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wolverine [178]
4 years ago
12

A meterstick is initially standing vertically on the floor. If the meterstick falls over, with what angular velocity will it hit

the floor? Assume that the end in contact with the floor experiences no friction and slips freely.
Physics
1 answer:
notsponge [240]4 years ago
8 0

L = length of the meter stick = 1 m

h = height of center of mass of stick from bottom end on the floor = L/2 = 1/2 = 0.5 m

m = mass of the meter stick

I = moment of inertia of the meter stick about the bottom end

w = angular velocity as it hits the floor

moment of inertia of the meter stick about the bottom end is given as

I = m L²/3

using conservation of energy

rotational kinetic energy of meter stick as it hits the floor = potential energy when it is vertical

(0.5) I w² = m g h

(0.5) (m L²/3) w² = m g h

( L²) w² =  6g h

( 1²) w² =  6 (9.8) (0.5)

w = 5.4 rad/s

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A train travels up a hill that is 100 meters long. If the train has climbed 50 meters vertically. How far the train traveled hor
NeTakaya

Answer:

27.3 meters

Explanation:

A train travels up a hill that is 100 meters long. If the train has climbed 50 meters vertically, it traveled 27.3 meters vertically. Therefore, the answer is 27.3 meters.

(100)² = (50)²+x²

10000 - 2500 = x²

7500 = x²

x = 27.3 or 27.3 meters

Hope this helped!

4 0
3 years ago
If a 400 watt motor is left on for 10 minutes, assuming no energy is lost to friction, how fast could a 100 kg cart be moving?
Verdich [7]

Answer:

69.28 m/s

Explanation:

From the question given above, the following data were obtained:

Power = 400 Watt

Time (t) = 10 minutes

Mass (m) = 100 Kg

Velocity (v) =?

Next, we shall convert 10 mins to seconds (s). This can be obtained as follow:

1 min = 60 s

Therefore,

10 mins = 10 × 60

10 mins = 600 s

Next, we shall determine the energy. This can be obtained as follow:

Power = 400 Watt

Time (t) = 600 s

Energy (E) =?

E = Pt

E = 400 × 600

E = 240000 J

Finally, we shall determine how fast the cart is moving. This can be obtained as illustrated below:

Mass (m) = 100 Kg

Energy (E) = Kinetic energy (KE) = 240000 J

Velocity (v) =?

KE = ½mv²

240000 = ½ × 100 × v²

240000 = 50 × v²

Divide both side by 50

v² = 240000 / 50

v² = 4800

Take the square root of both side

v = √4800

v = 69.28 m/s

Thus, the cart is moving with a speed of 69.28 m/s

5 0
3 years ago
What is the total current flowing through a 45 ohm resistor (1.4 amps) and a 20 ohm resistor (1.8 amps)?
MAXImum [283]
Need the circuit diagram. ...
4 0
3 years ago
Nasa has developed deep-space 1 (ds-1), a spacecraft that is scheduled to rendezvous with the asteroid named 1992 kd (which orbi
andrezito [222]
I can't give an exact number if the original velocity of ds-1 is not given. In that case, the final answer should just be in terms of an equation. Let's denote the original velocity to be v₀ and the days to be d.

Part a.)
v = v₀ + 9.23d
3440 = v₀ + 9.23d
9.23d = 3,440 - v₀
d = (3,440 - v₀)/9.23

Part b.)

The acceleration is the change in velocity per unit time. So, that would be 9.23 m/s per day. Since there are 86,400 s in a day:

a = 9.23 m/s / day * 1 day/ 86,400 s
a = 0.0001068 m/s²
6 0
3 years ago
In an experiment, a variable, position-dependent force F(x)F(x) is exerted on a block of mass 1.0kg1.0kg that is moving on a hor
leonid [27]

Answer:

The function F(x) for 0 < x < 5, the block's initial velocity, and the value of F(f).

(C) is correct option.

Explanation:

Given that,

Mass of block = 1.0 kg

Dependent force = F(x)

Frictional force = F(f)

Suppose, the following information would students need to test the hypothesis,

(A) The function F(x) for 0 < x < 5 and the value of F(f).

(B) The function a(t) for the time interval of travel and the value of F(f).

(C) The function F(x) for 0 < x < 5, the block's initial velocity, and the value of F(f).

(D) The function a(t) for the time interval of travel, the time it takes the block to move 5 m, and the value of F(f).

(E) The block's initial velocity, the time it takes the block to move 5 m, and the value of F(f).

We know that,

The work done by a force is given by,

W=\int_{x_{0}}^{x_{f}}{F(x)\ dx}.....(I)

Where, F(x) = net force

We know, the net force is the sum of forces.

So, \sum{F}=ma

According to question,

We have two forces F(x) and F(f)

So, the sum of these forces are

F(x)+(-F(f))=ma

Here, frictional force is negative because F(f) acts against the F(x)

Now put the value in equation (I)

W=\int_{x_{0}}^{x_{f}}{(F(x)-F(f))dx}

We need to find the value of \int_{x_{0}}^{x_{f}}{(F(x)-F(f))dx}

Using newton's second law

\int_{x_{0}}^{x_{f}}{(F(x)-F(f))dx}=\int_{x_{0}}^{x_{f}}{ma\ dx}...(II)

We know that,

Acceleration is rate of change of velocity.

a=\dfrac{dv}{dt}

Put the value of a in equation (II)

\int_{x_{0}}^{x_{f}}{(F(x)-F(f))dx}=\int_{x_{0}}^{x_{f}}{m\dfrac{dv}{dt}dx}

\int_{x_{0}}^{x_{f}}{(F(x)-F(f))dx}=\int_{v_{0}}^{v_{f}}{mv\ dv}

\int_{x_{0}}^{x_{f}}{(F(x)-F(f))dx}=\dfrac{mv_{f}^2}{2}+\dfrac{mv_{0}^2}{2}

Now, the work done by the net force on the block is,

W=\dfrac{mv_{f}^2}{2}+\dfrac{mv_{0}^2}{2}

The work done by the net force on the block is equal to the change in kinetic energy of the block.

Hence, The function F(x) for 0 < x < 5, the block's initial velocity, and the value of F(f).

(C) is correct option.

7 0
3 years ago
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