Betty weighs 427 N and she is sitting on
a playground swing seat that hangs 0.22 m above the ground. Tom pulls the swing back and releases it when the seat is 0.88 m above the ground.
The acceleration of gravity is 9.8 m/s2.
How fast is Betty moving when the swing
passes through its lowest position?
Answer in units of m/s
Answer= 3.5967m/s
If Betty moves through the lowest point at 0.6 m/s, what is the magnitude of the work done on the swing by friction?
Answer in units of J
To calculate the speed of Betty at the lowest point of the swing, you can use the principle of conservation of mechanical energy. At the highest point, the swing has gravitational potential energy, and at the lowest point, this energy is converted into kinetic energy.
To find the speed, you can equate the initial potential energy to the final kinetic energy:
mgh = (1/2)mv^2
where m is Betty's weight (or mass divided by the acceleration due to gravity), g is the acceleration due to gravity, h is the initial height, and v is the final velocity (or speed).
Given:
Weight of Betty, W = 427 N
Height above the ground at the highest point, h1 = 0.22 m
Height above the ground at the lowest point, h2 = 0.88 m
Acceleration due to gravity, g = 9.8 m/s^2
First, calculate Betty's mass (m) using the weight and acceleration due to gravity:
m = W / g
m = 427 N / 9.8 m/s^2 ≈ 43.57 kg
Next, calculate the initial potential energy and the final kinetic energy:
Initial potential energy, PE1 = m * g * h1
Final kinetic energy, KE2 = (1/2) * m * v^2
Since the mechanical energy is conserved, we can equate the two:
PE1 = KE2
m * g * h1 = (1/2) * m * v^2
Simplifying the equation:
g * h1 = (1/2) * v^2
Substituting the given values:
9.8 m/s^2 * 0.22 m = (1/2) * v^2
2.156 m/s^2 = v^2
Now, take the square root of both sides to find the velocity:
v ≈ √2.156 m/s^2
v ≈ 1.47 m/s
Therefore, the speed of Betty when the swing passes through its lowest position is approximately 1.47 m/s.
To find the magnitude of the work done on the swing by friction, we know that work is equal to force multiplied by displacement. In this case, the force of friction acts in the opposite direction to the displacement of the swing.
Using the equation for work:
Work = Force * Displacement
Since friction is the only force acting on the swing, the work done by friction is given by:
Work = Force of friction * Displacement
The magnitude of the work done on the swing by friction can be found by multiplying the force of friction by the displacement. However, to calculate the force of friction, we need additional information such as the coefficient of friction and the contact area. Please provide these values to proceed with the calculation.
To find the magnitude of the work done on the swing by friction, we need to use the work-energy principle. The work done by friction can be calculated as the change in kinetic energy:
Work done by friction = Change in kinetic energy
The initial kinetic energy of Betty at the highest point (when the swing is released) is zero, as she is momentarily at rest. At the lowest point, her kinetic energy is given by:
Kinetic energy = 0.5 * mass * velocity^2
Given that Betty moves through the lowest point at a velocity of 0.6 m/s, we can calculate her mass using her weight:
Weight = mass * acceleration due to gravity
mass = Weight / acceleration due to gravity
Plugging in the values:
mass = 427 N / 9.8 m/s^2 = 43.57 kg
Now, we can calculate the change in kinetic energy:
Change in kinetic energy = 0.5 * mass * (velocity^2 - 0)
Change in kinetic energy = 0.5 * 43.57 kg * (0.6 m/s)^2
Change in kinetic energy = 6.2742 J
Therefore, the magnitude of the work done on the swing by friction is 6.2742 J.
mgh at start=1/2 m v^2 at end
v^2=2g*(.880.22)
solve for v