PHYSICS COLLEGE

Ezra (m = 20.0 kg) has a tire swing and wants to swing as high as possible. He thinks that his best option is to run as fast as he can and jump onto the tire at full speed. The tire has a mass of 10.0 kg and hangs 3.50 m straight down from a tree branch. Ezra stands back 10.0 m and accelerates to a speed of 3.62 m/s before jumping onto the tire swing. (a) How fast are Ezra and the tire moving immediately after he jumps onto the swing? m/s (b) How high does the tire travel above its initial height?

Answers

Answer 1

Answer:

Answer:

a) $v=5.6725\,m.s^(-1)$

b) $h= 1.6420\,m$

Explanation:

Given:

mass of the body, $M=20\,kg$

mass of the tyre, $m=10\,kg$

length of hanging of tyre, $l=3.5m$

distance run by the body, $d=10m$

acceleration of the body, $a=3.62m.s^(-2)$

(a)

Using the equation of motion :

$v^2=u^2+2a.d$ ..............................(1)

where:

v=final velocity of the body

u=initial velocity of the body

here, since the body starts from rest state:

$u=0m.s^(-1)$

putting the values in eq. (1)

$v^2=0^2+2* 3.62 * 10$

$v=8.5088\,m.s^(-1)$

Now, the momentum of the body just before the jump onto the tyre will be:

$p=M.v$

$p=20* 8.5088$

$p=170.1764\,kg.m.s^(-1)$

Now using the conservation on momentum, the momentum just before climbing on the tyre will be equal to the momentum just after climbing on it.

$(M+m)* v'=p$

$(20+10)* v'=170.1764$

$v'=5.6725\,m.s^(-1)$

(b)

Now, from the case of a swinging pendulum we know that the kinetic energy which is maximum at the vertical position of the pendulum gets completely converted into the potential energy at the maximum height.

So,

$(1)/(2) (M+m).v'^2=(M+m).g.h$

$(1)/(2) (20+10)* 5.6725^2=(20+10)* 9.8* h$

$h\approx 1.6420\,m$

above the normal hanging position.

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Answers

The unit that should be used to measure energy when calculating specific heat capacity is Energy is in Joules ( J ).

What unit is used to measure energy?

The specific heat capacity should be determined in joules per kilogram degree-celsius ( J k g − 1 ∘ C − 1 ).

It is to be supplied for the substance with respect to mass and it increased the temperature.

Hence, The unit that should be used to measure energy when calculating specific heat capacity is Energy is in Joules ( J ).

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The unit used to measure energy when calculating specificheat capacity is the joule (J).

The joule (J), a unit used to quantify energy, is used to calculate specific heat capacity. In the International System of Units (SI), the joule serves as the default unit of energy.

It is described as the quantity of energy that is delivered when one newton of force is exerted across a one-meter distance.

Thus, the quantity of heat energy needed to increase the temperature of a particular substance by a specific amount is measured as specificheat capacity. J/kg°C, or joules per kilogramme per degree Celsius, is the unit of measurement.

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A electromagnetic wave of light has a wavelength of 500 nm. What is the energy (in Joules) of the photon representing the particle interpretation of this light?

Answers

Answer:

Energy, $E=4.002* 10^(-19)\ J$

Explanation:

It is given that,

Wavelength of the photon, $\lambda=500\ nm=5* 10^(-7)\ m$

We need to find the photon representing the particle interpretation of this light. it is given by :

$E=(hc)/(\lambda)$

$E=(6.67* 10^(-34)* 3* 10^8)/(5* 10^(-7))$

$E=4.002* 10^(-19)\ J$

So, the energy of the photon is $4.002* 10^(-19)\ J$ . Hence, this is the required solution.

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Answers

Answer:

90 m/s

Explanation:

The formula for velocity of wave in a string is given as,

v' = √(T/m') ................ Equation 1

Where v' = velocity of the string, T = Tension on the string, m' = mass per unit length of the string.

Given: T = 4050 N, and

m' = m/l where m = mass of the string, l = length of the spring.

m = 0.5 kg, l = 1 m

m' = 0.5/1 = 0.5 kg/m

Substitute into equation 1

v' = √(4050/0.5)

v' = √(8100)

v' = 90 m/s.

Hence the velocity of the wave in the string = 90 m/s

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Answers

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If f1= 300, F2= 60, and f2=260, find f1 to the nearest unit.

Answers

Answer:

F1 = 80

Explanation:

f1= f2 √ (F1/F2)

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Putting in the above formula

300 = 260√(F1/60)

Dividing both sides by 260

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Squaring both sides

=> 1.33 = F1/60

Multiplying both sides by 60

=> F1 = 80

A gate with a circular cross section is held closed by a lever 1 m long attached to a buoyant cylinder. The cylinder is 25 cm in diameter and weighs 200 N. The gate is attached to a horizontal shaft so it can pivot about its center. The liquid is water. The chain and lever attached to the gate have negligible weight. Find the length of the chain such that the gate is just on the verge of opening when the water depth above the gate hinge is 10 m.