As shown in the figure, a bullet of mass 0.010 kg moving horizontally suddenly s

Question

As shown in the figure, a bullet of mass 0.010 kg moving horizontally suddenly strikes n block of wood of mass 1.5 kg that is suspended as a pendulum. The bullet lodges in the wood, and together they swing upward a vertical distance of 0.40 m. The length of the string is 2.0 m. What was the speed of the bullet just before it struck the wooden block? A) 650 m/s B) 420 m/s C) 250 m/s D) 67 m/s E) 370 m/s An 8.0-g bullet is suddenly shot into a 4.0-kg block that is at rest on a frictionless horizontal surface, as shown in the figure. The bullet remains lodged in the block. The block then moves against a spring and compresses it by 3.7 cm. The force constant (spring constant) of the spring is 2500 N/m. What was the initial speed upsilon of the bullet? A) 480 m/s B) 520 m/s C) 460 m/s D) 440 m/s E) 500 m/s A block of mass m = 4.4 kg, moving on frictionless surface with a speed upsilon_i - 9.2 m/s, makes a sudden perfectly elastic collision with a second block of mass M, as shown in the figure. The second block is originally at rest. Just after the collision, the 4.4-kg block recoils with a speed of upsilon_f = 2.5 m/s. What is the mass M of the second block? A) 0 kg B) 0 kg C) 0 kg D) 0 kg E) 7.7 kg

Explanation / Answer

(1)

initial KE Grav.PE ..
½(M +m)v² = (M +m) gh
v = (2gh) = (2 x 9.81 x 0.4) = 2.8014 m/s

now, m*V=(m+M)*v

V = (1.510 x 2.8014) / 0.010 =424.91 m/s... (b)

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