Black-body radiation is the energy that is released as light from any object with a non-zero temperature (0 Kelvin, or about –273.15 degrees Celcius). An everyday example of black-body radiation is an electric stovetop. When an electric stove is at its highest setting, energy is pumped into the stovetop, and some of the energy will be released as light, causing it to glow orange. This is black-body radiation at the wavelength of light that corresponds with the color orange.

The visible spectrum of light wavelengths is from about 400 nanometers (high energy) to about 750 nanometers (low energy). The wavelength of light is correlated with the energy of that light, while the intensity refers to the amount of light. For example, a stovetop with very bright orange color does not have different energy per photon of light than a stovetop with a dim orange, as long as they are the same shade. Rather, the brighter stovetop just emits more photons.

A scientist decides to conduct an experiment to see how the temperature of an object affects the total energy released in its black body radiation. The scientist conducts the experiment at very low temperatures and measures the energy released by the object in units of a hundred-millionth of a joule . The results are shown below:

Based on the data collected, how can we describe the relationship between the temperature of an object, and the total energy released as black body radiation?

Black-body radiation is the energy that is released as light from any object with a non-zero temperature (0 Kelvin, or about –273.15 degrees Celcius). An everyday example of black-body radiation is an electric stovetop. When an electric stove is at its highest setting, energy is pumped into the stovetop, and some of the energy will be released as light, causing it to glow orange. This is black-body radiation at the wavelength of light that corresponds with the color orange.

The visible spectrum of light wavelengths is from about 400 nanometers (high energy) to about 750 nanometers (low energy). The wavelength of light is correlated with the energy of that light, while the intensity refers to the amount of light. For example, a stovetop with very bright orange color does not have different energy per photon of light than a stovetop with a dim orange, as long as they are the same shade. Rather, the brighter stovetop just emits more photons.

The above diagram displays the amount of light emitted as black-body radiation at different wavelengths by an object. If the color violet corresponds to wavelengths around 400 nanometers, and the color red corresponds to wavelengths of around 600 nanometers; how can we describe the black-body radiation of the above object?

Engineers are evaluating four potential technologies. These technologies are to be used as power plants that are considered "clean" energy. The estimated energy output of these plants were calculated and the resources needed to run these were also listed. 

In a desert region, which two technologies can possibly be used?

A student conducts an experiment in which she suspends a ball mass  from a string and swings it in a perfect circular motion. What is often referred to as centrifugal force appears to push the ball away from the center of the circle of its motion with a force   in the string. The force is described by the formula  where  is the mass,  is the speed of the ball, and  is the radius of its motion.

At one point in the student's experiment,  is equal to a certain value ,  is equal to a certain value , and  is equal to a certain value . The resulting force is calculated at  (units of force). What can we predict the force to be if the student chooses to halve the speed, double the mass, and keep the same value for the radius?

A student conducts an experiment in which she suspends a ball mass  from a string and swings it in a perfect circular motion. What is often referred to as centrifugal force appears to push the ball away from the center of the circle of its motion with a force   in the string. The force is described by the formula  where  is the mass,  is the speed of the ball, and  is the radius of its motion.

What is the relationship between the force in the string and the mass of the ball?

A student is performing a science experiment for his class. The student creates a ramp that contains four different surfaces, carpet, glass, wood and plastic. The ramp is held at a constant angle and a ball is allowed to roll down the ramp. The student tests each material by releasing a ball at different distances from the bottom of the ramp and recording the time it takes for the ball to travel the distance of the ramp. 

What is the slowest material that the student tested?

Metal wires are often used to conduct electricity. The electricity that flows through a wire is measured as "current." Therefore, a wire with an electric current is called a current carrying wire. 

Current carrying wires also have a tendency to produce magnetic fields that circulate around them. The strength of that magnetic field is determined by the following equation where  is the magnetic field strength (Teslas),  is the electric current (Amps),  is the distance (meters) of an object to the current carrying wire.  is a constant.

If a wire has a magnetic field of  at a distance of 1 meter, what would the magnetic field be at 4 meters?

Sometimes scientists need to scale down experiments because collecting full-scale data may not be practical or possible. Most of the time, the data collected during a small scale-experiment is an accurate indicator of full-scale results. For example, research of craters on the Earth’s surface has indicated that the Earth has experienced a history of massive meteor collisions. It has been hypothesized that, amongst other things, these impacting meteorites caused the Earth’s oceans to vaporize. The detrimental effects associated with meteor collisions would have made the planet to be uninhabitable to humans. Due to these adverse effects, an experiment that could produce meteor-sized craters would not be possible in a full-scale setting.

Researchers have developed small-scale experiments that are exemplary of Newton’s three laws of motion. Newton’s first law states that an object in motion will stay in motion unless it is acted on by another force. This phenomenon is known as inertia. The second law comes in the form of an equation that calculates how much force is exerted on two colliding objects with respect to mass and acceleration. In other words force is equal to the mass of an object multiplied by its acceleration. The third law states that for every action there is an equal and opposite reaction. In other words, forces always occur in pairs. A counter force that is equal in magnitude and opposite in direction compliments each force in a particular direction. For example, if you push downwards on a table then the table, in theory, pushes upwards with the same force.

In a particular small-scale exercise, students were asked to design an experiment in which two “meteorites” would be dropped into a medium of sand and the subsequent crater diameters would be measured. Afterwards, the sand would be leveled and the experiment would be repeated. The students were asked to identify all of the factors that could affect the formation of the craters. This was done in order to ensure that each experiment was testing one independent and one dependent variable at a time. Otherwise, it would be unclear which variable is causing the observed effect. Possible variables that could alter the outcome of the experiment included but were not limited to the following: height of the fall, speed of the “meteorite,” angle of impact, and the mass of meteorite.

Consider an experiment that seeks to identify the mass of the meteorite analog. All other variables would have to remain constant in order to ensure accurate results.  In order to do this, the height of the fall was set to one meter. The object was placed on top of a vertical meter stick. In order to keep the acceleration and height of the drop constant, it was rolled off of the stick instead of being pushed or simply dropped. Last, a protractor was used to keep the meter stick at a ninety-degree angle. In the procedure, a marble and a golf ball were used as “meteorites” of different masses.

The results of the experiment were recorded in the table and figure provided.

Predict what would happen to the crater size if the experiment changed the velocity instead of the mass of the objects. 

Laura is performing an experiment with a 5kg weight tied to a 3m rope tied to the ceiling as shown:

Laura drops the weight and allows it to swing freely. She measures how long it takes for the weight to return to it's original position (assume no forces outside of gravity are acting upon the pendulum). This is also called one oscillation.

Experiment 1:

Laura created the following table for her first measurement of the pendulum's oscillations.

Experiment 2:

Laura performed the experiment again, this time using a 6kg weight.

Experiment 3:

Laura performed the experiment again, this time using a 3kg weight and a 5m rope.

Jerry reads about this experiment, and attempts to recreate the experiment at home. He observes that when he lets go of the pendulum, it never reaches its original height. It gets close, but never fully reaches it. Why?

A student was interested in determining the relationship between the current, voltage, and resistance in a direct circuit, such as those exemplified by batteries connected to light bulbs. The student built the circuit presented in Figure 1 using a 2 ohm resistor.

Figure 1:

The current that flows through the circuit can be calculated using the equation , where  is the voltage of the battery,  is the current flowing through the circuit, and  is the resistance of the resistor.

The student used a 2 ohm resistor and batteries of various voltages to obtain the results in Table 1. The currents shown in the table are NOT calculated using the formula , but instead directly measured from the circuit using an ammeter. It is important to note that the measured current will only exactly equal the calculated current if the system contains no internal resistance.

In Experiment 2, the student calculated the current to be 10 amps using the equation. However, when the student measured the current, it did not equal exactly 10 amps, but instead 9.99 amps. Which of the following is a possible explanation for the discrepancy?