5 N
This problem involves applying the principles of Newtonian mechanics, specifically the work-energy theorem. Since there's no friction, the work done on the object is equal to its change in kinetic energy.
1. Calculate the change in kinetic energy:
The initial kinetic energy is zero because the object is initially at rest. The final kinetic energy is given by:
\(KE_f = \frac{1}{2}mv^2\)
where:
- \(m\) = mass = 500 g = 0.5 kg
- \(v\) = final velocity = 20 m/s
Substituting the values:
\(KE_f = \frac{1}{2}(0.5 kg)(20 m/s)^2 = 100 J\)
2. Calculate the work done:
The work-energy theorem states that the work done on an object is equal to its change in kinetic energy. Therefore, the work done is 100 J.
3. Calculate the force:
Work is defined as the product of force and displacement:
\(W = Fd\)
where:
- \(W\) = work done = 100 J
- \(F\) = force (effort)
- \(d\) = displacement = 20 m
Solving for \(F\):
\(F = \frac{W}{d} = \frac{100 J}{20 m} = 5 N\)
Therefore, the force required is 5 N.
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