Get the Gizmo ready:

Question

Click Reset.
Set the Initial velocity of the cart to 0.0 m/s.
Place three fans on the cart, all blowing to the left.

Question: How do mass and force affect acceleration?

(2 points)
1A. Experiment: Turn on the fans. Click Play and watch the cart, then select the TABLE tab.

Scroll to the bottom of the table. What is the final velocity of the cart? (You must include the unit of measurement).

B. How long did it take the cart to reach the end of the track?

2. Calculate: Acceleration is a measure of how much the velocity of the cart changes each second. To calculate acceleration, divide the final velocity by the amount of time it took to reach that velocity. The units of acceleration are meters per second per second, or m/s 2
.
.(4 points)
A. What is the acceleration of the cart? (Include units.)

B. Check your answer on the TABLE tab. Were you correct?

Yes or No?

3. Form hypothesis: (2 points)
A. How do you think changing the mass of the cart will affect its acceleration?

If the mass is changed, the acceleration will
.

B. How do you think the number of fans will affect the cart’s acceleration

If the number of fans is changed, then the acceleration will
.

B. A cart with two blocks and three fans has twice the mass as a cart with just three fans. How did doubling the mass affect the acceleration of the cart?

6B. What do you notice about the force and the product of mass and acceleration, ma?(1 point)

Draw conclusions: Newton’s second law states that force is equal to mass times acceleration: F = ma. This law can be rearranged as a = F / m, or a = F ÷ m.

7. How does this experiment demonstrate Newton’s second law? (1 point)

Apply: Suppose the cart contains 2 fans and 3 blocks. Recall that each fan supplies a force of 4.0 N. The total mass of the cart will be 22.5 kg.

8. What will be the acceleration of the cart?

Check your answer using the Gizmo.

(1 point)

Answer 1

Certainly! Let's go through the exercise step by step, addressing each section of your inquiry.

1. Experiment

(A) After turning on the fans and clicking Play, you should observe the cart moving to the left. The final velocity of the cart would depend on how long you ran the simulation and the specific settings in the Gizmo. For example, if the final velocity is 3.0 m/s, that would be stated as 3.0 m/s.

(B) The time it took for the cart to reach the end of the track will again depend on how long you ran the simulation. Let's say for this example it took 5.0 seconds.

2. Calculate Acceleration

(A) To calculate acceleration, use the formula: \[ \text{acceleration} = \frac{\text{final velocity}}{\text{time}} \] Using our example values, it would be: \[ \text{acceleration} = \frac{3.0 , \text{m/s}}{5.0 , \text{s}} = 0.6 , \text{m/s}^2 \]

(B) Now, you would check the TABLE tab to confirm if your calculation of acceleration (0.6 m/s²) was correct.

3. Form Hypothesis

(A) If the mass is changed, the acceleration will decrease if the force remains constant, according to Newton's second law (F=ma).

(B) If the number of fans is changed, then the acceleration will increase because more fans means more force acting on the same mass, leading to a greater acceleration.

(C) A cart with two blocks and three fans has twice the mass as a cart with just three fans. Doubling the mass will likely reduce the acceleration because, while the force (from the fans) remains the same, the increase in mass leads to a smaller acceleration (again, reinforcing F = ma).

(D) In relation to the force and the product of mass and acceleration (ma): you will notice that force is directly proportional to mass and acceleration; as the mass increases or acceleration increases, the force required to achieve that acceleration also increases.

4. Draw Conclusions

(A) This experiment demonstrates Newton’s second law because it showcases how an increase in the number of fans (and thus force) results in greater acceleration, supporting the relationship F = ma. Moreover, when mass is increased without changing the force, the acceleration decreases, further exemplifying the law.

5. Apply

Given:

• Cart with 2 fans each providing a force of 4.0 N (Total force = 8.0 N)
• 3 blocks gives a total mass of 22.5 kg.

To find acceleration: \[ a = \frac{F}{m} = \frac{8.0 , \text{N}}{22.5 , \text{kg}} \approx 0.356 , \text{m/s}^2 \]

You would then check your answer using the Gizmo to verify if the calculated acceleration is aligned with what the simulation produces.

Let me know if you need assistance with any of the specific values or if there's anything else you'd like to delve deeper into!