A dart strikes a 0.45cm thick dart board at a velocity of 15m/s and accelerates uniformly to rest. What force does the dartboard apply to the 80g dart in bringing it to rest
The answer is 2000N but I dunno how to get it
The answer is 2000N but I dunno how to get it
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Given data : mass = m = 80 x10^-3 kg
dart board thickness = S = 0.45cm = .0045 m
initial velocity of dart = u = 15m/s
final velocity of dart = v = 0 m/s
retarding acceleration = a (m/s^2)
Force applied by dart to board = F = m x a
but we know
v^2 - u^2 = 2aS
0 - 15^2 = 2 x a x 0.0045
therefore a = - 25000 m/s^2
F = 80x10^-3 x (-25000)
F = 2000 N
hence proved
dart board thickness = S = 0.45cm = .0045 m
initial velocity of dart = u = 15m/s
final velocity of dart = v = 0 m/s
retarding acceleration = a (m/s^2)
Force applied by dart to board = F = m x a
but we know
v^2 - u^2 = 2aS
0 - 15^2 = 2 x a x 0.0045
therefore a = - 25000 m/s^2
F = 80x10^-3 x (-25000)
F = 2000 N
hence proved
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Use an equation of motion to first find out the acceleration of the dart. I would use this one.
(v final)^2 = (v initial)^2 + 2*a*x
In this equation x is the distance traveled while the object is accelerating. Your initial velocity is 15 m/s and the final velocity is 0. Use the .45cm as your "x" but first make sure your units are in meters. Once you find the acceleration you can use F=ma to find the force applied. Again, make sure your units are consistent, your mass needs to be in kilograms.
Hope this helps. Good Luck.
(v final)^2 = (v initial)^2 + 2*a*x
In this equation x is the distance traveled while the object is accelerating. Your initial velocity is 15 m/s and the final velocity is 0. Use the .45cm as your "x" but first make sure your units are in meters. Once you find the acceleration you can use F=ma to find the force applied. Again, make sure your units are consistent, your mass needs to be in kilograms.
Hope this helps. Good Luck.
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Start by working out the force that the dart applies to the board.
You've got the mass so you just need to work out the stopping acceleration right. Work that out by realising that the final velocity is zero - so use the appropriate equation of motion.
Then apply Newton's third law and you're done.
You've got the mass so you just need to work out the stopping acceleration right. Work that out by realising that the final velocity is zero - so use the appropriate equation of motion.
Then apply Newton's third law and you're done.
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If the mass is changed to kg, initial kinetic energy = ½mv² = ½ x 0.080 x 15² = 9 J
Assuming the dart is brought to rest over a distance of 0.45cm (=0.0045m), work done by the force is F x d = 0.0045F.
The work done by the force stops the dart and therefore equals the change in kinetic energy:
0.0045F = 9
F = 9/0.0045 = 2000N
Assuming the dart is brought to rest over a distance of 0.45cm (=0.0045m), work done by the force is F x d = 0.0045F.
The work done by the force stops the dart and therefore equals the change in kinetic energy:
0.0045F = 9
F = 9/0.0045 = 2000N