Q: A steel wire of length $$2\ \mathrm{m}$$ and cross-sectional area $$1\ \mathrm{mm^2$} is $$stretched by $$1\ \mathrm{mm}$$ under a load. What is the Young's modulus of steel if the force applied is $$200\ \mathrm{N}$$?

$$4 \times 10$$^{11}$$\ \mathrm{N/m^2$}$$

Question 1

A car accelerates uniformly from rest to a velocity of $$20\ \mathrm{m/s} in$$ $$10\ \mathrm{s}. $$What is the displacement of the car during this time?

Accepted Answer

$$100\ \mathrm{m}$$

Question 2

A solid disk of mass $$2\ \mathrm{kg}$$ and radius $$0.5\ \mathrm{m}$$ rotates about its center with an angular velocity of $$4\ \mathrm{rad/s}. $$What is its rotational kinetic energy?

Accepted Answer

$$2\ \mathrm{kg\cdot m^2$}$$

Question 3

A $$5\ \mathrm{kg}$$ object is dropped from a height of $$10\ \mathrm{m}. $$Ignoring air resistance, what is its velocity just before hitting the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$14\ \mathrm{m/s}$$

Question 4

A $$0.2\ \mathrm{kg}$$ ball is attached to a string and swung in a horizontal circle of radius $$0.5\ \mathrm{m} at a $$speed of $$3\ \mathrm{m/s}. $$What is the tension in the string?

Accepted Answer

$$3.6\ \mathrm{N}$$

Question 5

A copper rod of length $$2\ \mathrm{m} is $$heated from $$20^\circ\mathrm{C} to$$ $$100^\circ\mathrm{C}. If $$the coefficient of linear expansion for copper is $$1.7 	imes 10$$^{-5}$$\ \mathrm{K}^{-1}$$, what is the change in length?

Accepted Answer

$$0.0027\ \mathrm{m}$$

Question 6

A hydraulic lift has a small piston of area $$0.01\ \mathrm{m^2$}$$ and a large piston of area $$0.5\ \mathrm{m^2$}. If a $$force of $$100\ \mathrm{N} is $$applied to the small piston, what is the maximum weight that can be lifted by the large piston (ignoring friction)?

Accepted Answer

$$5000\ \mathrm{N}$$

Question 7

A $$1\ \mathrm{kg}$$ block slides down a frictionless incline of height $$5\ \mathrm{m}. $$What is its speed at the bottom?

Accepted Answer

$$10\ \mathrm{m/s}$$

Question 8

A gas in a sealed container is heated at constant volume. According to the ideal gas law, what happens to the pressure?

Accepted Answer

It increases linearly with temperature.

Question 9

A $$0.5\ \mathrm{kg}$$ mass is attached to a spring with spring constant $$k = 200\ \mathrm{N/m}. $$What is the period of oscillation?

Accepted Answer

$$0.314\ \mathrm{s}$$

Question 10

A $$2\ \mathrm{kg}$$ object moving at $$3\ \mathrm{m/s}$$ collides elastically with a stationary $$1\ \mathrm{kg}$$ object. What is the velocity of the $$2\ \mathrm{kg}$$ object after the collision?

Accepted Answer

$$1\ \mathrm{m/s}$$

Question 11

A $$0.1\ \mathrm{kg}$$ sample of water at $$20^\circ\mathrm{C}$$ absorbs $$8.36\ \mathrm{kJ} of $$heat. What is the final temperature of the water? (Specific heat of water $$= 4186\ \mathrm{J/kg\cdot K})$$

Accepted Answer

$$40^\circ\mathrm{C}$$

Question 12

A cylinder contains $$0.5\ \mathrm{mol} of an $$ideal gas at $$300\ \mathrm{K}. $$What is the pressure if the volume is $$10\ \mathrm{L}$$? ($$R = 8.31\ \mathrm{J/(mol\cdot K)})$$

Accepted Answer

$$124.65\ \mathrm{kPa}$$

Question 13

A steel wire of length $$2\ \mathrm{m}$$ and cross-sectional area $$1\ \mathrm{mm^2$} is $$stretched by $$1\ \mathrm{mm}$$ under a load. What is the Young's modulus of steel if the force applied is $$200\ \mathrm{N}$$?

Accepted Answer

$$4 	imes 10$$^{11}$$\ \mathrm{N/m^2$}$$

Question 14

A $$0.2\ \mathrm{kg}$$ object is attached to a string and swung in a vertical circle of radius $$0.5\ \mathrm{m}. $$What is the minimum speed at the top of the circle to keep the string taut?

Accepted Answer

$$2.2\ \mathrm{m/s}$$

Question 15

A $$0.5\ \mathrm{kg}$$ block is pushed against a spring (with $$k = 100\ \mathrm{N/m}) $$and compresses it by $$0.2\ \mathrm{m}. $$What is the maximum speed of the block when released?

Accepted Answer

$$2\ \mathrm{m/s}$$

Question 16

A $$1\ \mathrm{kg}$$ object is moving in a circle of radius $$2\ \mathrm{m} at a $$constant speed of $$4\ \mathrm{m/s}. $$What is the centripetal force acting on the object?

Accepted Answer

$$8\ \mathrm{N}$$

Question 17

A $$0.1\ \mathrm{kg}$$ aluminum cube at $$100^\circ\mathrm{C} is $$dropped into $$0.5\ \mathrm{kg} of $$water at $$20^\circ\mathrm{C}. $$What is the final equilibrium temperature? (Specific heat of aluminum $$= 900\ \mathrm{J/kg\cdot K}$$, water $$= 4186\ \mathrm{J/kg\cdot K})$$

Accepted Answer

$$22^\circ\mathrm{C}$$

Question 18

A $$0.5\ \mathrm{kg}$$ ball is thrown vertically upward with an initial speed of $$10\ \mathrm{m/s}. $$What is the maximum height reached?

Accepted Answer

$$5.1\ \mathrm{m}$$

Question 19

A $$2\ \mathrm{kg}$$ object is moving at $$5\ \mathrm{m/s}. $$What is its momentum?

Accepted Answer

$$10\ \mathrm{kg\cdot m/s}$$

Comprehensive Physics Formula Sheet: Mechanics, Fluids, Heat, and Material Properties

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