A block of mass 10 gram slides from rest down an incline (θ = 30°) without friction and hits a spring (with k = 4 N/m). The spring is compressed by a distance of 10 cm before the block comes to a stop. Calculate the distance between the initial position of the block and the initial position of the top end of the spring.
Can someone please show me HOW to do this. You don't need to actually solve it, but a few good hints would be very appreciated!
Thanks.
Can someone please show me HOW to do this. You don't need to actually solve it, but a few good hints would be very appreciated!
Thanks.
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Gravity supplies energy. As the slope is 30 degrees the component of the force along the slope is mg sin(theta)
F = 0.010 * 9.8 * 0.5
The weight slides along some distance INCLUDING the distance while the spring is compressing and it gains energy = F d and you have already calculated F
This energy goes into the spring 1/2 k x^2 but you know both k and x for the spring.
So you know the amount of energy in the spring and can calculate d.
Finally you must remember that this is the distance until the weight came to a stop. It hits the spring 10 cm before this.
F = 0.010 * 9.8 * 0.5
The weight slides along some distance INCLUDING the distance while the spring is compressing and it gains energy = F d and you have already calculated F
This energy goes into the spring 1/2 k x^2 but you know both k and x for the spring.
So you know the amount of energy in the spring and can calculate d.
Finally you must remember that this is the distance until the weight came to a stop. It hits the spring 10 cm before this.