Physics, 31.10.2020 02:00 jep88

7. Challenge: The unit of force is the newton (N). One newton is the force required to accelerate a 1-kg object at a rate of 1 m/s2 Suppose each fan supplies a force of 2 N. Use Newton's second law and the Gizmo to find the following A. The mass of the cart: B. The mass of a fan: C. The mass of one of the draggable mass units:

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Answer from: kjmesser33

(A) The mass of the cart is 1.214 kg

(B) The mass of one fan is 1.262 kg

The given parameters:

From the image uploaded, in the Gizmo there are 3 fans and 1 cart with two draggable mass.the force supplied by each fan = 2 Nthe total force supplied by the three fans = 3 x 2 N = 6 N

To find:

A. The mass of the cart.

B. The mass of a fan.

C. The mass of one of the draggable mass units

Applying the Gizmo observation:

3 fans on, and zero draggable mass unit gives acceleration of 1.2 m/s²2 fans on, and zero draggle mass unit gives acceleration of 1.07 m/s²2 fans on, and 2 draggable mass unit gives acceleration of 0.4 m/s²

Applying Newton's second law of motion:

$F = ma\\\\where;\\\\m \ is \ the \ mass \ of \ the \ object s\\\\m = mass \ of \ cart\ (m_c)+ mass \ of \ fans \ (m_f) + \ draggable \ mass \ (m_d) \\\\$

For 3 fans (all -on) and zero draggable mass:

$3(2) = 1.2(m_c + 3m_f)\\\\\frac{6}{1.2} = m_c + 3m_f\\\\5 = m_c + 3m_f \ \ -----(1)$

For 3 fans (2 -on) and zero draggable mass:

$2(2) = 1.07(m_c + 2m_f)\\\\\frac{4}{1.07} = (m_c + 2m_f)\\\\3.738 = m_c + 2m_f \ \ ------(2)$

For 3 fans (2 - on) and 2 draggable mass:

$2(2) = 0.4(m_c + 2m_f + 2m_d)\\\\\frac{4}{0.4} = (m_c + 2m_f+ 2m_d)\\\\10 = m_c + 2m_f + 2m_d\ \ ------(3)$

Find the mass of a fan by subtracting equation 2 from equation 1:

$\ \ \ \ 5 \ \ \ \ \ \ = \ m_c + 3m_f\\-(3.738 \ = \ mc + 2m_f)\\ \\1.262 \ kg = m_f$

Find the mass of the cart:

$m_c = 5 - 3m_f\\\\m_c = 5 - 3(1.262)\\\\m_c = 1.214 \ kg$

Find the mass of one of the draggable mass units:

$2m_d = 10 - (2m_f + m_c)\\\\2m_d = 10 - (3.738)\\\\2m_d = 6.262 \\\\m_d = \frac{6.262}{2} \\\\m_d = 3.131 \ kg$

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Answer from: hollisjune3047

A) 1.21 kg

B) 1.26 kg

C) 3.13 kg

Explanation:

Let's say the mass of the cart is mc, the mass of each fan is mf, and the mass of the draggable mass units is M.

Newton's second law says the net force equals the mass times the acceleration.

∑F = ma

When there are three fans, the acceleration is 1.20 m/s².

∑F = ma

3 (2 N) = (mc + 3 mf) (1.20 m/s²)

5 kg = mc + 3 mf

When there are two fans, the acceleration is 1.07 m/s².

∑F = ma

2 (2 N) = (mc + 2 mf) (1.07 m/s²)

3.74 kg = mc + 2 mf

When there are three fans (one off) and two draggable mass units, the acceleration is 0.40 m/s².

∑F = ma

2 (2 N) = (mc + 3 mf + 2 M) (0.40 m/s²)

10 kg = mc + 2 mf + 2 M

Solving the system of equations, first subtract the second equation from the first:

mf = 1.26 kg

Now plug into either of the first two equation to find mc.

mc = 1.21 kg

Finally, plug both into the third equation to find M.

M = 3.13 kg

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