Q: A student drops a ball from a height of $$2\ \text{m}. $$Ignoring air resistance, what is the speed of the ball just before it hits the ground? (Take $$g = 9.8\ \text{m/s}^2.)$$

The speed is $$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 2}.$$

Question 1

A block of mass $$m = 2.0\ 	ext{kg} is $$suspended from a spring with spring constant $$k = 50\ 	ext{N/m}. If $$the block is released from rest at a height $$h = 0.5\ 	ext{m}$$ above its equilibrium position, what is the maximum extension of the spring? (Assume $$g = 9.8\ 	ext{m/s}^2.)$$

Accepted Answer

The maximum extension is $$x = \frac{mg}{k} + \sqrt{\frac{2mgh}{k}}.$$

Question 2

A mass $$m is $$attached to a vertical spring and allowed to oscillate. Which of the following best describes the energy transformation during one complete oscillation?

Accepted Answer

Energy alternates between kinetic and potential, with total mechanical energy conserved.

Question 3

A student drops a ball from a height of $$2\ 	ext{m}. $$Ignoring air resistance, what is the speed of the ball just before it hits the ground? (Take $$g = 9.8\ 	ext{m/s}^2.)$$

Accepted Answer

The speed is $$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 2}.$$

Question 4

In a pulley system, two masses $$m_1$$ and $$m_2$$ are connected by a string over a frictionless pulley. If $$m_1$$ \u003e $$m_2$$, what is the acceleration of the system?

Accepted Answer

The acceleration is $$a = \frac{(m_1$ - m_2$)g}{m_1$ + m_2$}.$$

Question 5

A block of mass $$m is $$released from rest and falls freely under gravity. Which equation best describes the displacement $$s$$ after time $$t$$?

Accepted Answer

$$s = \frac{1}{2}gt^2$

Question 6

A mass $$m is $$attached to a spring and oscillates with angular frequency $$\omega. $$What is the relationship between $$\omega$$, $$k ($$spring constant), and $$m$$?

Accepted Answer

$$\omega = \sqrt{\frac{k}{m}}$$

Question 7

A student swings a pendulum in a circle. If the length of the pendulum is doubled, what happens to the period of oscillation?

Accepted Answer

The period increases by a factor of $$\sqrt{2}.$$

Question 8

A block of mass $$m is $$placed on a frictionless incline of angle $$	heta. $$What is the acceleration of the block down the incline?

Accepted Answer

$$a = g\sin	heta$$

Question 9

A mass $$m is $$dropped from a height $$h$$ and rebounds to a height $$h/2. $$What fraction of the energy is lost during the collision with the ground?

Accepted Answer

The fraction lost is $$\frac{1}{2}.$$

Question 10

A student uses a spring scale to measure the weight of an object. If the spring constant is $$k$$ and the extension is $$x$$, what is the weight of the object?

Accepted Answer

Weight is $$W = kx$$

Question 11

A mass $$m is $$attached to a spring and oscillates with amplitude $$A. $$What is the maximum speed of the mass?

Accepted Answer

Maximum speed is $$v_{max} = \omega A$$

Question 12

A block of mass $$m is $$dropped from a height $$h$$ onto a spring with spring constant $$k. $$What is the maximum compression $$x of $$the spring?

Accepted Answer

$$x = \sqrt{\frac{2mgh}{k}}$$

Question 13

A student observes a pendulum and measures its period. If the acceleration due to gravity increases, what happens to the period?

Accepted Answer

The period decreases.

Question 14

A block of mass $$m is $$attached to a spring and oscillates with total energy $$E. $$What is the potential energy when the displacement is $$x$$?

Accepted Answer

Potential energy is $$U = \frac{1}{2}kx^2$

Question 15

A student drops a mass $$m$$ from a height $$h$$ and it lands on a spring, compressing it by $$x. $$Which equation relates the gravitational potential energy to the elastic potential energy?

Accepted Answer

$$mgh = \frac{1}{2}kx^2$

Question 16

A block of mass $$m is $$attached to a spring and oscillates with frequency $$f. $$What is the relationship between $$f$$, $$k$$, and $$m$$?

Accepted Answer

$$f = \frac{1}{2\pi} \sqrt{\frac{k}{m}}$$

Question 17

A student observes a mass oscillating on a spring. If the mass is doubled, what happens to the period of oscillation?

Accepted Answer

The period increases by a factor of $$\sqrt{2}.$$

Question 18

A block of mass $$m is $$placed on a frictionless surface and attached to a spring. If the spring is compressed by $$x$$ and released, what is the speed of the block as it passes through equilibrium?

Accepted Answer

$$v = \sqrt{\frac{k}{m}}x$$

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