Question

Hello! If you could please explain and solve these problems it would be very much appreciated!

1. A 4.0 kg cart has a force of 20.0 N pushing East and a force of 5.0 N pushing west. The initial speed of the cart is 20. m/sec. At time = 12.0 sec, what will Vf and (delta)X be?

2. A 200kg person is standing on a bathroom scale inside an elevator that is accelerating up at 2.5 m/s^2. What will the bathroom scale read? How far will he travel in 1.5sec?

Answer 1

1. A $4.0\mathrm{kg}$ cart has a force of $20.0\mathrm{N}$ pushing East and a force of $5.0\mathrm{N}$ pushing west. The initial speed of the cart is 20. m/sec. At time = 12.0 sec, what will Vf and (delta)X be?

2. A 200kg person is standing on a bathroom scale inside an elevator that is accelerating up at $2.5 \, \text{m/s}^2$ . What will the bathroom scale read? How far will he travel in 1.5sec?

Solution.

1.

Newton's second law in vector form:

$$m \vec {a} = \overrightarrow {F _ {E}} + \overrightarrow {F _ {W}};$$

Projection on $\mathrm{OX}$

$$m a = F _ {E} - F _ {W}.$$

Acceleration:

$$a = \frac {F _ {E} - F _ {W}}{m}.$$ $$v _ {f} = v _ {i} + a t;$$ $$v _ {f} = v _ {i} + \frac {F _ {E} - F _ {W}}{m} t.$$ $$v _ {f} = 2 0 + \frac {2 0 - 5}{4} 1 2 = 6 5 \left(\frac {m}{s}\right).$$ $$\Delta x = v _ {i} t + \frac {a t ^ {2}}{2};$$ $$\Delta x = v _ {i} t + \frac {(F _ {E} - F _ {W}) t ^ {2}}{2 m}.$$ $$\Delta x = 2 0 \cdot 1 2 + \frac {(2 0 - 5) 1 2 ^ {2}}{2 \cdot 4} = 5 1 0 (m).$$

2.

$$m _ {0} = 2 0 0 k g, a = 2. 5 \frac {m}{s ^ {2}}, t = 1. 5 s;$$

$m - ?h - ?$

The weight of the person when an elevator at rest:

$$G _ {0} = m _ {0} g.$$

The weight of the person when an elevator is accelerating up in vector form:

$$\vec {G} = m _ {0} (\vec {g} - \vec {a}).$$

Projection on Y:

$$G = m _ {0} (g + a).$$

The bathroom scale read (mass):

$$m = \frac {G}{g};$$ $$m = \frac {2 0 0 (9 . 8 + 2 . 5)}{9 . 8} = 2 5 1 (k g).$$

How far will he travel in 1.5sec:

$$h = \frac {2.5 \cdot 1.5^{2}}{2} = 2.81 (m).$$

**Answer:**

1. $v_{f} = 65\frac{m}{s}, \Delta x = 510m.$

2. $m = 251kg, h = 2.81m.$