Calculate the maximum height of ball 1

In summary, two balls connected by a string are released from different heights, with ball 2 falling to the ground and losing 30% of its kinetic energy before rebounding to a maximum height. Ball 1 rises to a maximum height before starting to fall, assuming no tension in the string. Using the equations for kinetic and potential energy, the maximum height of ball 1 can be calculated as 0.35 V^2/g, where V is the velocity of ball 2 just before impact. The rebound height of ball 2 can be calculated as 0.88 + 0.88 = 1.62 m above the ground.
  • #1
myoplex11
45
0

Homework Statement


Two balls are connected by a string that stretches over a massless, frictionless pulley. Ball 1 has a mass of 0.45 kg and is held 0.74 m above the ground. Ball 2 has a mass of 5.7 kg and is held 0.88 m above the ground. When the balls are released, ball 2 falls to the ground, looses 30 % of its kinetic energy and rebounds to some maximum rebound height. When the balls are released, ball 1 travels to some maximum height before starting to fall. Assume that ball 1 reaches its maximum height during ball 2's rebound so that the string doesn't pull.
Calculate the maximum height of ball 1 from and ground and the rebound height of ball 2.

Homework Equations





The Attempt at a Solution


can you check my work i am stuck
I would calculate the kinetic energy of ball 2 just before and after it hits the ground, using
Just before impact, ball 2 (M) and ball 1 (m) have acquired kinetic energy
(1/2)mV^2 + (1/2)MV^2
= M g*0.74 - m g*0.74 Solve for V of both balls, and the kinetic energy of ball 2.

(1/2)(m + M)V^2 = 0.74 (M-m)g
V^2 = [(M-m)/(M+m)]g*1.48 = 12.38 m^2/s^2
V = 3.52 m/s

= After impact, ball 2 will have 70% of the pre-impact kinetic energy, and its velocity will be V' = sqrt(0.7)V= 0.8367V = 2.94 m/s
Right after ball 2's impact, Ball 1 will continue to rise for a while because it suffered no impact and maintained its velocity V when ball 2 hits the ground. There will be no tension in the string while ball 2 and ba1l 1 both rise.
Ball 1 rises a distance H1 given by
M g H1 = (1/2) M V'^2 = (1/2)M(0.7)V^2
H1 = (0.7)V^2/(2g) = 0.35 V^2/g

When ball 1 hits the ground, ball 2 has already risen from 0.74 to 0.74 + 0.88 = 1.62 m above the ground. It will rise an additional distance until its kinetic energy (1/2) mV^2(at impact)is converted to potential energy
 
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  • #2
Hi myoplex11! :smile:

Looks good down to …
myoplex11 said:
Ball 1 rises a distance H1 given by
M g H1 = (1/2) M V'^2 = (1/2)M(0.7)V^2
H1 = (0.7)V^2/(2g) = 0.35 V^2/g
… where you should still be using V = 3.52 (not 0.7V) :wink:

(are you mixing up ball 1 and 2?)

Apart from that, everything's fine.

What are you getting for the maximum and rebound heights? :smile:
 
  • #3
m g H2, where H2 is the rebound height of ball 2.
(1/2)m V^2 = m g H2
V^2 = 2 g H2
V = sqrt(2 g H2) = 2.83 m/s

Now, the string will start to pull ball 1 down, and ball 1 will start to fall. It will fall a distance H2, given by
(1/2)m V^2 = m g H2
H2 = V^2/(2g) = 0.25 V^2/g

Therefore, the maximum height reached by ball 1 is H1 + H2 = 0.35 V^2/g + 0.25 V^2/g = 0.6 V^2/g = 0.6 (3.52)^2/9.8 = 0.75 m.

The rebound height of ball 2 is H2 = V^2/(2g) = (2.83)^2/(2*9.8) = 0.4 m.

Please note that this is just a rough calculation and may not be completely accurate. It is always important to double check your work and make sure all units are consistent. Additionally, it is always a good idea to draw a diagram and label all variables before attempting a calculation.
 

1. How do you calculate the maximum height of ball 1?

To calculate the maximum height of ball 1, you will need to know the initial velocity, launch angle, and acceleration due to gravity. You can use the equation h = (v2sin2θ) / 2g to calculate the maximum height, where h is the maximum height, v is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity.

2. What is the initial velocity?

The initial velocity is the speed at which the ball is launched into the air. It is typically measured in meters per second (m/s).

3. How do you determine the launch angle?

The launch angle is the angle at which the ball is launched into the air. It is typically measured in degrees. You can use a protractor or a device that measures angles to determine the launch angle.

4. What is the acceleration due to gravity?

The acceleration due to gravity is a constant value that represents the rate at which objects accelerate towards the Earth. It is typically denoted by g and has a value of 9.8 meters per second squared (m/s2) on Earth.

5. Can you calculate the maximum height of ball 1 without knowing the initial velocity or launch angle?

No, you cannot calculate the maximum height of ball 1 without knowing the initial velocity or launch angle. These two variables are essential components in the equation for calculating maximum height.

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