Find the components of the force

[kreil]

I know the answers to these problems but I'm having trouble obtaining them:

1)To model a spacecraft , a toy rocket engine is securely fastened to a large hockey puck, which can glide with negligible friction over a horizontal surface, taken as the xy plane. The 4.0 kg puck has a velocity of $300\hat{x}$m/s at one instant. 8 seconds later, it is to have a velocity of $v=(800\hat{x}+10\hat{y})m/s$. Assuming the rocket engine exerts a constant horizontal force, find
a) the components of the force
b)its magnitude

If someone could just show me how to set up part (a) I can easily go from there.

2) The distance between 2 telephone poles is 50m. When a 1.0 kg bird lands on the wire midway between the poles, the wire sags 0.2m. How much tension does the bird produce in the wire? (ignore the weight of the wire)

This one seems easy, but the answer is 613N and I can't seem to get that.


Any quick help is much appreciated!

 

[hotvette]

As a start, draw a free body diagram w/ forces, write F=MA, solve the resulting differential equation. Hint: since the final velocity has components in 2 different directions, the applied force must also be in 2 different directions. Thus, you'll likely end up with 2 differential equations.

 

[quicknote]

For the first problem, we can use Newton's Second Law, which states that the net force on an object is equal to its mass times its acceleration. In this case, the object is the hockey puck and the force is the rocket engine.

a) To find the components of the force, we need to break the force vector into its x and y components. The x component of the force will be responsible for changing the velocity in the x direction, while the y component will be responsible for changing the velocity in the y direction. We can use the formula F=ma to solve for the components.

The mass of the puck is 4.0 kg and the acceleration in the x direction is (800-300)/8 = 62.5 m/s^2. Therefore, the x component of the force is Fx = (4.0 kg)(62.5 m/s^2) = 250 N.

Similarly, the y component of the force is responsible for changing the velocity in the y direction from 0 to 10 m/s in 8 seconds. Using the same formula, we can solve for the y component of the force: Fy = (4.0 kg)(10 m/s)/8 = 5 N.

b) To find the magnitude of the force, we can use the Pythagorean theorem: F = √(Fx^2 + Fy^2) = √(250^2 + 5^2) = 250.13 N.

For the second problem, we can use the concept of tension in a string or wire. The tension in a wire is equal to the force pulling on either end of the wire. In this case, the bird is pulling down on the wire with its weight, and the wire is pulling up on the bird with an equal and opposite force. Therefore, the tension in the wire is equal to the weight of the bird.

Using the formula F=ma, we can solve for the weight of the bird: F = (1.0 kg)(9.8 m/s^2) = 9.8 N. Since there are two equal and opposite forces (the weight of the bird and the tension in the wire), the tension in the wire is also 9.8 N.

Hope this helps! Remember to always use the correct units in your calculations.