Question

1. A mass of 0.019 kg attached to a spring with spring constant 27.0 N/m is pulled to the right 8.0 cm and released. The mass oscillates with a frequency of 6.0 Hz. If the mass is pulled to the right 16.0 cm before being released, what is the frequency?

a. 6.0 Hz

b. 3.0 Hz

c. 1.5 Hz

d. 12 Hz

e. 24 Hz

2. A window loses power/heat energy through a pane of glass to the cold outside. If the thickness of the glass is doubled and the area of the glass is halved, then the power loss to the cold outside will be?

a. one half of the original power loss

b. twice the original power loss

c. the same as the original power loss

d. four times the original power loss

e. one quarter of the original power loss

3. A skater spins on ice. When she pulls in her arms, she reduces her rotational inertia and her angular speed increases. Compared to her initial rotational kinetic energy, the rotational kinetic energy when she has pulled in her arms must be?

a. smaller

b. the same

c. larger

Answer 1

1. The equation of the frequency of the oscillation on a spring f = 1/2π .√(k/m).

And from the equation,it is clear that the frequency is indipendent of the displacement x.

So frequency remain same.

So the Correct answer is( a) 6 Hz.

2. The equation for the heat transfer through a surface is

Q = Ak/L dT

Where A is the area L is the thickness, k is a constant and dT is the temperature difference.

Here A is made half so A = A/2

Thickness is doubled , so L = 2L

So the heat transfer Q = A k /2*2L. dT

Or Q becomes Q/4.

So heat lost will become one quarter of first value.

The correct answer is,( e. )One quarter of the original power loss

3.

The equation for the rotational KE is,

KE = 1/2 I w² ,where I is the moment of inertia and w is the angular velocity.

KE = 1/2 . ( I w). w = 1/2 * L * w

Where L is the angular momentum and angular momentum is conserved here.But since the w increase upon decreasing the radius we can see that it will make the kinetic energy increase.

So kinetic energy increase on decreasing radius.

So the Correct answer is( c .) Larger

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