You're using a wedge to split a log. You are hitting the wedge with a large hammer to drive it into the log. It takes a force of 3500 N to push the wedge into the wood. The work you do on the wedge, pushing it into the log, is the work it does on the wood, separating its two halves. If the two halves of the log only separate by a distance of 0.07 m while the wedge travels 0.2 m into the log, how much force is the wedge exerting on the two halves of the log to rip them apart?

Question

Mathematics

Brodie Norris

14 September, 22:29

You're using a wedge to split a log. You are hitting the wedge with a large hammer to drive it into the log. It takes a force of 3500 N to push the wedge into the wood. The work you do on the wedge, pushing it into the log, is the work it does on the wood, separating its two halves. If the two halves of the log only separate by a distance of 0.07 m while the wedge travels 0.2 m into the log, how much force is the wedge exerting on the two halves of the log to rip them apart?

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Answers (1)

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Aron Whitehead · Answer 1

10,000 N

Step-by-step explanation:

Data provided in the question:

Force applied by the Hammer = 3500 N

Distance between the two halves of the wood = 0.07 m

Distance traveled by the wedge = 0.2 m

Now,

Let the force exerted by wedge = F N

also,

Work done = Force * Displacement

Therefore,

Work done by hammer on wedge

= Force by hammer * Displacement of the wedge

= 3500 * 0.2

= 700 J

Also,

Work done by wedge = F * 0.07

= 0.07F

Since, the work done on the wedge, pushing it into the log, is the work done on the wood, separating its two halves

Thus,

0.07F = 700

or

F = 10,000 N