- #1
jones123
- 10
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Hi,
I tried to solve this problem myself and I'd like someone to check it :) Thanks already!
A ball is rolling towards a block, which is connected to a spring. Assume no friction occurs. The initial velocity of the ball is 10 m/s. The spring constant is k = 5 N/m. Mass of the ball = 5 kg and mass of the block connected to the spring = 2 kg. After the ball hit the block, the spring starts oscillating harmonically. Calculate:
(a) the final velocity of the ball if it rolls back immediately.
=> i don't really know if you should concern the 'rolling motion' but I used the formula of an elastic collision where m1 = block and m2 = mass
=> v2f = ((m2-m1)v2i + 2m1v1i) / (m1+m2) = (5-2)(10) / 7 = 4,28 m/s
(b) what is the amplitude of the oscillation?
=> conservation of energy : (1/2)mv² = (1/2)kx²
where v = v1f = ((m1-m2)v1i + 2m2v2i) / (m1+m2) = 2(5)(10) / 7 = 14.28 m/s
=> putting this into the formula:
x² = 2(14.28) / 5 => x = 2.38m
(c) the max acceleration of the block
a(max) = kx/m = (5)(2.38)/(2) = 5.95 m/s² or a(max) = Aw² = (2.38)(5/2) = 5.95 m/s²
I tried to solve this problem myself and I'd like someone to check it :) Thanks already!
A ball is rolling towards a block, which is connected to a spring. Assume no friction occurs. The initial velocity of the ball is 10 m/s. The spring constant is k = 5 N/m. Mass of the ball = 5 kg and mass of the block connected to the spring = 2 kg. After the ball hit the block, the spring starts oscillating harmonically. Calculate:
(a) the final velocity of the ball if it rolls back immediately.
=> i don't really know if you should concern the 'rolling motion' but I used the formula of an elastic collision where m1 = block and m2 = mass
=> v2f = ((m2-m1)v2i + 2m1v1i) / (m1+m2) = (5-2)(10) / 7 = 4,28 m/s
(b) what is the amplitude of the oscillation?
=> conservation of energy : (1/2)mv² = (1/2)kx²
where v = v1f = ((m1-m2)v1i + 2m2v2i) / (m1+m2) = 2(5)(10) / 7 = 14.28 m/s
=> putting this into the formula:
x² = 2(14.28) / 5 => x = 2.38m
(c) the max acceleration of the block
a(max) = kx/m = (5)(2.38)/(2) = 5.95 m/s² or a(max) = Aw² = (2.38)(5/2) = 5.95 m/s²
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