Compute the force exerted on the palm of your hand by the beam from a 1.0 W flashlight ( a ) if

Compute the force exerted on the palm of your hand by the...

Key Concepts

Radiation Pressure

Radiation pressure is the pressure exerted upon any surface due to the exchange of momentum between the surface and the electromagnetic radiation (light) striking it. It depends on whether the light is absorbed or reflected; absorption transfers one unit of momentum per photon, while reflection transfers twice that amount due to the reversal of the photon's direction.

Photon Momentum

Despite having no mass, photons carry momentum, which is related to their energy by the formula p = E/c. This relationship is fundamental to understanding how light can exert forces, as the momentum from many photons adds up to create a measurable force when they interact with a surface.

Force from Light

The force exerted by light on a surface is calculated as the rate of momentum transfer. For a given power P, if the light is fully absorbed the force is F = P/c, and if it is fully reflected the force doubles, F = 2P/c. This concept links the energy of the light beam with the resulting mechanical force.

Mass Equivalent

The mass equivalent of a force is determined by relating it to the gravitational force experienced by a mass at Earth's surface using the equation F = mg. This allows one to determine the effective mass that would produce an equivalent force when subjected to Earth's gravitational acceleration.

Transcript

00:01 Hi there.

00:02 So for this problem, we need to determine the force that is asserted on the palm of your hand.

00:09 And when a bin of light of one watts that we call p, that's the power of one watts.

00:23 And we need to determine what is that force if the hand absorbs the light as in part b.

00:33 And if the light reflects from the hand.

00:37 And after that, we need to determine the mass of the particle if we hold it on earth's surface.

00:44 So to do that, we need first to determine the momentum that that particle has.

00:52 And by using the impulse momentum theorem, we can determine the force.

01:04 And just by applying newton's second.

01:06 Law that you know and we know that is force equals to mass times the acceleration and we can use the acceleration due to gravity and on earth and we can determine the mass of this particle on earth so to do the first thing we need to remember that power if we just know is equal to the units of power are joules over second.

01:47 And then the momentum, we know that the momentum, and we know that the energy is of a particle, is if we just suppose that the kinetic energy of a particle is much greater than its rest energy.

02:11 So we will obtain this relation between the energy and the momentum.

02:16 And then solving for the momentum, we will have e over c.

02:21 So in this case, we just simply put the value of that energy.

02:37 So it will be the momentum is equal to 1 joules over seconds over c.

02:48 We're going to live it with that without the value of c.

02:53 We're going to put it after.

02:57 So for part a of this problem of being absorbed by the hand, the momentum change is just equal to this because we know that the momentum change for part a, the momentum change is the final momentum minus the initial momentum.

03:15 And in this case, the final momentum is just the momentum that we obtain at the beginning of this.

03:27 It's just we don't have any initial momentum because there is no reflection from the hand.

03:48 So we know that from the impulse momentum theorem, the impulse momentum, impose momentum, theorem, tell us that the force times, an interval of time, is the change in momentum.

04:22 So we simply need to solve for f, for the force, and then obtained the force, asserted by that being of on the hat.

04:38 So we'll obtain that this is equal to the momentum over this time.

04:53 And having this, we just simply put all of those values that we know, one joules per second over c times the time this take.

05:13 And we know that that is one second.

05:19 And this gives us 3 .3 .3 .3.

05:35 3 times 10 to the minus 9 newtons.

05:45 And here we just have used the value for c that is 3 times 10 to the 8 meters per second.

05:55 So we obtain this force.

05:57 Now to obtain the mass of that particle, we know that the force is equal to the mass times the acceleration.

06:03 In this case, the acceleration of gravity on earth.

06:08 So we just simply need to divide the force over the value of g.

06:16 And doing that, sorry, in here we put minus 9 utons...

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