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babymother [125]

3 years ago

13

A bowling ball weighing 71.2 N is attached to the ceiling by a 3.70 m rope. The ball is pulled to one side and released; it then

swings back and forth like a pendulum. As the rope swings through its lowest point, the speed of the bowling ball is measured at 4.20 m/s.At this instant, what are (a) the acceleration of the bowling ball, in magnitude and direction, and (b) the tension in the rope?

1 answer:

amm18123 years ago

5 0

Answer:

a, 7.26kg

b, 36.59N

Explanation:

The question says it swings like a pendulum, as such, we would use the formula for circular acceleration.

a = v²/r

a = 4.2²/3.7

a = 17.64/3.7

a = 4.77m/s²

The acceleration of the ball is directed towards the centre because circular acceleration is usually directed towards the centre

To find tension, recall, F = ma

m = F/a

m = 71.2/9.81

m = 7.26kg

In solving for tension then, we use our acceleration to be (9.81 - 4.77) = 5.04m/s²

Tension = ma

Tension = 7.26 * 5.04

Tension = 36.5904

Hence the tension in the rope is 36.59N

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What mass of steam at 100°C must be mixed with 490 g of ice at its melting point, in a thermally insulated container, to produce

sukhopar [10]

Answer:

the mass of steam at 100°C must be mixed is 150 g

Explanation:

given information:

ice's mass, $m_{i}$ = 490 g = 0.49 kg

steam temperature, T = 100°C

liquid water temperature, T = 89.0°C

specific heat of water, $c_{w}$ = 4186 J/kg.K = 4.186 kJ/kg.K

latent heat of fusion, $L_{f}$ = 333 kJ/kg

latent heat of vaporization, $L_{v}$ = 2256 kJ/kg

first, we calculate the heat of melted ice to water

Q₁ = $m_{i} L_{f}$

where

Q = heat

$m_{i}$ = mass of the ice

$L_{f}$ = latent heat of fusion

thus,

Q₁ = $m_{i} L_{f}$

= 0.49 x 333

= 163.17 kJ

then, the heat needed to increase the temperature of water to 89.0°C

Q₂ = $m_{i}$ $c_{w}$ (89 - 0), the temperature of ice is 0°C

$c_{w}$ = specific heat of water

so,

Q₂ = $m_{i}$ $c_{w}$ (89 - 0)

= 0.49 x 4.186 x 89

= 182.55 kJ

so, the heat absorbed by the ice is

Q = Q₁ + Q₂

= 163.17 + 182.55

= 345.72 kJ

the temperature of the steam is 100°C, so the mass of the steam is

Q = $m_{s}$ $L_{v}$ + $m_{s}$ $c_{w}$ (100 - 89)

Q = $m_{s}$ ( $L_{v}$ + $c_{w}$ (11))

$m_{s}$ = Q/ [ $L_{v}$ + $c_{w}$ (11)]

= 345.72/ [2256 + (4.186 x 11)]

= 0.15 kg

= 150 g

5 0

3 years ago

laurens suv was detected exceeding the posted speed limit of 60 kilometers per hour, how many kilometers per hour would she have

MaRussiya [10]

Answer:

Laurens suv have been travelling 60km/h speed if she can covers the distance of 10 kilometers in 5 minutes.

Explanation:

As per the given question,

Distance = 10 km

Time = 5 minutes

Convert minutes into hour.

There are 60 minutes in one hour, hence 5 minutes in hours is written as

$\text { time }=\frac{5}{60}$

$\text { time }=\frac{1}{12}$

We know the relationship between distance, speed and time is as follows,

$\text { Distance }(\mathrm{d})=\text { speed }(\mathrm{s}) \times \text { time }(\mathrm{t})$

$\text { speed }=\frac{\text {distance}}{\text {time}}$

$\text { speed }=\frac{10}{\frac{1}{12}}$

$\text { Speed }=10 \mathrm{km} \times 12 \mathrm{hour}$

Speed = 120km/h

Laurens suv exceeds the limit by = 120 – 60

Thus the speed limit exceeds by 60km/h .

3 0

4 years ago

As ocean waves approach shore, their velocity decreases. How does a decrease in velocity affect the frequency and wavelength of

timama [110]

Explanation:

As ocean waves approach shore, their velocity decreases. The relation between the velocity, wavelength and the frequency of a wave is given by :

$v=f\times \lambda$

f = frequency

$\lambda$ = wavelength

$f=\dfrac{v}{\lambda}$ ..............(1)

So, as the velocity of the wave increases, the wavelength and frequency also increases as per equation (1). When the velocity decreases, the frequency and the wavelength also decreases.

3 0

3 years ago

Read 2 more answers

Objects of equal mass are oscillating up and down in simple harmonic motion on two different vertical springs. The spring consta

Zanzabum

Answer:

$k_2=920\ N/m$

Explanation:

Given that,

The spring constant of spring 1, $k_1=230\ N/m$

The motion of the object on spring 1 has twice the amplitude as the motion of the object on spring 2, $A_1=2A_2$

As the magnitude of the maximum velocity is the same in each case, it means the maximum kinetic energy is same in each case. In other words, the total energy is same.

$\dfrac{1}{2}k_1A_1^2=\dfrac{1}{2}k_2A_2^2$

$k_1A_1^2=k_2A_2^2$

$k_1(2A_2)^2=k_2A_2^2$

$k_2=920\ N/m$

So, the spring constant of spring 2 is 920 N/m. Hence, this is the required solution.

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3 years ago

Two identical loudspeakers that are 5.00 m apart and face toward each other are driven in phase by the same oscillator at a freq

Lunna [17]

Answer:0.0982 m

Explanation:

Given

distance between two loudspeaker is 5 m

frequency (f )=875 Hz

speed of sound (v)=344 m/s

Let $x_0$ be the smallest distance moved by observer then

Position of observer w.r.t to first speaker is

$x_1=\frac{L}{2}-x_0$

Position of observer w.r.t to second speaker is

$x_2=\frac{L}{2}+x_0$

$\Delta x=2x_0$

For Destructive interference

$\Delta x=\left ( m+\frac{1}{2}\right )\cdot lambda$

For minimum m=0

and $\lambda =\frac{v}{f}$

$2x_0=\frac{v}{2f}$

$x_0=\frac{v}{4f}=\frac{344}{4\times 875}=0.0983 m$

8 0

3 years ago