A 0.9 kg block is moving with speed 7 m/s towards a spring that has a spring constant of 1.3 N/m. The block hits the spring and compresses it.
a) How far did the block compress the spring?(draw a pie graph also)
b) When the block is still moving and the spring has been compressed only 3m, how fast is the block moving ?(draw a pie graph also)
To answer this question, we can use the principles of conservation of energy and Hooke's Law.
a) To determine how far the block compresses the spring, we need to calculate the potential energy stored in the spring when it is compressed and equate it to the initial kinetic energy of the block.
Step 1: Calculate the initial kinetic energy of the block:
The formula for kinetic energy is KE = (1/2) * mass * velocity^2
Substituting the given values: KE = (1/2) * 0.9 kg * (7 m/s)^2
Step 2: Calculate the potential energy stored in the spring:
The formula for potential energy stored in a spring is PE = (1/2) * k * x^2
where k is the spring constant and x is the compression distance.
We need to find x, so we rearrange the formula:
x = sqrt((2 * KE) / k)
Substituting the given values: x = sqrt((2 * KE) / 1.3 N/m)
Step 3: Calculate the compression distance:
Substituting the calculated values into the previous equation:
x = sqrt((2 * 0.9 kg * (7 m/s)^2) / 1.3 N/m)
Now, plug in the values and solve for x:
x = sqrt((2 * 0.9 * 49) / 1.3)
After calculating, you will find that the block compresses the spring by an approximate distance of x meters.
To draw the pie graph, you would need information about the compression distance within a certain range. Since it is not provided in the question, we cannot draw a pie graph.
b) When the block is still moving and the spring has been compressed to 3m, we can use the principle of conservation of mechanical energy to find the new velocity of the block.
Step 1: Calculate the potential energy stored in the spring:
Using the formula mentioned earlier: PE = (1/2) * k * x^2
Substituting the given values: PE = (1/2) * 1.3 N/m * (3 m)^2
Step 2: Calculate the new kinetic energy of the block:
We know that the total mechanical energy (KE + PE) remains constant.
So, total mechanical energy = initial kinetic energy
KE = total mechanical energy - PE
Substituting the calculated values into the equation:
KE = (1/2) * 0.9 kg * (7 m/s)^2 - (1/2) * 1.3 N/m * (3 m)^2
Step 3: Calculate the new velocity of the block:
Using the formula for kinetic energy mentioned earlier, solve for velocity:
velocity = sqrt((2 * KE) / mass)
Substituting the calculated values into the equation:
velocity = sqrt((2 * KE) / 0.9 kg)
After calculating, you will find the new velocity of the block when the spring is compressed to 3m.
Similar to the first part, since the compression distance is fixed at 3m, we cannot draw a pie graph without further information about the compression distance within a certain range.