Conservation of Energy of a block and spring

[kimlu]

Homework Statement

A .500 kg block rests on a horizontal, frictionless surface as in the figure below. The block is pressed back against a spring having a constant of k=625 N/m, compressing the spring by 10cm to point A. Then the block is released.

a) Find the maximum distance d the block travels up the frictionless incline if θ= 30°

b) How fast is the block going when halfway to its maximum height?

Homework Equations

Kinitial+PEinitial= Kfinal+PEfinal

not exactly sure what other equations to use

The Attempt at a Solution

First I found the velocity of the block using KE=PEs (1/2mv^2=1/2kx^2) and ended up with equation of v=√kx/m and got 11.18 m/s for velocity but not sure what to do next or if I'm even doing this right I have the answers as shown in my attachment but I'm struggling to figure out how to get there please help I just started this topic in my AP Physics B course :(

 

[gneill]

Homework Statement

A .500 kg block rests on a horizontal, frictionless surface as in the figure below. The block is pressed back against a spring having a constant of k=625 N/m, compressing the spring by 10cm to point A. Then the block is released.

a) Find the maximum distance d the block travels up the frictionless incline if θ= 30°

b) How fast is the block going when halfway to its maximum height?

Homework Equations

Kinitial+PEinitial= Kfinal+PEfinal

not exactly sure what other equations to use

The Attempt at a Solution

First I found the velocity of the block using KE=PEs (1/2mv^2=1/2kx^2) and ended up with equation of v=√kx/m and got 11.18 m/s for velocity but not sure what to do next or if I'm even doing this right I have the answers as shown in my attachment but I'm struggling to figure out how to get there please help I just started this topic in my AP Physics B course :(

Hi kimlu, Welcome to Physics Forums.

This problem is largely about conservation of energy. You won't need to deal directly with velocities until the very end of part b.

Have you identified all the forms that energy can take in this problem? What are they?

 

[Panphobia]

The a) part suggests the maximum distance UP the incline plane, so what form of energy gets larger when height gets bigger with respect to the ground?

 

[kimlu]

Hey guys I figured it out and identified the forms of energy as PEs initial=PEgfinal/ mgdsin30=1/2kx^2 and rearranged the formula for d and plugged in numbers, I believe I got the right answer now thanks for the help <:

 

[Nickie]

I would like to first commend you for attempting to solve this problem and seeking help when you are struggling. It shows a great dedication to learning and improving your understanding of physics.

To solve this problem, we need to use the principle of conservation of energy, which states that the total energy of a system remains constant. This means that the initial kinetic energy (KE) of the block when released from the compressed spring will be equal to the final potential energy (PE) when it reaches its maximum height on the incline.

a) To find the maximum distance d the block travels up the frictionless incline, we can use the conservation of energy equation:

KEinitial + PEinitial = KEfinal + PEfinal

Since the surface is frictionless, there is no initial kinetic energy, so we can ignore the first term. The initial potential energy (PEinitial) is equal to the potential energy stored in the compressed spring, which can be calculated using the formula PE = 1/2kx^2, where k is the spring constant and x is the compression distance. Plugging in the values given in the problem, we get:

PEinitial = 1/2(625 N/m)(0.1 m)^2 = 3.125 J

Now, at the maximum height, the block will have zero kinetic energy and its potential energy will be equal to its gravitational potential energy (PEfinal). We can calculate this using the formula PE = mgh, where m is the mass of the block, g is the acceleration due to gravity, and h is the height. Rearranging the equation, we get:

h = PEfinal / (mg)

Plugging in the values, we get:

h = 3.125 J / (0.5 kg)(9.8 m/s^2) = 0.638 m

This is the maximum height the block will reach on the incline. To find the distance d, we need to subtract the initial compression distance of the spring (0.1 m) from the maximum height:

d = 0.638 m - 0.1 m = 0.538 m

Therefore, the maximum distance the block travels up the incline is 0.538 m.

b) To find the speed of the block when it is halfway to its maximum height, we can use the same conservation of energy equation. At this point, the block will have some kinetic energy and