The position of an object is given by x = at3 - bt2 + ct,where a = 4.1 m/s3, b = 2.2 m/s2, c = 1.7 m/s, and x and t are in SI un

Answer:

             U = 1 / r²

Explanation:

In this problem, the task does not require calculating potential energy via the force equation since these two variables are interconnected.

         F = - dU / dr

This derivative represents a gradient, meaning it indicates direction, leading us to write

          dU = - F. dr

The formula for force becomes

         F = B / r³

Now, let’s apply this in the integral:

          ∫ dU = - ∫ B / r³  dr

Here, the force aligns with the displacement, simplifying the scalar product to the product of magnitudes.

Now, we can solve the integrals:

            U - Uo = -B (- / 2r² + 1 / 2r₀²)

To finalize the calculations, a reference point for energy must be designated; commonly, potential energy is set to zero (Uo = 0) at infinity (r = ∞).

             U = B / 2r²

Substituting B = 2, we arrive at:

             U = 1 / r²

Answer:

a) The jogger's acceleration is 1.5 m/s²

b) The car's acceleration is also 1.5 m/s²

c) Yes, the car covers a distance 76 m greater than the jogger.

Explanation:

a) Acceleration is the change in velocity over a given time interval:

a = (final velocity - initial velocity) / time

For the jogger:

a = (3.0 m/s - 0 m/s) / 2.0 s = 1.5 m/s²

b) For the car:

a = (41.0 m/s - 38.0 m/s) / 2.0 s = 1.5 m/s²

c) To find how far the car has traveled after 2 seconds, use the formula for position under acceleration along a straight path:

x = x₀ + v₀ t + ½ a t²

where

x = position at time t

x₀ = initial position

v₀ = initial velocity

t = elapsed time

a = acceleration

Assuming x₀ = 0 (origin at car's starting point):

x = 38.0 m/s × 2 s + ½ × 1.5 m/s² × (2.0 s)²

x = 79 m

Similarly, position of the jogger after 2 seconds is:

x = 0 m/s × 2 s + ½ × 1.5 m/s² × (2.0 s)² = 3 m

The difference traveled by the car compared to the jogger is 79 m - 3 m = 76 m

Answer:

La magnitud del momento total es de 21.2 kg m/s y su dirección es de 39.5° respecto al eje x.

Explanation:

¡Hola!

El momento total se calcula como la suma de los momentos de las piezas.

El momento de cada pieza se calcula de la siguiente manera:

p = m · v

Donde:

p = momento.

m = masa.

v = velocidad.

El momento es un vector. La pieza de 200 g se mueve a lo largo del eje x, por lo que su momento será:

p = (m · v, 0)

p = (0.200 kg · 82.0 m/s, 0)

p = (16.4 kg m/s, 0)

La pieza de 300 g se mueve a lo largo del eje y. Su vector momento será:

p =(0, m · v)

p = (0, 0.300 kg · 45.0 m/s)

p = (0, 13.5 kg m/s)

El momento total es la suma de cada momento:

Momento total = (16.4 kg m/s, 0) + (0, 13.5 kg m/s)

Momento total = (16.4 kg m/s + 0, 0 + 13.5 kg m/s)

Momento total = (16.4 kg m/s, 13.5 kg m/s)

La magnitud del momento total se calcula de la siguiente manera:

La dirección del vector de momento se calcula utilizando trigonometría:

cos θ = px/p

Donde px es el componente horizontal del momento total y p es la magnitud del momento total.

cos θ = 16.4 kg m/s / 21.2 kg m/s

θ = 39.3 (39.5° si no redondeamos la magnitud del momento total)

Complete Question:

Picture yourself on an aluminum ladder on the ground, attempting to fix an electrical connection with a metal screwdriver featuring a metallic handle. Since you are sweating profusely, your body has a resistance of 1.60 kΩ.

(a) If you accidentally contact the "hot" wire from the 120 V power line, what current will flow through your body?

(b) What is the amount of electrical power transferred to your body?

Answer:

(a) 0.075A

(b) 9W

Explanation:

According to Ohm's law, the voltage (V) applied to or passing through a body corresponds to the current (I) via the relationship:

V ∝ I

=> V = I x R                 ----------------------(i)

Where;

R denotes the resistance of the body

(a) As mentioned;

Due to wet conditions, the body will conduct electricity, and possesses the following values;

V = supplied voltage = 120V

R = resistance of the wet body = 1.60kΩ = 1.6 x 1000Ω = 1600Ω

Substituting these values into equation(i):

120 = I x 1600

To find I;

I =

I = 0.075A

Thus the current passing through your body is 0.075A

(b) Electrical power (P), which is expressed in Watts (W), delivered to the body is the product of current (I) and voltage (V) received. Thus:

P = I x V           ---------------------(ii)

Where;

I equates to 0.075A   [as derived above]

V is 120V     [as outlined in the question]

Plugging these values into equation (ii):

P = 0.075 x 120

P = 9W

Hence, the electrical power received by your body is 9W