Virtual Physics Lab

Explore how launch angle and initial speed affect the path of a projectile.

1. Set the launch angle and speed with the sliders.
2. Press Start to launch the projectile and watch the path.
3. Observe how the range and peak height change as you adjust the settings.
4. Record your observations and answer the reflection questions.

The horizontal range R is given by (v squared sin(2 theta)) divided by g. The highest point is (v squared sin squared theta) divided by (2 g). Time of flight is (2 v sin theta) divided by g when launched from ground level.

• Which angle gives the greatest range for a fixed speed?
• How does doubling the launch speed change the range and peak height?
• What happens if the angle is very small or very large?

Observe how gravity, friction, and an applied force combine to move a box on an inclined plane.

1. Set the incline angle, mass, and friction coefficient.
2. Adjust the applied force and press Start to see the motion.
3. Compare the calculated forces and acceleration as values change.
4. Pause the simulation and record your observations.

The force pulling the box down the plane is m g sin(theta). Friction acts opposite motion with size mu N where N = m g cos(theta). The net acceleration is the total unbalanced force divided by the mass.

• How does increasing the incline angle change the weight component?
• When does the box remain at rest, and why?
• How does friction affect the net acceleration?

• Understand the relationship between distance and time
• Interpret distance-time graphs
• Calculate speed from graphs

1. Set the speed using the slider (0-20 m/s).
2. Choose a starting position if needed.
3. Select a motion scenario (uniform, at rest, or changing speed).
4. Press Start to begin the simulation and observe the graph.
5. Note how the slope of the distance-time graph relates to speed.

For uniform motion, distance = speed × time. On a distance-time graph, a straight line indicates constant speed, where the gradient (slope) equals the speed. A horizontal line means the object is at rest. A curved line indicates changing speed (acceleration or deceleration).

• What does the slope of a distance-time graph represent?
• How can you tell if an object is moving faster or slower by looking at the graph?
• What does a horizontal section on the graph indicate?
• How would you calculate the average speed from a distance-time graph?

• Understand acceleration and its effect on velocity
• Interpret velocity-time graphs
• Calculate acceleration from the slope of v-t graphs
• Calculate distance from the area under v-t graphs

1. Set the initial velocity using the slider (0-30 m/s).
2. Adjust the acceleration (-5 to +5 m/s²).
3. Choose the simulation duration.
4. Press Start and observe how velocity changes over time.
5. Note the shaded area under the graph represents distance traveled.

The velocity-time graph shows how velocity changes with time. The slope of the graph equals acceleration (a = Δv/Δt). The area under the curve equals the distance traveled. For constant acceleration: v = v₀ + at and d = v₀t + ½at². Positive acceleration increases velocity, negative acceleration (deceleration) decreases it.

• What does the slope of a velocity-time graph represent?
• How do you calculate distance from a velocity-time graph?
• What happens to the velocity when acceleration is zero?
• How does negative acceleration affect the motion?
• Can you predict when the object will stop if decelerating?

• Understand gravitational acceleration (g ≈ 9.8 m/s²)
• Verify that g is independent of object mass
• Measure height, time, and final velocity relationships
• Calculate g from experimental data

1. Set the drop height using the slider (5-50 m).
2. Adjust the object mass to observe mass independence.
3. Use slow motion to observe the fall clearly.
4. Press Drop and record the time of fall.
5. Run multiple trials and calculate the average g.
6. Toggle air resistance to see its effect.

In free fall, all objects accelerate at g ≈ 9.81 m/s² regardless of mass (in a vacuum). The equations are: h = ½gt², v = gt, and v² = 2gh. From measured height and time, g can be calculated as g = 2h/t². Air resistance creates a drag force that depends on velocity and object properties, reducing acceleration.

• Does the mass of the object affect the fall time? Why?
• How does your calculated g compare to 9.81 m/s²?
• What effect does air resistance have on the motion?
• Why do we run multiple trials and calculate an average?
• What sources of error might affect your measurements?

• Understand the concept of inertia (Newton's First Law)
• Observe that motion continues without force until opposed
• Understand friction as an opposing force
• Compare how different surfaces affect motion

1. Set the initial push velocity using the slider.
2. Adjust the object mass to see how inertia relates to mass.
3. Select different surface types to compare friction effects.
4. Press Push to set the object in motion.
5. Observe how the object gradually stops due to friction.
6. Compare distances on different surfaces.

Newton's First Law states that an object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless acted upon by a net external force. The stopping distance is d = v²/(2μg). Friction force is f = μmg. On a frictionless surface (μ = 0), the object would continue forever.

• Why does the object eventually stop moving?
• How does the surface type affect the stopping distance?
• Does the mass affect the stopping distance? Why or why not?
• What would happen if there was no friction at all?
• How does this relate to wearing seatbelts in cars?