To solve this problem, let's follow the given formula for work done:
[tex]\[ W = F \times d \][/tex]
Where:
- [tex]\( W \)[/tex] is the work done,
- [tex]\( F \)[/tex] is the force applied, and
- [tex]\( d \)[/tex] is the distance over which the force is applied.
Given:
- The force applied [tex]\( F = 2.6 \times 10^4 \)[/tex] newtons,
- The distance [tex]\( d = 3.7 \times 10^3 \)[/tex] meters.
Step-by-step solution:
1. Multiply the Force and Distance:
[tex]\[
W = (2.6 \times 10^4 \, \text{N}) \times (3.7 \times 10^3 \, \text{m})
\][/tex]
2. Carry out the multiplication:
[tex]\[
W = 2.6 \times 3.7 \times 10^4 \times 10^3
\][/tex]
3. Multiply the coefficients (2.6 and 3.7):
[tex]\[
2.6 \times 3.7 = 9.62
\][/tex]
4. Add the exponents of 10 (because when you multiply powers of 10, you add the exponents):
[tex]\[
10^4 \times 10^3 = 10^{4+3} = 10^7
\][/tex]
So,
[tex]\[
W = 9.62 \times 10^7 \, \text{newton-meters (or joules)}
\][/tex]
Therefore, the work done on the particle is [tex]\( 9.62 \times 10^7 \)[/tex] newton-meters.
