2. Am 80.0 kg astronaut is training for accelerations that he will experience upon re-entry to earth’s gravity from space. He is placed in a centrifuge (r = 25.0 m) and spun at a constant angular velocity of 10.0 rpm (revolutions per minute). a. Find the linear velocity of the centrifuge in m/s. Show your work

b. Find the magnitude and direction of the centripetal acceleration when he is spinning at this constant velocity.

c. How many g’s is the astronaut experiencing? (at constant velocity)

d. Find the linear deceleration and torque required to bring the centrifuge (5000.0 kg) to a stop over a 5 minute time period.

a)   v = 26.2 m / s, b) acceleration is radial, a = 27.4 m / s², c)   a = 2.8 g and

d) a = - 8.73 10⁻² m / s²,  τ = 1.09 10⁴ N m

Explanation:

a) For this exercise we can use the relationships between rotational and linear motion

           v = w r

let's reduce the magnitudes to the SI system

          w = 10 rpm (2pi rad / 1 rev) 1 min / 60s) = 1,047 rad / s

          r = 25.0 m

let's calculate

          v = 1.047 25.0

          v = 26.2 m / s

b) When the body is rotating at constant speed, the relationship must be perpendicular to the speed, therefore the direction of acceleration is radial, that is, towards the center of the circle and its magnitude is

            a = v² / r

            a = 26.2²/25

            a = 27.4 m / s²

c) Let's look for the relationship between the centripetal acceleration and the acceleration due to gravity

           a / g = 27.4 / 9.8

           a / g = 2.8

           a = 2.8 g

d) let's find the deceleration and torque to stop the centripette in 5 min

           t = 5 min (60 s / 1min) = 300 s

let's use the rotational kinematics relations

           w = w₀ + α t

initial angular velocity is wo = 1,047 rad / s and the final as is stop do w = 0

           α = - w₀ / t

           α = - 1,047 / 300

           α = -3.49 10⁻³ rad / s²

angular and linear are related

           a = α r

           a = -3.49 10⁻³ 25

           a = - 8.73 10⁻² m / s²

the negative sign indicates that the acceleration is stopping the movement

torque is

           τ = F r

The force can be found with Newton's second law

          F = m a

we substitute

         τ = m a r

         τ = 5000.0   8.73 10⁻²  25

         τ = 1.09 10⁴ N m

Answer:

Step-by-step explanation:

To solve this problem, we can use the conservation of energy and conservation of momentum principles.

Conservation of energy:

The total initial energy is the rest energy of the proton and neutron, which is given by:

Ei = (mp + mn)c^2

where mp and mn are the masses of the proton and neutron, respectively, and c is the speed of light.

The total final energy is the rest energy of the deuteron plus the energy of the gamma ray, which is given by:

Ef = (md)c^2 + Eg

where md is the mass of the deuteron and Eg is the energy of the gamma ray.

According to the conservation of energy principle, the initial energy and final energy must be equal, so we have:

Ei = Ef

(mp + mn)c^2 = (md)c^2 + Eg

Conservation of momentum:

The total initial momentum is zero because the proton and neutron are at rest. The total final momentum is the momentum of the deuteron and the momentum of the gamma ray. Since the gamma ray is massless, its momentum is given by:

pg = Eg/c

where pg is the momentum of the gamma ray.

According to the conservation of momentum principle, the total final momentum must be equal to zero, so we have:

0 = pd + pg

where pd is the momentum of the deuteron.

Solving for md and pd:

From the conservation of energy equation, we can solve for md:

md = (mp + mn - Eg/c^2)/c^2

Substituting this expression into the conservation of momentum equation, we get:

pd = -pg = -Eg/c

Substituting the given values, we have:

mp = 1.6726 × 10^-27 kg mn = 1.6749 × 10^-27 kg Eg = 2.2 × 10^6 eV = 3.52 × 10^-13 J

Using c = 2.998 × 10^8 m/s, we get:

md = (1.6726 × 10^-27 kg + 1.6749 × 10^-27 kg - 3.52 × 10^-13 J/(2.998 × 10^8 m/s)^2)/(2.998 × 10^8 m/s)^2 = 3.3435 × 10^-27 kg

pd = -Eg/c = -(3.52 × 10^-13 J)/(2.998 × 10^8 m/s) = -1.1723 × 10^-21 kg·m/s

Therefore, the mass of the deuteron is 3.3435 × 10^-27 kg, and its momentum is -1.1723 × 10^-21 kg·m/s.

Answer:

Step-by-step explanation:

Time taken by the tomatoes to each the ground

using h = 1/2 g t^2 

t^2 = 2h/g = 2 x 50/ 9.8 = 10.2

t = 3.2 sec 

horizontal ditance = speed x time = 3 x 3.2 = 9.6 meters

The question specifies the diameter of the screw, therefore the IMA of this screw is 0.812? / 0.318 = 8.02