Since the floor is rough, it exerts both a normal force N, and a frictional force f, on the ladder. However, since the wall is frictionless, it exerts only a normal force N, on the ladder. The ladder has a length of L- 4.7 m, a weight of W, - 57.5 N, and rests against the wall a distance d- 3.75 m above the floor. If a person with a mass of m - 90 kg is standing on the ladder, determine the following. (a) the forces exerted on the ladder when the person is halfway up the ladder (Enter the magnitude only.) N. N

Elements Of Electromagnetics
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ChapterMA: Math Assessment
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### Problem Description

A uniform ladder stands on a rough floor and rests against a frictionless wall as shown in the figure.

**Figure Description:**
- The ladder makes an angle with the floor, leaning against the wall.
- The ladder is acted upon by various forces:
  - \(N_1\) - the normal force exerted by the floor.
  - \(f_1\) - the frictional force exerted by the floor.
  - \(N_2\) - the normal force exerted by the wall.
  - \(mg\) - the weight of the person standing on the ladder, acting vertically downward at the point where the person stands.
  - \(W\) - the weight of the ladder, acting vertically downward at its center of mass.
- Designated distances and segments:
  - \(L = 4.7 \text{ m}\) - length of the ladder.
  - \(d = 3.75 \text{ m}\) - height above the floor where the ladder rests against the wall.

**Given Data:**
- Length of the ladder, \(L = 4.7 \text{ m}\)
- Weight of the ladder, \(W = 57.5 \text{ N}\)
- Distance from the wall, \(d = 3.75 \text{ m}\)
- Mass of the person standing on the ladder, \(m = 90 \text{ kg}\)
- Gravitational acceleration, \(g = 9.8 \text{ m/s}^2\)

### Questions

Determine the following:

#### (a) Forces exerted on the ladder when the person is halfway up the ladder (Enter the magnitude only):
- \(N_1 =\) ________ N
- \(N_2 =\) ________ N
- \(f_1 =\) ________ N

#### (b) Forces exerted on the ladder when the person is three-fourths of the way up the ladder (Enter the magnitude only):
- \(N_1 =\) ________ N
- \(N_2 =\) ________ N
- \(f_1 =\) ________ N
Transcribed Image Text:### Problem Description A uniform ladder stands on a rough floor and rests against a frictionless wall as shown in the figure. **Figure Description:** - The ladder makes an angle with the floor, leaning against the wall. - The ladder is acted upon by various forces: - \(N_1\) - the normal force exerted by the floor. - \(f_1\) - the frictional force exerted by the floor. - \(N_2\) - the normal force exerted by the wall. - \(mg\) - the weight of the person standing on the ladder, acting vertically downward at the point where the person stands. - \(W\) - the weight of the ladder, acting vertically downward at its center of mass. - Designated distances and segments: - \(L = 4.7 \text{ m}\) - length of the ladder. - \(d = 3.75 \text{ m}\) - height above the floor where the ladder rests against the wall. **Given Data:** - Length of the ladder, \(L = 4.7 \text{ m}\) - Weight of the ladder, \(W = 57.5 \text{ N}\) - Distance from the wall, \(d = 3.75 \text{ m}\) - Mass of the person standing on the ladder, \(m = 90 \text{ kg}\) - Gravitational acceleration, \(g = 9.8 \text{ m/s}^2\) ### Questions Determine the following: #### (a) Forces exerted on the ladder when the person is halfway up the ladder (Enter the magnitude only): - \(N_1 =\) ________ N - \(N_2 =\) ________ N - \(f_1 =\) ________ N #### (b) Forces exerted on the ladder when the person is three-fourths of the way up the ladder (Enter the magnitude only): - \(N_1 =\) ________ N - \(N_2 =\) ________ N - \(f_1 =\) ________ N
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