Spring launching 3 kg block

• jjd101
In summary, a 3.00 kg block is launched by a horizontal spring with a spring constant of 200.0 N/m, compressed at 25.0 cm. The block then travels up a 32 degree incline with a coefficient of friction of 0.25, with a normal reaction of 24.93 N and a frictional force of 6.23 N. Using the equation for energy conservation, the distance traveled along the incline is approximately 0.286m before the block stops.

Homework Statement

A horizontal spring with a spring constant of 200.0 N/m is compressed 25.0 cm and used to launch a 3.00 kg block across a frictionless surface. After the block travels some distance, the block goes up a 32 degree incline that has a coefficient of friction of 0.25 between the block and the surface of the incline. How far along the incline does the block go before stopping?

motion equations
f=-ks
f=ma

The Attempt at a Solution

i tried taking the force of the spring at .25m compression which is 50N times sin32 to account for incline i got 26.5N, minus the force of the friction which i got as 6.23 so a total force of 20.27 divided by the mass gives acceleration of 6.76. Then i was not able to use a motion equation to find a distance up the incline

jjd101 said:
... i tried taking the force of the spring at .25m compression which is 50N times sin32 to account for incline i got 26.5N,...

When the mass is on the incline there is no component of the force of the spring anymore. The effect of the spring appears only in the velocity of the mass up the plane.

Which forces do you think act on the mass while it is moving up the incline?

force of friction and gravity?

There is also the normal reaction of the incline on the mass.

Now which method are you going to use, energy or equations of motion?

okay

it would be mgsin32 i believe

the normal reaction is mgcos32.

so normal incline is mgcos32 = 24.93 N and ff = .25mg =7.35N so total resistance along the incline is 32.28N?

normal reaction = 0.25x24.93=6.23N

frictional force = coefficient of friction x normal reaction

thats what i got originally, how do i use that to find a distance up the ramp?

are you going to use energy or equations of motion?

im guessing energy because i didnt see a way of doing it with motion equations?

so initial energy = final energy
what is formula for the initial energy?
what is formula for final energy?

initial energy = Us=1/2kX^2 = 1/2(200)(.25)^2 = 6.25 KE=1/2mv^2 6.25=1/2(3)V^2
Vi= 2.04?

correct.
In what form is the final energy?

Kinetic Energy with a velocity 0? or maybe potential energy cause its not moving?

if v = 0 there is not ke
So final energy is mgh.

Hence can you write an equation showing what happened to the intial energy?

so 6.25=mgh so h= .213m ?

6.25J has to provide energy for the final PE (mgh) and ALSO for the work done against friction.

how do i find the work done by friction?

initial energy = PE + work against friction

6.25 = mgh + frictional force x distance along incline

6.25 = mg x distance along incline x sin32 + frictional force x distance along incline

i just did that calculation and i got .0314m along the incline?

i got 0.286m

1. How does the mass of the block affect its launch during spring launching?

The mass of the block does not have a direct effect on its launch during spring launching. The force exerted by the spring is what determines the launch distance. However, a heavier block may require a stronger spring to achieve the desired launch distance.

2. What factors affect the launch distance of a 3 kg block using a spring?

The launch distance of a 3 kg block using a spring can be affected by several factors, including the force exerted by the spring, the angle at which the block is launched, the surface on which the block is resting, and any external forces acting on the block.

3. How can the launch distance of a 3 kg block using a spring be increased?

The launch distance of a 3 kg block using a spring can be increased by increasing the force exerted by the spring, launching the block at a higher angle, using a smoother surface for the block to slide on, and minimizing any external forces acting on the block.

4. Is the launch distance of a 3 kg block using a spring affected by the position of the spring?

The position of the spring does not have a significant effect on the launch distance of a 3 kg block. However, the further the spring is stretched, the greater the potential energy stored in the spring and the greater the launch distance.

5. Can the launch distance of a 3 kg block using a spring be calculated?

Yes, the launch distance of a 3 kg block using a spring can be calculated using the formula d = (k * x^2) / (2 * m * g), where d is the launch distance, k is the spring constant, x is the distance the spring is stretched, m is the mass of the block, and g is the acceleration due to gravity.