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mojhsa [17]
3 years ago
14

The force in Newtons on a particle directed along the x-axis is given by F(x)=exp(−(x/2)+6) for x≥0 where x is in meters. The pa

rticle is constrained to move along the x-axis. Find the work done in Joules on the particle, W, in moving it from x=0 to x=1 using the fact that F=dW/dx. For your reference, 1 Joule = 1 Newton × 1 meter.,
Physics
1 answer:
HACTEHA [7]3 years ago
3 0

To find the work done on the particle, the following is the solution:

Dw = F dx

W = integral over the path ( F(x) dx)

W = integral from 0 to 1 (e^(-x/5 + 5) dx)

W = -5e^(-x/5 + 5) from 0 to 1

W = 135 J

The work done is 135 J.

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Answer:

-9.6\cdot 10^{-19} C

Explanation:

The charge of a single electron is:

q=-1.60\cdot 10^{-19} C

If a droplet contains N electrons, then its charge would be:

Q=Nq

In this case, the droplet has

N = 6

electrons, so its total charge is

Q=(6)(-1.60\cdot 10^{-19}C)=-9.6\cdot 10^{-19} C

7 0
3 years ago
A tungsten wire is 1.5m long and has a diameter of A current of flows through the wire. The resistivity of the wire is 5.6 * 10
7nadin3 [17]

Complete Question:

A tungsten wire is 1.5 m long and has a diameter of 1.0 mm. A current of 60 mA flows through the wire. The resistivity of the wire is 5.6 * 10^-8 Ωm. What is the potential difference across the ends of the wire?

Answer:

Potential difference, V = 0.00642 Volts.

Explanation:

Given the following data;

Diameter = 1 mm to meters = 1/1000 = 0.001 m

Length = 1.5m

Current = 60mA = 60/1000 = 0.06 Amperes.

Resistivity = 5.6 * 10^-8 Ωm

To find the potential difference across the ends of the wire;

First of all, we would determine the cross-sectional area of the wire (circle);

Radius, r = \frac {diameter}{2}

Radius = \frac {0.001}{2}

Radius = 0.0005 m

Area of wire (circle) = πr²

Substituting into the above formula, we have;

Area  = 3.142 × (0.0005)²

Area = 3.142 × 2.5 × 10^-7

Area = 7.855 × 10^-7 m²

Next, we find the resistance of wire;

Mathematically, resistance is given by the formula;

Resistance = P \frac {L}{A}

Where;

P is the resistivity of the material.

L is the length of the material.

A is the cross-sectional area of the material.

Substituting into the formula, we have;

Resistance = 5.6 * 10^{-8} \frac {1.5}{7.855 * 10^{-7}}

Resistance = 5.6 * 10^{-8} * 1909611.712

Resistance = 0.107 Ohms.

Now, we can find the potential difference using the formula;

V = IR

Where;

V represents voltage or potential difference measured in volts.

I represents current measured in amperes.

R represents resistance measured in ohms.

Substituting into the formula, we have;

V = 0.06*0.107

Potential difference, V = 0.00642 Volts.

7 0
3 years ago
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