m1 = 1.7 kg block slides on a frictionless horizontal surface and is connected on one side to a spring (k = 60 N/m) as shown in the figure above. The other side is connected to the block m2 = 3.4 kg that hangs vertically. The system starts from rest with the spring unextended
b) What is the speed of block m2 when the extension is 40 cm?
Sigh..."as shown".
Perhaps the amazing Kreskin can help you.
kreshnik ? loooool
To find the speed of block m2 when the extension of the spring is 40 cm, we need to use the principle of conservation of mechanical energy.
1. Calculate the potential energy stored in the spring:
- First, convert the extension from centimeters to meters: 40 cm = 0.4 m.
- The potential energy stored in the spring is given by the equation: PE_spring = (1/2) * k * x^2, where k is the spring constant and x is the extension.
- Substitute the values into the equation: PE_spring = (1/2) * 60 N/m * (0.4 m)^2.
2. Calculate the gravitational potential energy of block m2:
- The gravitational potential energy is given by the equation: PE_gravity = m * g * h, where m is the mass, g is the acceleration due to gravity, and h is the height.
- The height, h, is equal to the extension, x.
- Substitute the values into the equation: PE_gravity = 3.4 kg * 9.8 m/s^2 * 0.4 m.
3. Calculate the initial total energy of the system:
- The initial total energy is the sum of the potential energy stored in the spring and the gravitational potential energy of block m2: E_initial = PE_spring + PE_gravity.
4. Calculate the final total energy of the system:
- When the spring is extended to 40 cm, the block m2 will have gained potential energy, which will then be converted into kinetic energy.
- Since there is no friction, the total mechanical energy is conserved: E_initial = E_final.
- The final energy is the sum of the kinetic energy of block m2 and the potential energy stored in the spring when it is fully extended: E_final = KE_m2 + PE_spring.
5. Equate the initial and final total energies and solve for the kinetic energy of block m2:
- Set E_initial = E_final.
- Substitute the values for PE_spring, PE_gravity, and kinetic energy into the equation.
- Solve for the kinetic energy of block m2.
6. Calculate the speed of block m2:
- The kinetic energy is given by the equation: KE = (1/2) * m * v^2, where m is the mass and v is the speed.
- Rearrange the equation to solve for the speed: v = sqrt((2 * KE) / m).
By following these steps, you can find the speed of block m2 when the extension of the spring is 40 cm.
To find the speed of block m2 when the extension is 40 cm, we need to apply the laws of physics, specifically those related to kinetic energy and potential energy.
First, let's determine the potential energy stored in the spring at the given extension. The potential energy of a spring is given by the equation:
PE = (1/2) k x^2
Where PE is the potential energy, k is the spring constant, and x is the extension. In this case, the extension is given as 40 cm, but we need to convert it to meters:
x = 40 cm = 0.4 m
Substituting the values into the equation, we have:
PE = (1/2) * 60 N/m * (0.4 m)^2 = 4.8 J
Next, let's find the kinetic energy of block m2. The kinetic energy of an object is given by the equation:
KE = (1/2) m v^2
Where KE is the kinetic energy, m is the mass of the object, and v is the velocity. We can assume that all the potential energy of the spring is converted into kinetic energy of block m2. Therefore, the potential energy is equal to the kinetic energy:
KE = 4.8 J
Now, let's find the velocity of block m2. Rearranging the kinetic energy equation, we have:
v^2 = (2 * KE) / m
Substituting the values into the equation, we have:
v^2 = (2 * 4.8 J) / 3.4 kg = 2.82 m^2/s^2
Taking the square root of both sides, we find:
v = sqrt(2.82 m^2/s^2) = 1.68 m/s
Therefore, the speed of block m2 when the extension is 40 cm is 1.68 m/s.