Q: In the calorimetry problem, which equation represents the conservation of energy for the system?

$$Q_{\text{lost}} = Q_{\text{gained}}$$

Q: A $$75.0 \ \mathrm{kg}$$ person stands $$4.25 \ \mathrm{m}$$ from the end of a $$5.00 \ \mathrm{m}$$ long, $$100 \ \mathrm{kg}$$ uniform bar. If the bar is supported at one end and by a string at the other, what is the torque due to the person about the support point?

$$\tau = 75.0 \times 9.8 \times 4.25 = 3123.75 \ \mathrm{N \cdot m}$$

Question 1

Two small spheres with a mass of 50.0 g each are suspended by a light string. A mysterious force repels the spheres so that each string makes an angle of $$20^\circ$$ with the vertical. What is the magnitude of the unknown repulsive force acting on each sphere?

Accepted Answer

$$F = 0.178 \ \mathrm{N}$$

Question 2

A ball of mass $$0.2 \ \mathrm{kg} is $$launched from a table that is $$0.8 \ \mathrm{m}$$ high at a speed of $$3.0 \ \mathrm{m/s}$$ and at an angle of $$30^\circ$$ above the horizontal. Neglecting air resistance, what is the range of the ball from the base of the table? (Use $$g = 9.8 \ \mathrm{m/s^2$})$$

Accepted Answer

$$x = 2.71 \ \mathrm{m}$$

Question 3

A uniform bar with length $$5.00 \ \mathrm{m}$$ and mass $$100 \ \mathrm{kg} is $$suspended by a string. If a person with mass $$75.0 \ \mathrm{kg}$$ stands $$4.25 \ \mathrm{m}$$ from the end of the bar, what is the tension in the string? (Assume the bar is horizontal and the string is vertical.)

Accepted Answer

$$T = 1710 \ \mathrm{N}$$

Question 4

A $$1200 \ \mathrm{g}$$ container holds $$150 \ \mathrm{g} of $$water at $$21.0^\circ \mathrm{C}. $$Two objects are dropped into the water: a $$50.0 \ \mathrm{g}$$ piece of aluminum at $$100^\circ \mathrm{C}$$ and a $$200 \ \mathrm{g}$$ piece of copper at $$85^\circ \mathrm{C}. If $$the final temperature is $$25.0^\circ \mathrm{C}$$, what is the mass of the aluminum container? (Specific heats: $$c_{Al} = 900 \ \mathrm{J/kg \cdot K}$$, $$c_{Cu} = 387 \ \mathrm{J/kg \cdot K}$$, $$c_{H_2O} = 4186 \ \mathrm{J/kg \cdot K})$$

Accepted Answer

$$m_{Al} = 258 \ \mathrm{g}$$

Question 5

A $$0.45$$ caliber bullet of mass $$16.2 \ \mathrm{g}$$ strikes a stationary wood block of mass $$500 \ \mathrm{g} at$$ $$331 \ \mathrm{m/s}. $$The block is attached to a light spring, which is initially at rest with a spring constant of $$550 \ \mathrm{N/m}. $$How much does the bullet-block system compress the spring?

Accepted Answer

$$x = 0.318 \ \mathrm{m}$$

Question 6

In the problem involving two spheres suspended by strings and repelled by a mysterious force, which of the following equations correctly relates the repulsive force $$F to $$the mass $$m$$, gravitational acceleration $$g$$, and angle $$	heta$$?

Accepted Answer

$$F = mg 	an 	heta$$

Question 7

A block slides off a table of height $$h$$ with an initial horizontal velocity $$v_0. $$Which of the following expressions gives the time $$t it $$takes to hit the ground?

Accepted Answer

$$t = \sqrt{\dfrac{2h}{g}}$$

Question 8

In the spring compression problem, after the bullet embeds in the block, which conservation law is used to find the velocity of the combined mass immediately after the collision?

Accepted Answer

Conservation of momentum

Question 9

A uniform bar is in static equilibrium, supported at one end and by a string at the other. Which condition must be satisfied for equilibrium?

Accepted Answer

The sum of torques about any point must be zero.

Question 10

In the calorimetry problem, which equation represents the conservation of energy for the system?

Accepted Answer

$$Q_{	ext{lost}} = Q_{	ext{gained}}$$

Question 11

A $$0.2 \ \mathrm{kg}$$ ball is launched horizontally from a $$0.8 \ \mathrm{m}$$ high table at $$3.0 \ \mathrm{m/s}. $$How long does it take to hit the ground?

Accepted Answer

$$t = 0.404 \ \mathrm{s}$$

Question 12

In the spring compression problem, after the collision, which equation is used to relate the kinetic energy of the block-bullet system to the compression $$x of $$the spring?

Accepted Answer

$$\dfrac{1}{2} m v^2$ = \dfrac{1}{2} k x^2$

Question 13

A $$75.0 \ \mathrm{kg}$$ person stands $$4.25 \ \mathrm{m}$$ from the end of a $$5.00 \ \mathrm{m}$$ long, $$100 \ \mathrm{kg}$$ uniform bar. If the bar is supported at one end and by a string at the other, what is the torque due to the person about the support point?

Accepted Answer

$$	au = 75.0 	imes 9.8 	imes 4.25 = 3123.75 \ \mathrm{N \cdot m}$$

Question 14

Which of the following best describes the energy transformation that occurs when the bullet-block system compresses the spring?

Accepted Answer

Kinetic energy is converted into elastic potential energy.

Question 15

In the calorimetry problem, if the final temperature is higher than expected, which of the following could be a possible reason?

Accepted Answer

The mass of the aluminum container was underestimated.

Question 16

A $$0.2 \ \mathrm{kg}$$ ball is launched at $$3.0 \ \mathrm{m/s}$$ from a $$0.8 \ \mathrm{m}$$ high table at $$30^\circ$$ above the horizontal. What is the initial vertical component of velocity?

Accepted Answer

$$v_{0y} = 3.0 \sin 30^\circ = 1.5 \ \mathrm{m/s}$$

Physics Assignment 10: Forces, Energy, Rotational Dynamics, and Thermodynamics

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