A 395.0 g block is dropped onto a vertical spring with a spring constant k = 252.0 N/m. The block becomes attached to the spring, and the spring compresses 0.29 m before momentarily stopping. While the spring is being compressed, what work is done by the block's weight?
What work is done by the spring?
What was the speed of the block just before it hit the spring?
W(block) =kx²/2=252•0.29²/2=10.6 J
W(spring) = - 10.6 J
mv²/2 = kx²/2
v=x•sqrt(m/k)=
=0.29•sqrt(0.395/252) =0.0115 m/s
To calculate the work done by the block's weight, you need to find the force exerted by gravity on the block and then multiply it by the displacement.
Step 1: Find the force exerted by the block's weight (F_gravity):
F_gravity = m * g
where m is the mass of the block and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Given that the mass of the block is 395.0 g (0.395 kg), we can calculate the force:
F_gravity = 0.395 kg * 9.8 m/s^2
Step 2: Calculate the work done by the weight (W_gravity):
W_gravity = F_gravity * d
where d is the displacement.
The displacement of the block in this case is equal to the compression of the spring, which is given as 0.29 m.
Now, we can calculate the work done by the block's weight:
W_gravity = F_gravity * 0.29 m
To calculate the work done by the spring, we can use Hooke's Law.
Step 3: Find the spring force (F_spring):
F_spring = k * x
where k is the spring constant and x is the compression of the spring.
Given that the spring constant k is 252.0 N/m and x is 0.29 m, we can calculate the spring force:
F_spring = 252.0 N/m * 0.29 m
Finally, the work done by the spring (W_spring) can be calculated as the negative of the work done by the block's weight:
W_spring = - W_gravity
Now, to find the speed of the block just before it hit the spring, we can use the principle of conservation of mechanical energy.
Step 4: Use the conservation of energy equation:
Potential energy + Kinetic energy = 0
At the maximum height before hitting the spring, the potential energy is zero. Therefore, the initial potential energy is equal to the final kinetic energy.
Step 5: Calculate the initial potential energy:
Potential energy = (1/2) * k * x^2
where k is the spring constant and x is the compression of the spring.
Given that the spring constant k is 252.0 N/m and x is 0.29 m, we can calculate the potential energy:
Potential energy = (1/2) * 252.0 N/m * (0.29 m)^2
Step 6: Calculate the final kinetic energy:
Kinetic energy = (1/2) * m * v^2
where m is the mass of the block and v is the velocity.
Given that the mass of the block is 395.0 g (0.395 kg), we can calculate the kinetic energy:
Kinetic energy = (1/2) * 0.395 kg * v^2
Since the potential energy is equal to the final kinetic energy, we can set them equal to each other and solve for v:
(1/2) * 252.0 N/m * (0.29 m)^2 = (1/2) * 0.395 kg * v^2
Solve the equation for v, and you will find the speed of the block just before it hit the spring.