A research balloon of total mass 200 kg is descending vertically with a downward acceleration of 3.2 m/s^2. How much ballast must be thrown from the car to give the balloon an upward acceleration equal to 2.8 m/s^2, presuming that the upward lift of the balloon does not change?
Could someone at least show me the first steps? I don't even know where to begin.
The upward lift is constant, it depends only on the size of the balloon.
netforce= mass*acceleration
Lift-mg=m*a
lift-g(m-deltam)=(m-deltam)*newacc
1)solve for lift in the original equation, knowing m, a, and g.
2) solve for deltamass in the second equation knowing lift, g, m, and the new acceleration.
For lift I got 1320, and for deltamass I got 304.76. Is this right? If so, do I have to add those to the netforce?
To solve this problem, you can apply Newton's second law of motion. Newton's second law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
First, let's find the current net force acting on the descending balloon:
Net force = Mass * Acceleration
Given that the mass of the balloon is 200 kg and its current acceleration is 3.2 m/s^2, we can calculate the net force:
Net force = 200 kg * 3.2 m/s^2
Net force = 640 N (Newtons)
Since the balloon is descending, the current net force is equal to the sum of the downward force of gravity (weight) and the upward lift force from the balloon. In this problem, we assume that the upward lift force remains constant as we throw ballast from the car.
The upward acceleration we want to achieve is 2.8 m/s^2, so the new net force required would be:
Net force required = Mass * New acceleration
To find the mass, we need to calculate the difference in ballast thrown from the car. So, let's assume the mass of ballast thrown is 'm' kg.
The new net force required can be calculated as:
Net force required = (200 kg - m kg) * 2.8 m/s^2
According to Newton's second law, the net force required is equal to the difference between the force of gravity and the upward lift force:
Net force required = Weight - Lift force
We can set up an equation using the weight (force due to gravity) and the lift force:
(200 kg - m kg) * 2.8 m/s^2 = (200 kg * 9.8 m/s^2) - Lift force
Now, we need to determine the lift force. We know that the lift force is equal to the weight (force due to gravity) when the balloon is in equilibrium (not accelerating). So, we can set the lift force equal to the weight:
(200 kg * 9.8 m/s^2) - Lift force = 200 kg * 9.8 m/s^2
Simplifying this equation, we get:
Lift force = (200 kg * 9.8 m/s^2) - (200 kg - m kg) * 2.8 m/s^2
We can now substitute this expression for lift force back into the previous equation:
(200 kg - m kg) * 2.8 m/s^2 = (200 kg * 9.8 m/s^2) - [(200 kg * 9.8 m/s^2) - (200 kg - m kg) * 2.8 m/s^2]
Simplifying this equation will allow us to solve for 'm', which will give us the mass of the ballast that needs to be thrown from the car.