Explanation:

The height, h, in terms of time, t, is given as:

h(t) = 650 + 80t − 16t²

Velocity is the derivative of distance with respect to time:

v(t) = dh(t)/dt = 80 - 32t

Final answer:

The velocity of the object as a function of time is given by the derivative of the height function, which is v(t) = 80 - 32t.

Explanation:

The height h(t) of an object is given by the equation h(t) = 650 + 80t − 16t2. To find the velocity v(t), we need to take the derivative of h(t) with respect to time t. Using the power rule, we get:

v(t) = dh/dt = 0 + 80 - 32t.

So, the velocity of the object as a function of time t is v(t) = 80 - 32t.

Learn more about Velocity Function here:

brainly.com/question/33157131

#SPJ11

In an experiment to measure the acceleration of g due to gravity, two values, 9.96m/s (s is squared) and 9.72m/s (s is squared), are determined. Find (1) the percent difference of the measurements, (2) the percent error of each measurement, and (3) the percent error of their mean. (Accepted value:g=9.80m/s (s is squared))

Answers

Answer:

a)2.46 %

b)For 1 :101.52 %

For 2 : 99.08 %

c)100..4 %

Explanation:

Given that

g₁ = 9.96 m/s²

g₂ = 9.72 m/s²

The actual value of g = 9.8 m/s²

The difference Δ g = 9.96 -9.72 =0.24 m/s²

$The\ percentage\ difference=(0.24)/(9.72)* 100=2.46\ percentage\n$

For first one :

$Error\ in\ the\ percentage =(9.96)/(9.81)* 100 =101.52\ perncetage$

For second :

$Error\ in\ the\ percentage =(9.72)/(9.81)* 100 =99.08\ perncetage$

The mean g(mean )

$g(mean )=(9.96+9.72)/(2)\ m/s^2\ng(mean)=9.84\ m/s^2$

$The\ percentage=(9.84)/(9.8)* 100=100.40\ percentage$

a)2.46 %

b)For 1 :101.52 %

For 2 : 99.08 %

c)100..4 %

Final answer:

The percent difference between the two measurements is 2.44%. The percent error for the first measurement is 1.63%, and for the second measurement is 0.82%. The percent error of their mean is 0.41%.

Explanation:

In physics, the percent difference is calculated by subtracting the two values, taking the absolute value, dividing by the average of the two values, and then multiplying by 100. Therefore, the percent difference between the two measurements 9.96m/s² and 9.72m/s² is:

|(9.96-9.72)|/((9.96+9.72)/2)*100 = 2.44%

The percent error involves taking the absolute difference between the experimental value and the accepted value, divided by the accepted value, then multiplied by 100. So, the percent error for the two measurements with accepted value of 9.80m/s² are:

For 9.96m/s²: |(9.96-9.80)|/9.80*100 = 1.63%

For 9.72m/s²: |(9.72-9.8)|/9.8*100 = 0.82%

The percent error of the mean involves doing the above but using the mean of the experimental measurements:

|(Mean of measurements - Accepted value)|/Accepted value * 100 |(9.96+9.72)/2-9.8|/9.8*100 = 0.41%

Learn more about Percent Difference and Error here:

brainly.com/question/33836796

#SPJ3

Other Questions

A 2500 kg car traveling to the north is slowed down uniformly from an initial velocity of 27.0 m/s by a 7850 N braking force acting opposite the car’s motion. What is the car's velocity after 2.52s?How far does the car move during the 2.52 s?How long does it take the car to come to a complete stop?

A piston above a liquid in a closed container has an area of 0.75m^2, and the piston carries a load of 200kg. What will be the external pressure on the upper surface of the liquid?

Express the following speeds as a function of the speed of light, c: (a) an automobile speed (93 km/h) (b) the speed of sound (329 m/s) (c) the escape velocity of a rocket from the Earth's surface (12.1 km/s) (d) the orbital speed of the Earth about the Sun (Sun-Earth distance 1.5×108 km).

A cat leaps to catch a bird. If the cat's jump was at 60.0° off the ground and its initial velocity was point of its trajectory? 0.30 m 3.44 m/s, what is the highest O 13.76 m 0.45 m 0.90 m