A 505 g ball swings in a vertical circle at the end of a 1.2-m-long string. When

Question

A 505 g ball swings in a vertical circle at the end of a 1.2-m-long string. When the ball is at the bottom of the circle, the tension in the string is 20 N. What is the speed of the ball at that point?

A 380 g model rocket is on a cart that is rolling to the right at a speed of 3.0 m/s. The rocket engine, when it is fired, exerts an 7.0 N thrust on the rocket. Your goal is to have the rocket pass through a small horizontal hoop that is 20 m above the launch point. At what horizontal distance left of the loop should you launch?

Explanation / Answer

F=mv^2/r +mg at bottom
20= 0.505/1.2*v^2 +0.505*9.8
20-4.949 =0.421v^2
v^2=15.051/0.421
v^2= 35.751
v=under root 35.751
v= 5.979 m/s

2)

Fw = mg
Where Fw is the weight (in newtons), m is the mass (in kg) and g is the acceleration due to gravity (9.81 m/s²).

Fw = (0.380 kg)(9.81 m/s²)
Fw = 3.7278 N

The rocket engine exerts 7.0 N of force on the rocket. 3.7278 N of that force will be used to counter the rocket's weight, leaving 3.272 N of force available to provide acceleration. We should calculate the rocket's upward acceleration:

Fnet = ma

Where Fnet is the net force (the force that remains after the rocket's weight is compensated), and a is the rocket's acceleration (in m/s²)

3.272 N = (0.380 kg) a

a = 8.61 m/s²

So now that we know the rocket's upward acceleration we can calculate how long it will take to rise 20 meters into the air.

y = vo*t + 1/2 at²

The rocket's original velocity, vo, is 0 m/s. We can remove the vo*t term from the equation, leaving:

y = 1/2 at²

20 m = 1/2(8.61 m/s²)t²

20 m = (4.3 m/s²)t²

4.65 s² = t²

t = 2.1567 s

So the rocket will take 2.1567 seconds to reach the hoop. It should be launched when the cart is 2.1567 seconds away from being directly beneath the hoop. Given the cart's constant horizontal velocity of 3.0 m/s, we can calculate how far the cart will travel in 2.1567 s

v = x / t

3.0 m/s = x / 2.1567 s

x = 6.4701 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.