Where Does a Cut String Leave a Moving Mass After 4 Seconds?

[VinSoft]

A weight with a mass of 3 kg is attached to a string of length 50 cm. One end of the string is fixed at the origin (x=0, y =0) and the weight is pushed on a frictionless table top so that it moves horizontally in a circle with constant angular velocity %omega. The weight moves in the x-y plane, z=0. At a certain time the velocity of the mass is vx = -3m/s , vy = 2m/s.

The total force is 54i +24j [N] (Not a given, calculated)

The question is:

At the instant the velocity is as above the string is cut. Where is the mass 4 seconds later? Ignore the effects of gravity and friction.

I really need some help with this one.. Thanks alot

 

[stunner5000pt]

when cut the body is moving at -3m/s in the X
and 2m/s in the Y
will the direction or magnitude of any of these change after the string is cut?
what happens 4s later then? What is the displacement from the original position

 

[quicknote]

Based on the given information, we can use the equations of circular motion to determine the position of the weight 4 seconds after the string is cut. First, we can calculate the magnitude of the velocity using the given components: v = √(vx^2 + vy^2) = √((-3m/s)^2 + (2m/s)^2) = √(9m^2/s^2 + 4m^2/s^2) = √13m^2/s^2 = 3.6m/s.

Next, we can use the formula for angular velocity, ω = v/r, to find the angular velocity of the weight. The radius, or length of the string, is given as 50 cm or 0.5 m. Therefore, ω = 3.6m/s / 0.5m = 7.2 rad/s.

Since the weight is moving with constant angular velocity, we can use the equation θ = ωt to find the angle the weight has traveled in 4 seconds. θ = 7.2 rad/s * 4s = 28.8 radians.

Now, we can use the polar coordinate system to determine the position of the weight after 4 seconds. The weight was initially at the origin (0,0) and has traveled an angle of 28.8 radians. Using the conversion formula x = r cos(θ) and y = r sin(θ), we can find the coordinates of the weight as x = 0.5m * cos(28.8) = 0.38m and y = 0.5m * sin(28.8) = 0.24m.

Therefore, 4 seconds after the string is cut, the weight will be at the coordinates (0.38m, 0.24m) in the x-y plane. It is important to note that this calculation assumes no external forces acting on the weight, such as gravity or friction. If these forces were present, the position of the weight may differ.