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WARRIOR [948]
3 years ago
10

A rod of mass M and length L can rotate about a hinge at its left end and is initially at rest. A putty ball of mass m, moving w

ith speed V, strikes the rod at angle θ from the normal and sticks to the rod after the collision. What is the angular speed ωf of the system immediately after the collision, in terms of system parameters and I?
Physics
1 answer:
klio [65]3 years ago
3 0

Answer:

w_f =  m*V*cos(Q_n) / L*(m+M)

Explanation:

Given:

- mass of the putty ball m

- mass of the rod M

- Velocity of the ball V

- Length of the rod L

- Angle the ball makes before colliding with rod  Q_n

Find:

What is the angular speed ωf of the system immediately after the collision,

Solution:

- We can either use conservation of angular momentum or conservation of Energy. We will use Conservation of angular momentum of a system:

                                         L_before = L_after

- Initially the rod is at rest, and ball is moving with the velocity V at angle Q from normal to the rod. We know that the component normal to the rod causes angular momentum. Hence,

                                         L_before = L_ball = m*L*V*cos(Q_n)

- After colliding the ball sicks to the rod and both move together with angular speed w_f

                                         L_after = (m+M)*L*v_f

Where, v_f = L*w_f

                                         L_after = (m+M)*L^2 * w_f

- Now equate the two expression as per conservation of angular momentum:

                                       m*L*V*cos(Q_n) = (m+M)*L^2 * w_f

                                       w_f =  m*V*cos(Q_n) / L*(m+M)

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A bicyclist starts at rest and speeds up to 30 m/s while accelerating at 4 m/s^2. Determine the distance traveled.
raketka [301]

Answer:

Distance, d = 112.5 meters

Explanation:

Initially, the bicyclist is at rest, u = 0

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Read 2 more answers
A flat loop of wire consisting of a single turn of cross-sectional area 8.00 cm2 is perpendicular to a magnetic field that incre
Evgen [1.6K]

Complete Question

A flat loop of wire consisting of a single turn of cross-sectional area 8.00 cm2 is perpendicular to a magnetic field that increases uniformly in magnitude from 0.500 T to 1.60 T in 0.99 s. What is the resulting induced current if the loop has a resistance of 1.20  \ \Omega

Answer:

The current is   I =  0.0007 41 \ A

Explanation:

From the question we are told that

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   The initial magnetic field at t_o = 0 \ seconds  is B_i = 0.500 \ T

   The magnetic field at t_1 = 0.99 \ seconds is  B_f  = 1.60 \ T

     The resistance is  R = 1.20  \ \Omega

Generally the induced emf is mathematically represented as

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=>   \epsilon  =  8.0 *10^{-4} * \frac{1.60  - 0.500 }{ 0.99- 0  }

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The kinetic energy of the box can be equated to this force. Thus, the answer is also 350 J. 
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