Maria designs a test to see if lemon trees that receive more water produce larger lemons.

You have been hired to design a spring-launched roller coaster that will carry two passengers per car. The car goes up a 11-m-hi

True [87]

Answer:

m = maximum mass of the coaster = 410 kg

d = maximum spring compression = 2.3 m

h = maximum height of the track = 11 m

H = maximum difference in height of the track = 19 m

g = acceleration by gravity = 9.8 m/s²

k = spring constant (without safety margin) = ?

K = spring constant (with safety margin) = ?

V = maximum speed of the coaster = ?

The gravitational potential energy of the coaster on the top of the 11 m high hill (relative to its initial starting point) is:

PEg = m g h

PEg = (410 kg) (9.8 m/s²) (11 m)

PEg = 44198 J

To reach that height, the elastic potential energy stored in the spring must be the same, so:

PEg = PEe = k d² / 2

(44198 J) = k (2.3 m)² / 2

k = 16710 N/m

Adding 14% to that value, you get:

K = 1.14 (16710 N/m)

K = 19045 N/m - answer spring constant

When fully compressed, the elastic potential energy stored in the spring is:

PEe = K d² / 2

PEe = (19045 N/m) (2.3m)² / 2

PEe = 51326 J

The difference in height between the starting point and the lowest point of the track is:

Δh = H - h

Δh = (19 m) - (11 m)

Δh = 8 m

So the initial gravitational potential energy of 330 kg coaster, relative to the lowest point, is

PEg = m g Δh

PEg = (340 kg) (9.8 m/s) (8 m)

PEg = 26656 J

The total energy of the coaster at its starting point (again, relative to the lowest point) is:

TE = PEe + PEg

TE = (51326J) + (26656 J)

TE = 77982J

At the lowest point of the track, all that energy is converted to kinetic energy, so the speed at that point will be:

TE = KE = m V² / 2

(77982 J) = (340kg) V² / 2

V = 21.46 m/s - answer maximum speed

4 0

3 years ago

two objects are in uniform circular motion at the same speed but at different radii. the ones with the __ radius has the largest

Cerrena [4.2K]

Answer:the one with the smaller radius has the highest centripetal force

Explanation:

5 0

2 years ago

Read 2 more answers

Suppose a moving car has 2000 J of kinetic energy. If the carʹs speed doubles, how much kinetic energy would it then have?

Bond [772]

Answer:

option A

Explanation:

given,

Kinetic energy of the car = 2000 J

speed of the car is doubled

we know,

$KE_1 = \dfrac{1}{2}mv^2$

$2000= \dfrac{1}{2}mv^2$ ........(1)

now, speed of the car is doubled

v' = 2 v

$KE_2 = \dfrac{1}{2}mv'^2$

$KE_2 = \dfrac{1}{2}m(2v)^2$

from equation (1)

$KE_2 = 4\times \dfrac{1}{2}m(v)^2$

$KE_2 = 4\times 2000$

$KE_2 = 8000\ J$

Hence, the Kinetic energy would be equal to 8000 J.

The correct answer is option A.

8 0

2 years ago

Problem 8 I estimate that the Gauss gun (a solenoid) is wound with 500 turns over a distance of 15cm with an average radius of 1

stellarik [79]

Answer:

Energy stored, U = 66.6 J

Explanation:

It is given that,

Number of turns in the solenoid, n = 500

Radius of solenoid, r = 1.5 cm = 0.015 m

Distance, d = 15 cm = 0.15 m

Let U is the energy stored in the solenoid. Its formula is given by :

$U=\dfrac{1}{2}LI^2$

L is the self inductance of the solenoid

$L=\mu_o N^2A d$

N is the no of turns per unit length

$L=\mu_o (n/d)^2A d$

$L=\dfrac{4\pi\cdot10^{-7}\cdot500^{2}\cdot\pi\cdot\left(0.015\right)^{2}}{0.15}$

L = 0.00148 Henry

$U=\dfrac{1}{2}\times 0.00148\times 300^2$

U = 66.6 J

Out of given options, the correct option for the energy stored in the solenoid is 70 J. So, the correct option is (a) "70 J".

6 0

3 years ago

Would someone just answer this?

Alecsey [184]

Answer:

I answered :)

Explanation:

i just dk the right answer

8 0

3 years ago