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2 years ago

15

Assume that the cart is free to roll without friction and that the coefficient of static friction between the block and the cart

is μs. Derive an expression for the minimum horizontal force that must be applied to the block in order to keep it from falling to the ground. Express your answer in terms of acceleration of gravity g and some or all of the variables m, M, and μs.

2 answers:

Dahasolnce [82]2 years ago

6 0

Answer: $F=\frac{(M+m)g}{\mu _s}$

Explanation:

Given

Trolley of mass M is free to roll without friction

coefficient of friction between trolley and mass m is $\mu _s$

Force F is applied on mass m

Acceleration of the system is

$a=\frac{F}{M+m}$

friction Force will balance weight of block

friction force $=\mu _sN$

$N=ma$

$\mu _sN=mg$

$\mu _sma=mg$

$\mu _s=\frac{g}{a}$

$F=\frac{(M+m)g}{\mu _s}$

Ainat [17]2 years ago

3 0

Answer:<em> </em>N = <em>fa/g</em>

Explanation:

if the block is not to fall,the friction force, <em>f , </em>must balance the block's weight :

<em>f = mg</em><em>. </em>But the horizontal motion of the block is given by <em>N = ma</em>

Therefore,

<em>f / N = g/ a </em><em> </em>

<em>or </em><em>a = g/f / N</em>

Since the maximum value of <em>f / N is μs</em><em>, </em>we must have <em>a</em> ≥ <em>g/μs,</em><em> </em>if<em> </em>the block is not to fall. Q.E.D

N = <em>fa/g</em>

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What are the magnitude and direction of the force the pitcher exerts on the ball? (enter your magnitude to at least one decimal

murzikaleks [220]

Details are missing in the question. Complete text of the problem:

"The gravitational force exerted on a baseball is 2.28 N down. A pitcher throws the ball horizontally with velocity 16.5 m/s by uniformly accelerating it along a straight horizontal line for a time interval of 181 ms. The ball starts from rest.

(a) Through what distance does it move before its release? (m)
(b) What are the magnitude and direction of the force the pitcher exerts on the ball? (Enter your magnitude to at least one decimal place.)"

Solution

(a) The pitcher accelerates the baseball from rest to a final velocity of $v_f = 16.5 m/s$ , so $\Delta v=16.5 m/s$ , in a time interval of $\Delta t = 181 ms=0.181 s$ . The acceleration of the ball in the horizontal direction (x-axis) is therefore

$a_x = \frac{\Delta v}{\Delta t}= \frac{16.5 m/s}{0.181 s}=91.2 m/s^2$

And the distance covered by the ball during this time interval, before it is released, is:

$S= \frac{1}{2} a_x (\Delta t)^2 = \frac{1}{2} (91.2 m/s^2)(0.181 s)^2=1.49 m$

(b) For this part we need to consider also the weight of the ball, which is $W=mg=2.28 N$

From this, we find its mass: $m= \frac{W}{g}= \frac{2.28 N}{9.81 m/s^2}=0.23 Kg$

Now we can calculate the magnitude of the force the pitcher exerts on the ball. On the x-axis, we have

$F_x = m a_x = (0.23 kg)(91.2 m/s^2)=20.98 N$

We also know that the ball is moving straight horizontally. This means that the vertical component of the force exerted by the pitcher must counterbalance the weight of the ball (acting downward), in order to have a net force of zero along the y-axis, and so:

$F_y=W=mg=2.28 N$ (upward)

So, the magnitude of the force is

$F= \sqrt{F_x^2+F_y^2}= \sqrt{(20.98N)^2+(2.28N)^2}=21.2 N$

To find the direction, we should find the angle of F with respect to the horizontal. This is given by

$\tan \alpha = \frac{F_y}{F_x}= \frac{2.28 N}{20.98 N}=0.11$

From which we find $\alpha=6.2^{\circ}$

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2 years ago

Read 2 more answers

In the ENGR 10 lab (E391), there are 50 long light bulbs (P=100 W) and 30 regular bulbs (P=60 W). How much energy is consumed li

Alenkinab [10]

Answer:

Total energy saving will be 0.8 KWH

Explanation:

We have given there are 50 long light bulbs of power 100 W so total power of 50 bulb = 100×50 = 5000 W = 5 KW

30 bulbs are of power 60 W

So total power of 30 bulbs = 30×60 = 1800 W = 1.8 KW

Total power of 80 bulbs = 1.8+5 = 6.8 KW

Total time = 3 hour

We know that energy $E=power\times time=6.8\times 3=20.4KWH$

Now power of each CFL bulb = 25 W

So power of 80 bulbs = 80×25 = 2000 W = 2 KW

Energy of 80 bulbs = 2×3 = 6 KWH

So total energy saving = 6.8-6 = 0.8 KWH

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2 years ago

A small glider is coasting horizontally when suddenly a very heavy piece of cargo falls out of the bottom of the plane.

myrzilka [38]

Answer:

a. The plane speeds up but the cargo does not change speed.

Explanation:

Just to make it clear, the question is as follows from what I understand.

A small glider is coasting horizontally when suddenly a very heavy piece of cargo falls out of the bottom of the plane. You can neglect air resistance.

Just after the cargo has fallen out:

a. The plane speeds up but the cargo does not change speed.

b. The cargo slows down but the plane does not change speed.

c. Neither the cargo nor the plane change speed.

d. The plane speeds up and the cargo slows down.

e. Both the cargo and the plane speed up.

And we are requested to choose the right answer under the given conditions. We know the glider has no motor, then it must be in free fall movement, then it is experiencing some force that pulls it to the from due to the gravity effect on it, and a force in general is calculated by

F=m*a, m:= mass of the object, a:= acceleration.

Here we are only considering the horizontal effect of the forces, then since the mass is reduced the acceleration must increase to compensate and maintain the equilibrium of the forces, then the glider being lighter can travel faster due to the acceleration. On the other hand by the time the cargo left the glider there was no acceleration and the speed it had at the moment he left the plane continues, then the cargo does not change its speed, then horizontally speaking the answer would be a. The plane speeds up but the cargo does not change speed.

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2 years ago

Una columna de mármol, cuya área de sección transversal es de 2.0 m2 sostiene una masa de 25.000 kg. Encontrar: (3 pto )a) El es

bazaltina [42]

Responder:

122,500 Pa; 2.45 × 10 ^ -6; 2.94 × 10 ^ -5m

Explicación:

Dado lo siguiente:

Área de sección transversal (A) = 2m ^ 2

Masa (m) = 25000 kg

Módulo de Young = 50 x 10 ^ 9 N / m2

(1) estrés en la columna:

Estrés = Fuerza / Área

F = masa * aceleración debido a la gravedad

F = 25000kg * 9.8m / s ^ 2 = 245,000J

Estrés = 245,000J / 2m ^ 2

Estrés = 122,500 Pa

2) Deformación de la unidad (deformación):

Usando la relación:

Módulo de Young = Estrés / tensión

50 × 10 ^ 9 = 122,500 / CEPA

Cepa = 122500 / (50 × 10^9)

Cepa = 0.00000245

C) Si la altura es de 12 m, ¿cuánto se acorta la columna?

Cepa = extensión / longitud

0.00000245 = extensión / 12

0,00000245 * 12

0,0000294 m

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2 years ago

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weqwewe [10]

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Pkas

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2 years ago