You compress a spring with k = 3000 N/m a distance of 0.2 m with a block of mass

Question

You compress a spring with k = 3000 N/m a distance of 0.2 m with a block of mass 4 kg. You then release the block. It slides along a frictionless surface and then goes up an incline of 35 degrees. What is the velocity of the block after it leaves the spring but before it gets to the incline? How far up the incline (along the hypotenuse of the triangle) does the block travel? You have the same spring and same mass as #1. You compress the spring 0.3 m and release the block. After being released., the block hits a rough surface with a coefficient of friction of 0.6. How far does the block travel across the rough surface before it comes to a stop?

Explanation / Answer

Here,

1)

spring constant, k = 3000 N/m

distance ,x = 0.2 m

mass , m = 4 Kf

a) let the velocity of the block is v m/s

Using conseravtion of energy

0.5 * m * v^2 = 0.5 * k * x^2

4 * v^2 = 3000 * 0.2^2

v = 5.478 m/s

the speed of the block is 5.478 m/s

b)

let the distanceup the incline is d

Using conservation of energy

m * g * d * sin(theta) = 0.5 * k * x^2

4 * 9.8 * d * sin(35) = 0.5 * 3000 * 0.2^2

solving for d

d = 2.66 m

the distance travelled up the incline is 2.66 m

c)

let the distance travelled is d

Using work energy theorum

0.5 *k * x^2 - u * g * m * d= 0

0.5 * 3000 * 0.3^2 - 0.6 * 4 * 9.8 * d = 0

solving for d

d = 5.4 m

the distance travelled before stopping is 5.4 m

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