A block of mass M with width 3 cm and height 4 cm sits on a rough plank. The coe

Question

A block of mass M with width 3 cm and height 4 cm sits on a rough plank. The coefficient of static friction between the plank and the block is s = 2/3. The plank is slowly tipped up. Does the block slip first, or tip first? A ball of mass 1 kg is attached to a spring of spring constant 100 N/m. The spring is then attached to a wall, while the ball rests on a level, frictionless surface. If the ball is pulled back 10 cm and then let go, find: The speed of the ball when it reaches the equilibrium point. The maximum distance the spring is compressed. The period of oscillation.

Explanation / Answer

1) it is tipped because it is a rough surface

2) time period T = 2pisqrt(m/k)

T = 2*3.14sqrt(1/100) = 0.628 sec

w = 2pi/T = 10 rad/sec

f = kx

ma = kx

a = kx/m = a = 100*0.1/1 = 10 m/s^2

1/2mvmax^2 = 1/2kA^2

v max = 100*0.1^2/1 = 1 m/sec

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