Question(II) A $1200-\mathrm{N}$ crate rests on the floor. How much work is required to move it at constant speed (a) 6.0 m along the floor against a friction force of 230 N , and (b) 6.0 m vertically?

Studdy Solution

STEP 1

1. The crate has a weight of 1200 N.
2. The friction force opposing the movement along the floor is 230 N.
3. The crate is moved at a constant speed.
4. The distance moved is 6.0 m.
5. We need to calculate the work done in two scenarios: (a) moving along the floor against friction, and (b) moving vertically.

STEP 2

1. Calculate the work done moving the crate along the floor against friction.
2. Calculate the work done moving the crate vertically.

STEP 3

Calculate the work done moving the crate along the floor against friction.
The work done against friction is given by the formula: $W = F \times d$ where $F$ is the friction force and $d$ is the distance.
Substitute the given values: $W = 230 \, \text{N} \times 6.0 \, \text{m}$
Calculate: $W = 1380 \, \text{J}$

STEP 4

Calculate the work done moving the crate vertically.
The work done to lift the crate vertically is given by the formula: $W = F \times d$ where $F$ is the weight of the crate and $d$ is the vertical distance.
Substitute the given values: $W = 1200 \, \text{N} \times 6.0 \, \text{m}$
Calculate: $W = 7200 \, \text{J}$
The work required to move the crate (a) along the floor is $1380 \, \text{J}$ and (b) vertically is $7200 \, \text{J}$ .

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