The bird perched on the swing shown below has a mass of 41.6 g, and the base of the swing, y = 7.88 cm below the hook, has a mass of 147 g. The swing and bird are originally at rest, and then the bird takes off horizontally at 1.94 m/s. How high will the base of the swing rise above its original level? Disregard friction.
momentum=momentum
41.6*1.94=147*Vswing
solve for the initial velociyt of the swing, Vswing.
Now how high? it converts to graviational PE, or
mgh=1/2 m vswing^2
solve for height h.
To determine how high the base of the swing will rise above its original level, we can use the principle of conservation of mechanical energy. The initial total mechanical energy is equal to the final total mechanical energy.
The total mechanical energy of the system can be calculated as the sum of the kinetic energy and the potential energy.
Initially, the total mechanical energy is zero because the swing and bird are at rest. Therefore, the final total mechanical energy should also be zero because there is no external work done on the system.
The kinetic energy of the bird can be calculated using the formula:
KE = (1/2) * mass * velocity^2
Given:
Mass of the bird (m1) = 41.6 g = 0.0416 kg
Velocity (v1) = 1.94 m/s
KE of the bird = (1/2) * 0.0416 kg * (1.94 m/s)^2 = 0.078 J
Next, let's calculate the potential energy of the swing and bird system. The potential energy is given by:
PE = mgh
Where:
m = mass of the base of the swing (m2) = 147 g = 0.147 kg
g = acceleration due to gravity = 9.8 m/s^2 (approximate value)
h = height of the base of the swing above its original level
PE of the swing = 0.147 kg * 9.8 m/s^2 * h = 1.438 J * h
Since the initial and final total mechanical energy is zero, we can write:
Initial total mechanical energy = KE of the bird + PE of the swing = 0
Final total mechanical energy = KE of the bird + PE of the swing = 0
Substituting the values we calculated:
0 + 0.078 J + 1.438 J * h = 0
Then, rearranging the equation to solve for h:
1.438 J * h = -0.078 J
h = -0.078 J / 1.438 J
h = -0.054 m
The negative sign indicates that the base of the swing will rise 0.054 meters below its original level.
To find out how high the base of the swing will rise above its original level, we need to use the principle of conservation of mechanical energy.
The principle of conservation of mechanical energy states that the total mechanical energy of a system remains constant, assuming no external forces are acting on it. In this case, the system consists of the bird, the swing, and the Earth's gravity.
The total mechanical energy of the system consists of two parts: the kinetic energy (KE) and the gravitational potential energy (PE).
Initially, the swing and bird are at rest, so the initial total mechanical energy is zero since there is no kinetic energy or potential energy.
When the bird takes off horizontally, it gains kinetic energy. The formula for kinetic energy is KE = 0.5 * mass * velocity^2. Plugging in the values, we find:
KE = 0.5 * (41.6 g) * (1.94 m/s)^2
Next, we need to determine how much potential energy the base of the swing will gain due to its rising motion. The formula for gravitational potential energy is PE = mass * gravity * height. Plugging in the values, we get:
PE = (147 g) * (9.8 m/s^2) * height
Since the total mechanical energy remains constant, the kinetic energy gained by the bird is equal to the potential energy gained by the base of the swing. So we can set up the equation:
0.5 * (41.6 g) * (1.94 m/s)^2 = (147 g) * (9.8 m/s^2) * height
Now we can solve for height:
height = (0.5 * (41.6 g) * (1.94 m/s)^2) / ((147 g) * (9.8 m/s^2))
Calculating this expression will give us the height the base of the swing will rise above its original level.
wish I could help but I have to right 3 essays in 1 hour and have to finish a water rocket
love jazzy