Question

A spring, with a spring constant of 4000 N/m, is oriented horizontally, and compressed by 10cm. When released, the spring launches a block of mass 1.0 kg along a 5.0-m horizontal section of track, where the coefficient of friction between the block and track is 0.20. The block then goes up a frictionless ramp angled at 60o with the horizontal. How high up the ramp does the block go before it starts to slide back down

Answer 1

`d=1.2m`

Step-by-step explanation:

From the question we are told that:

Spring constant
`k= 4000 N/m`

Compressed
`l_d= 10cm=>0.10`

Mass
`m=1.0kg`

Length of horizontal section
`l=5.0-m`

Coefficient of friction
`\mu=0.20`

Angle
`\theta=60 \textdegree`

Generally the equation for Kinetic Energy K.E is mathematically given by

`K.E=\mu mgL+mgdsin\theta`

`(1)/(2)k*l_d^2=\mu mgL+mgdsin\theta`

`(1)/(2)(4000)*0.1^2=0.2*1*9.8*5+1*9.8*d*sin60`

`d=1.2m`