All categories

6 hours ago

The total charge that an automobile battery can supply without being recharged is given in terms of ampere-hours. A typical 12 V

battery has a rating of 60 ampere-hours (60 A for 1 h, 30 A for 2 h, and so on). Suppose that you forget to turn off the headlights in your parked automobile. If each of the two head-lights draws 3.8 A, how long will it be before your battery is dead?

Physics

You might be interested in

The amount of energy necessary to remove an electron from an atom is a quantity called the ionization energy, Ei. This energy ca

Keith_Richards [3271]

Answer:

The resulting value is $E_i = 1.5596 *10^{-18} \ J$ .

Explanation:

The question specifies that

The wavelength is $\lambda = 48.2 nm = 48.2 *10^{- 9 }\ m$ .

The velocity is $v = 2.371*10^6 \ m/s$ .

The mass of the electron is $m_e = 9.109*10^{-31} \ kg$ .

The energy of the incoming light is typically depicted mathematically as

$E = \frac{h * c}{\lambda}$ .

Here, c represents the speed of light with the value $c = 3.0 *10^{8} \ m/s$ .

h stands for Planck's constant with a value of $h = 6.62607015 * 10^{-34 } J\cdot s$ .

Thus,

$E = \frac{6.62607015 * 10^{-34 }* 3.0 *10^{8}}{48.2 *10^{- 9 }}$

=> $E = 4.12 *10^{-18} \ J$ .

Typically, kinetic energy is represented as

$E_k = \frac{1}{2} * m_e * v^2$

=> $E_k = \frac{1}{2} * 9.109*10^{-31} * (2.371*10^6 )^2$ .

=> $E_k = 2.56 *0^{-18} \ J$ .

The ionization energy is generally expressed mathematically as

$E_i = 4.12 *10^{-18} - 2.56 *0^{-18}$

=> $E_i = 1.5596 *10^{-18} \ J$ .

8 0

3 months ago

The figure above represents a stick of uniform density that is attached to a pivot at the right end and has equally spaced marks

Sav [3153]

Answer:

After a duration of 2.0 seconds, the angular momentum of the system is $L= 2(4A+3B+2C+D)x$ .

Explanation:

Let’s denote the forces acting on the rod as A, B, C, and D, and the distance between them as $x$ .

The torque produced by force A can be expressed as

$\tau_a = 4Ax$ ,

for force B the torque is

$\tau_b = 3Bx$ ,

the torque for force C is

$\tau_c = 2Cx$ ,

and the torque due to force D is

$\tau_d = Dx$ .

This leads to a total torque on the stick as

$\tau_{tot} =\tau_a+\tau_b+\tau_c+\tau_d$

$\tau_{tot} =4Ax+3Bx+2Cx+Dx$

$\tau_{tot} =x(4A+3B+2C+D)$

Subsequently, this torque results in an angular acceleration $\alpha$ in accordance with the formula

$I \alpha = \tau_{tot}$

where $I$ represents the moment of inertia of the stick, which has a value of

$I = \dfrac{1}{3} m(4x)^2$ .

Thus, the angular acceleration calculates to

$\alpha = \dfrac{\tau_{tot} }{I}$

$\alpha =\dfrac{x(4A+3B+2C+D)}{\dfrac{1}{3}m(4x)^2 }$

$\boxed{\alpha =\dfrac{3(4A+3B+2C+D)}{16mx } .}$ .

Now, the angular momentum $L$ of the rod is given by

$L = I\omega$ ,

where $\omega$ is considered the angular velocity.

Given $\omega = \alpha t$ , we conclude that

$L = \dfrac{1}{3}m (4x)^2 *\dfrac{3(4A+3B+2C+D)}{16mx }* t$

$L= (4A+3B+2C+D)x t$

Thus, $t = 2.0s$ , the angular momentum is

$\boxed{ L= 2(4A+3B+2C+D)x. }$

5 0

3 months ago

A roundabout in a fairground requires an input power of 2.5 kW when operating at a constant angular velocity of 0.47 rad s–1 . (

ValentinkaMS [3465]

Since the roundabout operates at a constant angular velocity, the input power equals the frictional power. Given that the frictional power is 2.5 kW, we can express this as frictional torque multiplied by angular velocity: frictional torque x 0.47 = 2.5 kW. Therefore, solving for frictional torque gives us 2.5 / 0.47 kN.m, which amounts to approximately 5.32 kN.m, leading to a rounded value of 5 kN.m. When the power supply is interrupted, the roundabout experiences deceleration due to the influence of the frictional torque.

5 0

2 months ago

A graph of the net force F exerted on an object as a function of x position is shown for the object of mass M as it travels a ho

Softa [3030]

The alteration in kinetic energy is $\Delta K = 3Fd$

Clarification:

According to the work-energy principle, the task performed on an object corresponds to the alteration in its kinetic energy. In mathematical terms:

$W=K_f -K_i= \Delta K$