A 25kg child on a 2m long swing is released from rest when the swing supports make an angle of 30 degrees with the vertical. (a) Neglecting friction, find the child's speed at the lowest position. (b) If the speed of the child at the lowest position is 2m/s, what is the mechanical energy lost due to friction?
(a) (9.8m/s^2)(2-2cos30)=1/2(v^2)
v=2.29m/s
(b)What am I suppose to do for b?
Can you tell me what kind of equation did you used to get v=2.29m/s?
I am also suffering from this kind of prob.
haha university of victoria assignment??? me too...
To find the mechanical energy lost due to friction, we need to calculate the initial mechanical energy of the system and subtract the final mechanical energy of the system (after friction).
The initial mechanical energy can be calculated using the formula:
E_initial = mgh + (1/2)mv^2
where m is the mass, g is the acceleration due to gravity, h is the height, and v is the initial velocity. In this case, the initial velocity is 2.29 m/s as calculated previously.
We know that the height of the swing is given by h = 2 - 2cos30, which equals 1.732 meters.
The mass of the child is 25 kg and the acceleration due to gravity is 9.8 m/s^2.
Therefore, the initial mechanical energy is:
E_initial = (25 kg)(9.8 m/s^2)(1.732 m) + (1/2)(25 kg)(2.29 m/s)^2
Next, we need to calculate the final mechanical energy of the system (after friction). Since friction causes energy loss, the final mechanical energy will be less than the initial mechanical energy.
Given that the speed at the lowest position is 2 m/s, we can say that the final velocity (vf) is 2 m/s.
The final mechanical energy can be calculated using the formula:
E_final = mgh + (1/2)mvf^2
where m, g, h, and vf have the same values as before.
Finally, the mechanical energy lost due to friction can be calculated by taking the difference between the initial and final mechanical energy:
Energy lost = E_initial - E_final
Substitute the respective values into these equations to find the mechanical energy lost due to friction.
To find the mechanical energy lost due to friction, you need to first calculate the initial mechanical energy of the child at the highest point of the swing using the concept of gravitational potential energy. Then, you can subtract the final mechanical energy at the lowest point of the swing to find the energy lost.
The initial mechanical energy of the child at the highest point is given by the sum of gravitational potential energy and kinetic energy:
Initial Mechanical Energy = Gravitational Potential Energy + Kinetic Energy
The gravitational potential energy is given by the formula:
Gravitational Potential Energy = mass x gravity x height
In this case, the height is the vertical distance between the highest and the lowest point, which is equal to the length of the swing, 2m.
So, the gravitational potential energy at the highest point is:
Gravitational Potential Energy = 25kg x 9.8 m/s^2 x 2m
Next, you can calculate the final mechanical energy at the lowest point. Since the child has a speed of 2m/s at the lowest point, the mechanical energy can be expressed as the sum of kinetic energy and gravitational potential energy:
Final Mechanical Energy = Kinetic Energy + Gravitational Potential Energy
The kinetic energy is given by the formula:
Kinetic Energy = 1/2 x mass x velocity^2
In this case, the mass is 25kg and the velocity is 2m/s.
Now, you can calculate the final mechanical energy at the lowest point using the above formulas.
Finally, to find the mechanical energy lost due to friction, you subtract the final mechanical energy from the initial mechanical energy:
Mechanical Energy Lost = Initial Mechanical Energy - Final Mechanical Energy.
By substituting the values and performing the calculations, you should be able to find the answer.