Projectile on a string

https://isaacphysics.org/questions/projectile_on_a_string?stage=a_level
I'm not sure how to approach it whatsoever. Some help would be appreciated

Reply 1

Kallisto

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Original post by Studious_Kumar

https://isaacphysics.org/questions/projectile_on_a_string?stage=a_level
I'm not sure how to approach it whatsoever. Some help would be appreciated

Sounds like a projectile on a pendulum. I guess that a sketch to the question is not in existence. If I get a plan, I let you know.

EDIT: okay I have not seen hint 3. So it is projectile motion, alright.

(edited 12 months ago)

Reply 2

Kallisto

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@Stonebridge
@mqb2766
@Joinedup

I have tried to get the equation for speed by triangle relationships of the projectile, in consideration of the kinetic and potential energy, but my solutions were always incorrect. Maybe one of you have a good idea.

Reply 3

mqb2766

Original post by Kallisto

@Stonebridge
@mqb2766
@Joinedup
I have tried to get the equation for speed by triangle relationships of the projectile, in consideration of the kinetic and potential energy, but my solutions were always incorrect. Maybe one of you have a good idea.

Id probably draw the radius which corresponds to the transition between circular and parabolic motion. Assuming this makes an angle theta with the axis, then the height is lsin(theta) so the KE at that point is
1/2mv^2 - mglsin(theta)
and as the tension is zero, it (centripetal) must equal the resolved weight so you can determine sin(theta) as a function of v^2 (and g and l). So for the projectile motion phase you have the initial speed and initial angle and you want to the parabolic motion to pass through the origin, so it should give, but not fully worked it through.

(edited 12 months ago)

Reply 4

Studious_Kumar

I assume that we have to find a value for theta that we can then substitute into the original equation for v^2. However I cannot seem to find a suitable method to get this value.Thanks in advance.

Reply 5

mqb2766

Original post by Studious_Kumar

I assume that we have to find a value for theta that we can then substitute into the original equation for v^2. However I cannot seem to find a suitable method to get this value.Thanks in advance.

Different v^2 will produce different values of theta which corresponds to the transition between circular and parabolic motion. However if you have
sin(theta) = #
then cos(theta) =... and tan(theta)=... using the usual simple identities/right triangle and you could sub into the parabolic equation of motion to get v^2=...

There is no need to think about finding the value for theta.

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