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Answer :
Final answer:
The work done by the 141 N force on a 17.8 kg block is calculated by determining the horizontal component of the force, accounting for the work against friction, and then combining these to find the net work done by the force over the displacement given.
Explanation:
To calculate the work done by the 141 N force on a 17.8 kg block, we need to consider both the component of the force in the direction of the displacement and the force of friction opposing the movement. The work done by the force (W) is given by the formula W = F * d * cos(θ), where F is the magnitude of the force, d is the displacement, and θ is the angle of the force with respect to the horizontal. The force can be decomposed into a horizontal component (Fh = F * cos(θ)) that does work and a vertical component (Fv = F * sin(θ)) that does not contribute to the work.
The work done by the frictional force (Wfric) is Wfric = μk * N * d, where μk is the coefficient of kinetic friction and N is the normal force, which is equal to the gravitational force minus the vertical component of the applied force (N = m * g - Fv). Combining these, the total work done is the work by the horizontal component of the 141 N force minus that done by friction.
Let's calculate each term:
- The horizontal component of the force: Fh = 141 N * cos(28.3°) = 141 N * cos(0.494 rad)
- The vertical component of the force: Fv = 141 N * sin(28.3°) = 141 N * sin(0.494 rad)
- The normal force: N = m * g - Fv = 17.8 kg * 9.8 m/s2 - Fv
- The work due to friction: Wfric = μk * N * d
Now we can compute the total work:
- Wtotal = (Fh * d) - Wfric
- Substitute the values into the above equations to find W
total , which is given in joules (J).
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