A pendulum of mass 2 kg is initially at rest at an angle of 45. It swings down a

Question

A pendulum of mass 2 kg is initially at rest at an angle of 45. It swings down and strikes a block at the lowest point in its swing in a perfectly elastic collision. The block also has mass 2 kg and is propelled forward at 2 m/s after the collision.

a. Calculate the tangential speed of the pendulum just before it strikes the block.

b. Calculate the length of the pendulum.

c. Calculate the radial and tangential acceleration of the pendulum just before it collides with the block. 45 mm

d. Calculate the angular speed and angular acceleration of the pendulum just before it collides with the block.

e. Calculate the torque on the pendulum about an axis through the top of the pendulum (the place where the pendulum is attached to the ceiling) due to the block if the collision lasts 0.2 s.

f. The block slides across the floor 0.5 m before striking a spring. The spring has a spring constant, k = 250 N/m, and is compressed by 9.5 cm. Is the floor frictionless? If not calculate the coefficient of friction between the block and the floor.

Explanation / Answer

(A) when mass is same and collision is elastic then velocities get exchanged.

so v0 = 2 m/s

(b) Applying energy conservation,

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

2 x 9.81 x L (1 - cos45) = 2^2

L = 0.696 m

(C) at = 0

and a_r = v^2 / L = 5.75 m/s^2

(D) angular acc= 0

angular speed = v / L = 2.87 rad/s

(e) torque x time = change in angular moementum

0.2 (torque ) = 2 x 2 x 0.696

torque = 13.92 N m

(f) 250(0.095^2) /2 =uk (2 x 9.81 x 0.5)

uk = 0.115

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