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7nadin3 [17]
3 years ago
14

A children's roller coaster is released from the top of a track. If its maximum speed at ground level is 3 m/s, find the height

it was released from.
Physics
1 answer:
san4es73 [151]3 years ago
4 0

Answer:

h = 0.46 m

Explanation:

According to the law of conservation of energy:

Potential Energy Lost by Roller Coaster = Kinetic Energy Gained by Roller Coaster

mgh = \frac{1}{2}mv^2\\\\2gh = v^2\\\\h = \frac{v^2}{2g}

where,

h = height = ?

v = speed at bottom = 3 m/s

g = acceleration due to gravity = 9.81 m/s²

Therefore,

h = \frac{(3\ m/s)^2}{(2)(9.81\ m/s^2)}

<u>h = 0.46 m</u>

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A spring with force constant of 59 N/m is compressed by 1.3 cm in a hockey game machine. The compressed spring is used to accele
Furkat [3]

Answer:

The puck moves a vertical height of 2.6 cm before stopping

Explanation:

As the puck is accelerated by the spring, the kinetic energy of the puck equals the elastic potential energy of the spring.

So, 1/2mv² = 1/2kx² where m = mass of puck = 39.2 g = 0.0392 g, v = velocity of puck, k = spring constant = 59 N/m and x = compression of spring = 1.3 cm = 0.013 cm.

Now, since the puck has an initial velocity, v before it slides up the inclined surface, its loss in kinetic energy equals its gain in potential energy before it stops. So

1/2mv² = mgh where h = vertical height puck moves and g = acceleration due to gravity = 9.8 m/s².

Substituting the kinetic energy of the puck for the potential energy of the spring, we have

1/2kx² = mgh

h = kx²/2mg

= 59 N/m × (0.013 m)²/(0.0392 kg × 9.8 m/s²)

= 0.009971 Nm/0.38416 N

= 0.0259 m

= 2.59 cm

≅ 2.6 cm

So the puck moves a vertical height of 2.6 cm before stopping

3 0
3 years ago
Where were the girls heading when the car broke down?<br> in the movie *hidden figures*
Ilia_Sergeevich [38]

Explanation:

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5 0
3 years ago
A dog jumps 0.80 m to catch a treat. The dog's displacement vector is shown below.
Brrunno [24]

Answer:D

Explanation:

It was right o khan academy

6 0
2 years ago
Using 0.500 g of nichrome, you are asked to fabricate a wire with uniform cross-section. The resistance of the wire is 0.673 Ω.
mojhsa [17]

Explanation:

Given that,

Mass of Nichrome, m = 0.5 g

The resistance of the wire, R = 0.673 ohms

Resistivity of the nichrome wire, \rho=10^{-6}\ \Omega -m

Density, d=8.31\times 10^3\ kg/m^3

(A) The length of the wire is given by using the definition of resistance as :

Volume,

V=A\times l\\\\A=\dfrac{V}{l}\\\\Since, V=\dfrac{m}{d}\\\\V=\dfrac{m}{d}\\\\V=\dfrac{0.5\times 10^{-3}}{8.31\times 10^3}\\\\V=6.01\times 10^{-8}\ m^3

Area,

A=\dfrac{V}{l}\\\\A=\dfrac{6.01\times 10^{-8}}{l}....(1)

R=\rho \dfrac{l}{A}\\\\l=\dfrac{RA}{\rho}\\\\l=\dfrac{0.673\times 6.01\times 10^{-8}}{l\times 10^{-6}}\\\\l=0.201\ m

(b)  Equation (1) becomes :

A=\dfrac{6.01\times 10^{-8}}{l}\\\\A=\dfrac{6.01\times 10^{-8}}{0.201}\\\\\pi r^2=3\times 10^{-7}\\\\r=\sqrt{\dfrac{3\times 10^{-7}}{\pi}} \\\\r=3.09\times 10^{-4}\ m

Hence, this is the required solution.                                                                  

5 0
3 years ago
1. A runner drops her phone as she is running at a constant speed of 3 miles per hour from point A to point B in a park. Describ
joja [24]

Answer:

Let's define the point A as our zero in the x-axis.

As the phone drops, it keeps the horizontal velocity that it had before, so the horizontal velocity is:

Vx = 3 mi/h.

Now, the only force acting on the phone is the gravitational force that acts in the vertical axis, then we have:

Ay = -g

where g = 9.8 m/s^2

It is dropped, so we do not have a vertical initial velocity, then for the vertical velocity we should integrate over time:

Vy = -g*t

And for the position again, we integrate over time, but now we have an initial position H, that is the height at which the phone is dropped.

Py = -(1/2)*g*t^2 + H

And the horizontal position can be found by integrating over time the horizontal velocity.

Px = (3mi/h)*t

This will be the two equations that describe the motion of the phone, and we can not solve it further because we do not know the initial height of the phone.

But in general, we have a linear equation in the horizontal axis and a quadratic equation with a negative leading coefficient in the vertical axis.

Position(t) = ( (3mi/h)*t,  -(1/2)*g*t^2 + H)

5 0
3 years ago
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