A 63 gg ice cube can slide without friction up and down a 30∘30∘ slope. The ice cube is pressed against a spring at the bottom of the slope,

Question

A 63 gg ice cube can slide without friction up and down a 30∘30∘ slope. The ice cube is pressed against a spring at the bottom of the slope, compressing the spring 10 cm. The spring constant is 30 N/mN/m . When the ice cube is released, what total distance will it travel up the slope before reversing direction?

in progress 0
Thu Cúc 4 years 2021-08-27T05:47:46+00:00 1 Answers 57 views 0

Answers ( )

  1. Eirian
    0
    2021-08-27T05:48:50+00:00
    Reply

    Given Information:

    slope angle = θ = 30°

    spring constant = k = 30 N/m

    compressed length = x = 10 cm = 0.10 m

    mass of ice cube = m = 63 g = 0.063 kg

    Required Information:

    distance traveled by ice cube = d = ?  

    Answer:

    distance traveled by ice cube = 0.48 m

    Explanation:

    Using the the principle of conversation of energy, the following relation holds true for this case,

    mgh = 1/2*kx²

    h = 1/2*kx²/mg

    Where h is the height of the slope, m is the mass of ice cube, k is the spring constant and x is the compressed length o the spring and g is gravitational acceleration.

    h = 1/2*kx²/mg

    h = 1/2*30(0.1)²/0.063*9.8

    h = 0.242 m

    From trigonometry ratio,

    sinθ = h/d

    d = h/sinθ

    d = 0.242/sin(30)

    d = 0.48 m

    Therefore, when the ice cube is released, it will travel a total distance 0.48 up the slope before reversing direction.

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )