Can you show work or explain? Thanks in advance! A pendulum, consisting of a bal

Question

Can you show work or explain? Thanks in advance!

A pendulum, consisting of a ball of mass m on a light string of length 1.00 m, is swung back to a 45° angle and released from rest. The ball swings down and, at its lowest point, collides with a block of mass 2m that is on a frictionless horizontal surface. After the collision, the block slides 1.00 m across the frictionless surface and an additional 0.280 m, before coming to rest, across a horizontal surface where the coefficient of friction between the block and the surface is 0.140. Use g = 9.80 m/s2. (a) What is the block's speed after the collision? m/s (b) What is the velocity of the ball immediately after the collision? Use a plus sign if the velocity is in the same direction as the velocity of the ball just before the collision, and a negative sign if the velocity is in the opposite direction as the velocity of the ball just before the collision. m/s

Explanation / Answer

(A) a = - uk g = -0.140 x 9.81 = - 1.37 m/s^2

Applying vf^2 - vi^2 = 2 a d

0^2 - v^2 = 2(-1.37)(0.280)

v = 0.88 m/s ........Ans

(b) velocity of ball just before collision,

m v0^2 /2 = m g h = m g L (1 - cos45)

v0 = (2 x 9.81 x 1 x ( 1 - cos45))

v0 = 2.40 m/s

Applying momentum conservation for the collision,

(m x 2.40) + (2m x 0) = (m vf) + (2m x 0.88)

vf = 0.65 m/s ......Ans

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