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garik1379 [7]
2 years ago
5

a 1 kg ball is confined to move on a. vertical circle of a radius 2 meters. There is no friciton between the bead and the circul

ar track. The bead has a speed of 10 m/s when at the top of the circle at point A, adn the total
Physics
1 answer:
monitta2 years ago
3 0

The total centripetal force is 50N

Given

mass of the ball= 1kg

speed of the ball = 10m/s

Radius = 2m

we know that

centripetal force = F =\frac {mv^2}{r}

F = \frac {1 \times {10}^2}{2} = 50 N

<h3>What is Centripetal force?</h3>
  • A force that causes a body to follow a curved path is known as a centripetal force.
  • It always moves in a direction that is the opposite of the body's velocity and in the direction of the immediate center of curvature of the path. It is "a force by which bodies are dragged or driven, or in any other way gravitate, towards a point as to a center," according to Isaac Newton.
  • Gravity is the centripetal force that drives astronomical orbits according to Newtonian mechanics.

To learn more about centripetal force with the given link

brainly.com/question/11324711

#SPJ4

Question:

a 1 kg ball is confined to move on a. vertical circle of a radius of 2 meters. There is no friction between the bead and the circular track. The bead has a speed of 10 m/s when at the top of the circle at point A, find the total centripetal force.

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A solid cylinder of mass M = 45 kg, radius R = 0.44 m and uniform density is pivoted on a frictionless axle coaxial with its sym
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Answer:

w_f = 1.0345 rad/s

Explanation:

Given:

- The mass of the solid cylinder M = 45 kg

- Radius of the cylinder R = 0.44 m

- The mass of the particle m = 3.6 kg

- The initial speed of cylinder w_i = 0 rad/s

- The initial speed of particle V_pi = 3.3 m/s

- Mass moment of inertia of cylinder I_c = 0.5*M*R^2

- Mass moment of inertia of a particle around an axis I_p = mR^2

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- What is the magnitude of its angular velocity after the collision?

Solution:

- Consider the mass and the cylinder as a system. We will apply the conservation of angular momentum on the system.

                                     L_i = L_f

- Initially, the particle is at edge at a distance R from center of cylinder axis with a velocity V_pi = 3.3 m/s contributing to the initial angular momentum of the system by:

                                    L_(p,i) = m*V_pi*R

                                    L_(p,i) = 3.6*3.3*0.44

                                    L_(p,i) = 5.2272 kgm^2 /s

- While the cylinder was initially stationary w_i = 0:

                                    L_(c,i) = I*w_i

                                    L_(c,i) = 0.5*M*R^2*0

                                    L_(c,i) = 0 kgm^2 /s

The initial momentum of the system is L_i:

                                    L_i = L_(p,i) + L_(c,i)

                                    L_i = 5.2272 + 0

                                    L_i = 5.2272 kg-m^2/s

- After, the particle attaches itself to the cylinder, the mass and its distribution around the axis has been disturbed - requires an equivalent Inertia for the entire one body I_equivalent. The final angular momentum of the particle is as follows:

                                   L_(p,f) = I_p*w_f

- Similarly, for the cylinder:

                                   L_(c,f) = I_c*w_f

- Note, the final angular velocity w_f are same for both particle and cylinder. Every particle on a singular incompressible (rigid) body rotates at the same angular velocity around a fixed axis.

                                  L_f = L_(p,f) + L_(c,f)

                                  L_f = I_p*w_f + I_c*w_f

                                  L_f = w_f*(I_p + I_c)

-Where, I_p + I_c is the new inertia for the entire body = I_equivalent that we discussed above. This could have been determined by the superposition principle as long as the axis of rotations are same for individual bodies or parallel axis theorem would have been applied for dissimilar axes.

                                  L_i = L_f

                                  5.2272 = w_f*(I_p + I_c)

                                  w_f =  5.2272/ R^2*(m + 0.5M)

Plug in values:

                                  w_f =  5.2272/ 0.44^2*(3.6 + 0.5*45)

                                  w_f =  5.2272/ 5.05296

                                  w_f = 1.0345 rad/s

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