Using Algebra, solve the following problem: Set-Up: A mass of 1.0kg is pushed ag

Question

Using Algebra, solve the following problem:
Set-Up: A mass of 1.0kg is pushed against a spring with a spring constant of 250N/m. As a result, the spring is compressed by 20cm. The mass is then released.
a) If the mass now slides along a smooth 1/4 circular loop, what will its speed be at the top of the curve when it is going directly upward if the radius of the loop is 25cm?
b) What is the size of the centripetal acceleration of the mass at the point c? (question 'c' result)
c) What is the centripetal force on the mass at point c? Find Fc(magnitude) and Fc(direction ).
* Potential energy when the spring is compressed is 5 Joules. The kinetic energy of the mass after it is released and is o longer in contact with the spring is 5 Joules

Explanation / Answer

A)

applied force F= kx = 250 * 20*10-3 = 50 N

velocity of the object

F = mv2/r = 50

v = ?(50*20*10-2 /1)

=3.16 m/s

B)

acceleration

F=ma = mv2/r

a = v2/r = 10/20*10-2 = 50 m/s2

C) F = 50N along the direction of tangent drawn in the direction of the movement at point c

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