Two masses are connected by a light string that passes over a frictionless pulle

Question

Two masses are connected by a light string that passes over a frictionless pulley as shown below. If the incline is frictionless, the angle of the incline is 50.0 degree, m_1 = 6.00 kg and m_2 = 2.00 kg find (a) acceleration of the masses, (b) tension in the string, and (c) the speed of each mass 2.00 s after being released from rest. Three blocks are in contact with each other on a frictionless horizontal surface, as shown below A horizontal force F is applied to m_1 If m_1 = 2.00 kg m_2 = 3.00 kg. m_3 = 4.00 kg and F = 18.0 N. draw a separate FBD for each block and find (a) the acceleration of the blocks (b) the NET force on each Mock, and (c) the magnitudes of the contact forces between the blocks. A 9.00-kg hanging block (m_2) is connected by a string over a pulley to a 5.00-kg block that is sliding on a flat table (m_1). If the coefficient of kinetic friction is 0.200, find the tension in the string.

Explanation / Answer

1) Here ,

let the tension in the string is T

and the accelration of the blocks is a

for block m1

6 * 9.8 * sin(50 degree) - T = 6 * a

for the block m2

T - 2 * 9.8 = 2 * a

solving these equations

a = 3.18 m/s^2

T = 26 N

a) the acceleration of the masses is 3.18 m/s^2

b) the tension in the string is 26 N

c) speed of each mass will be same

speed of each mass after 2 sec = a * time

speed of each mass after 2 sec = 3.18 * 2

speed of each mass after 2 sec = 6.36 m/s

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