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Chapter 4: Problem 419

How much is the work done in pulling up a block of wood weighing $2 \mathrm{KN}\( for a length of \)10 \mathrm{~m}$ on a smooth plane inclined at an angle of \(30^{\circ}\) with the horizontal? (A) \(1.732 \mathrm{KJ}\) (B) \(17.32 \mathrm{KJ}\) (C) \(10 \mathrm{KJ}\) (D) \(100 \mathrm{KJ}\)

Short Answer

Expert verified
The work done in pulling up a block of wood weighing \(2 \mathrm{KN}\) for a length of \(10 \mathrm{m}\) on a smooth plane inclined at an angle of \(30^{\circ}\) with the horizontal is \(10 \mathrm{KJ}\).

Step by step solution

01

Determine the component of weight along the inclined plane

We can find the force needed to pull the block up the inclined plane by calculating the component of the block's weight in the direction of the plane. The force required (F) can be found by the following formula: \[F = W \cdot sin(\theta)\] where W is the weight of the block and \(\theta\) is the angle of inclination. Step 2: Calculate the component of weight along the inclined plane
02

Calculate the component of weight

Given that the weight of the block (W) is \(2\mathrm{KN}\), and the angle of inclination \(\theta\) is \(30^{\circ}\), we can now plug these values into the formula from step one: \[F = 2\mathrm{KN} \cdot sin(30^{\circ})\] Since \(sin(30^{\circ}) = 0.5\), we have: \[F = 2\mathrm{KN} \cdot 0.5 = 1\mathrm{KN}\] Step 3: Calculate the work done in pulling up the block
03

Determine the work done using the force and distance

Now that we have found the force required to pull the block up the inclined plane, we can calculate the work done (W) using the following formula: \[W = F \cdot d\] where F is the force calculated in step 2, and d is the distance the block is pulled. Step 4: Calculate the work done
04

Calculate the work done

Given that the force required to pull the block is \(1\mathrm{KN}\) and the distance it is pulled is \(10\mathrm{m}\), we can now plug these values into the formula from step three: \[W = 1\mathrm{KN} \cdot 10\mathrm{m} = 10\mathrm{KJ}\] Based on our calculation, the work done in pulling up a block of wood weighing \(2 \mathrm{KN}\) for a length of \(10\mathrm{m}\) on a smooth plane inclined at an angle of \(30^{\circ}\) with the horizontal is \(10 \mathrm{KJ}\). Therefore, the correct answer is (C) \(10 \mathrm{KJ}\).

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Most popular questions from this chapter

Four identical balls are lined in a straight grove made on a horizontal frictionless surface as shown. Two similar balls each moving with a velocity v collide elastically with the row of 4 balls from left. What will happen (A) One ball from the right rolls out with a speed \(2 \mathrm{v}\) and the remaining balls will remain at rest. (B) Two balls from the right roll out speed \(\mathrm{v}\) each and the remaining balls will remain stationary. (C) All the four balls in the row will roll out with speed \(\mathrm{v}(\mathrm{v} / 4)\) each and the two colliding balls will come to rest. (D) The colliding balls will come to rest and no ball rolls out from right.

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