= 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?
can someone pls answer
To find the speed of block m2 when the extension of the spring is 40 cm, we need to use the principles of conservation of energy.
Step 1: Determine the potential energy of the system before and after the extension of the spring.
Before the extension, the system is at rest, so it only has potential energy due to the weight of block m2. The potential energy (PE) is given by the formula: PE = mgh, where m is the mass, g is the gravitational acceleration (9.8 m/s^2), and h is the height.
PE = m2 * g * h
Given that m2 = 3.4 kg and h = 0 (as the system is at rest), the initial potential energy (PE_initial) is zero.
PE_initial = 0
After the extension, the potential energy of block m2 is converted into kinetic energy. The spring potential energy (PE_spring) is given by the formula: PE_spring = 0.5 * k * x^2, where k is the spring constant and x is the extension.
PE_spring = 0.5 * k * x^2
Given that k = 60 N/m and x = 40 cm = 0.4 m, the spring potential energy (PE_spring) is:
PE_spring = 0.5 * 60 * (0.4)^2
Step 2: Determine the velocity of block m2 using the conservation of energy principle.
According to the conservation of energy, the initial potential energy (PE_initial) is equal to the final kinetic energy (KE_final) of the system.
PE_initial = KE_final
Since the initial potential energy is zero, we can write:
0 = KE_final
The kinetic energy (KE) is given by the formula: KE = 0.5 * m * v^2, where m is the mass and v is the velocity.
KE_final = 0.5 * m2 * v^2
Given that m2 = 3.4 kg, we can rewrite the equation as:
0 = 0.5 * 3.4 * v^2
Simplifying the equation, we get:
0 = 1.7 * v^2
Step 3: Solve for the velocity.
To solve for the velocity (v), isolate v^2:
v^2 = 0 / 1.7
Since 0 divided by any number is zero, we have:
v^2 = 0
Taking the square root of both sides, we get:
v = 0 m/s
Therefore, the speed of block m2 when the extension is 40 cm is 0 m/s.