Calculating Elastic Force and Projectile Motion: Energy/Work Questions

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AI Thread Summary
The discussion focuses on calculating the average force exerted by an elastic slingshot, the speed of a marble at different heights, and the relationship between work, energy, and force. The average force is derived from the work-energy principle, where the work done by the elastic is equal to the gravitational potential energy of the marble at its maximum height. Participants clarify that the height used in calculations should be the distance the marble travels after being launched, not the stretch of the elastic. The calculations involve using the equations for work and energy, leading to a determination of the force exerted by the elastic. Overall, the thread emphasizes the importance of correctly applying physics equations to solve the problems presented.
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Homework Statement


An elastic powered slingshot can launch a 100 g marble into the air 18 m by using elastics.
a) W hat is the average force exerted by the elastic if the elastics stretches 65.0 cm before it launches the
marble?
b) How fast is the marble going straight up when it is 10 m above the ground?
c) W hat speed does the marble leave the sling shot?
d) How high is the marble from the ground when it is moving at 10 m/s?

Thanks!

Homework Equations

The Attempt at a Solution


So i know W=Eg=mgh, but what height would i put for h? 18m or 65 cm?
 
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Madeline1844 said:

Homework Statement


An elastic powered slingshot can launch a 100 g marble into the air 18 m by using elastics.
a) W hat is the average force exerted by the elastic if the elastics stretches 65.0 cm before it launches the
marble?
b) How fast is the marble going straight up when it is 10 m above the ground?
c) W hat speed does the marble leave the sling shot?
d) How high is the marble from the ground when it is moving at 10 m/s?

Thanks!

Homework Equations

The Attempt at a Solution


So i know W=Eg=mgh, but what height would i put for h? 18m or 65 cm?

Welcome to the PF.

a) What is the equation for Work as a function of Force and Distance? Given your W=mgh equation, what is the energy that the marble has when it leaves the launcher?

b) What is the equation for Total Energy in terms of Potential Energy and Kinetic Energy?

c) (combine a & b...)

d) (similar to b)
 
which height has gravity being the only Force applied?
. . . how do you compute Work from Force?
 
so (.1)(9.8) (.65) should give me energy/work which i can then rearrange to find force?
 
Madeline1844 said:
so (.1)(9.8) (.65) should give me energy/work which i can then rearrange to find force?

Not quite. What equation are you trying to use there? What are the units of each quantity? It's a good idea to get in the habit of first writing the equation symbolically and then writing it with numbers and units for each symbol, and then etc... :smile:
 
I tried using W=Eg=mgh.
(0.1)(9.8)(0.65)
that would give me 0.637 as the p.g.e/work so then i could put it into W=Fd and solve for f
0.637=F(0.65)
0.98N=F
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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