physics(URGENT!!!!!)

A spherical non-rotating planet (with no atmosphere) has mass m1= 5 ×1024 kg and radius r1= 7000 km. A projectile of mass m2≪m1 is fired from the surface of the planet at a point A with a speed vA at an angle α=30∘ with respect to the radial direction. In its subsequent trajectory the projectile reaches a maximum altitude at point B on the sketch. The distance from the center of the planet to the point B is r2=(5/2)r1. Use G=6.674×10−11 kg−1m3s−2.

What is the initial speed vA of the projectile? (in m/s)

vA=

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  1. vA=Sqrt(5*G*m1/4*r)=6904.45 m/s

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  2. hai Greco A merry-go-round (pictured) is sitting in a playground. It is free to rotate, but is currently stationary. You can model it as a uniform disk of mass 210 kg and radius 120 cm (consider the metal poles to have a negligible mass compared to the merry-go-round). The poles near the edge are 109 cm from the center.

    Someone hits one of the poles with a 8 kg sledgehammer moving at 17 m/s in a direction tangent to the edge of the merry-go-round. The hammer is not moving after it hits the merry-go-round.

    How much energy |ΔE| is lost in this collision? (enter a positive number for the absolute value in Joules)

    |ΔE|= did u got it i need help ???

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  3. nizo your answer is 1111.96

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  4. Did you do 8b and 8c Greco??

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  5. not yet..

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  6. Thanks #Greco for nizo ans got it too!!! A ruler stands vertically against a wall. It is given a tiny impulse at θ=0∘ such that it starts falling down under the influence of gravity. You can consider that the initial angular velocity is very small so that ω(θ=0∘)=0. The ruler has mass m= 100 g and length l= 15 cm. Use g=10 m/s2 for the gravitational acceleration, and the ruler has a uniform mass distribution. Note that there is no friction whatsoever in this problem. (See figure)

    (a) What is the angular speed of the ruler ω when it is at an angle θ=30∘? (in radians/sec)

    ω=

    unanswered
    (b) What is the force exerted by the wall on the ruler when it is at an angle θ=30∘? Express your answer as the x component Fx and the y component Fy (in Newton)

    Fx=

    unanswered
    Fy=

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    (c) At what angle θ0 will the falling ruler lose contact with the wall? (0≤θ0≤90∘; in degrees) [hint: the ruler loses contact with the wall when the force exerted by the wall on the ruler vanishes.]

    θ0= need help for this question i got only omega !

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  7. I=1/3*m*L^2
    Eini= mg(L/2) + 0
    Efin= mg(L/2)cos30 + 1/2*I*w^2
    Eini=Efin ->
    w=sqrt(3*g (1-cos(theta))/L)

    b)
    alpha=3*mg/2*sin(theta)/L
    ax = -L/2*sin(theta) w^2 + L/2*cos(theta) alpha
    Fx=m*ax
    Fy=m*g*cos(theta)-m*w^2*(L/2)

    c)
    cos(theta)=2/3
    theta=48.19

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