Physics Study Guide | Mathematics in Physics
Physics uses mathematics as a powerful language. As illustrated in Figure 1-1, this use of mathematics often is spoofed in cartoons. In physics, equations are important tools for modeling observations and for making predictions. Physicists rely on theories and experiments with numerical results to support their conclusions. For example, think back to the Launch Lab. You can predict that if you drop a penny, it will fall. But how fast? Different models of falling objects give different answers to how the speed of the object changes, or on what the speed depends, or which objects will fall. By measuring how an object falls, you can compare the experimental data with the results predicted by different models. This tests the models, allowing you to pick the best one, or to develop a new model.
Electric Current The potential difference, or voltage, across a circuit equals the current multiplied by the resistance in the circuit. That is,
V (volts) = I (amperes) × R (ohms).
What is the resistance of a lightbulb that has a 0.75 amperes current when plugged into a 120-volt outlet?
-
1
Analyze the Problem
• Rewrite the equation.
• Substitute values.
Known:
I = 0.75 amperes
V = 120 volts
Unknown:
R = ? -
2
Solve for the Unknown
Rewrite the equation so the unknown is alone on the left.
V = IR
IR = V ← Reflexive property of equality
R = V / I ← Divide both sides by I.
R = 120 volts / 0.75 amperes
R = 160 ohms ← Resistance will be measured in ohms. -
3
Evaluate the Answer
• Are the units correct? 1 volt = 1 ampere-ohm, so the answer in volts/ampere is in ohms, as expected.
• Does the answer make sense? 120 is divided by a number a little less than 1, so the answer should be a little more than 120.
For each problem, give the rewritten equation you would use and the answer.
-
1A lightbulb with a resistance of 50.0 ohms is used in a circuit with a 9.0-volt battery.
What is the current through the bulb? -
2An object with uniform acceleration a, starting from rest, will reach a speed v in time t according to the formula v = at.
What is the acceleration of a bicyclist who accelerates from rest to 7 m/s in 4 s? -
3How long will it take a scooter accelerating at 0.400 m/s² to go from rest to a speed of 4.00 m/s?
-
4The pressure on a surface is equal to the force divided by the area: P = F / A.
A 53-kg woman exerts a force (weight) of 520 Newtons. If the pressure exerted on the floor is 32,500 N/m², what is the area of the soles of her shoes?