A block of weight 3.8N is launched up a 30? inclined plane of length 2.50m by a

Question

A block of weight 3.8N is launched up a 30? inclined plane of length 2.50m by a spring with spring constant 2.10kN/m and maximum compression 0.10m . The coefficient of kinetic friction is 0.50.

Part A: Does the block reach the top of the incline? Yes

Part B: If so, how much kinetic energy does it have there; if not, how close to the top, along the incline, does it get?

Express your answer using two significant figures. K = ? J

Example of how to do the question !! Not the same values, just an example:

Part A: Does the block reach the top of the incline?

First calculate the work done on the block by the spring:

Work = 0.5*k*x^2
= 0.5 * 2250N * (0.1m)^2
= 11.25J

Frictional force = 0.50 * 3.6
= 1.8N

Relate plane hypotenuse length to plane height:

Hyp = height/sin30

Work done by friction = 1.8 * [(Delta)height /sin30]
= 3.6 * (Delta)height

Work done by gravity = 3.6 * (Delta)height

Total work required to raise block 1m = Work done by friction + work done by gravity
= 7.2 * (Delta)height
When length is 2.25m height = 2.25*sin30 = 1.125m

Therefore work required to reach top of ramp = 7.2 * 1.125
= 8.1J
As 11.25J>8.1J The block will reach the top of the ramp.


Part B: If so, how much kinetic energy does it have there; if not, how close to the top, along the incline, does it get?

11.25J - 8.1J = 3.15J

Explanation / Answer

Part A: Does the block reach the top of the incline?

First calculate the work done on the block by the spring:

Work = 0.5*k*x^2
= 0.5 * 2100N * (0.1m)^2
= 10.50J

Frictional force = 0.50 * 3.8
= 1.9N

Relate plane hypotenuse length to plane height:

Hyp = height/sin30

Work done by friction = 1.9 * [(Delta)height /sin30]
= 3.8 * (Delta)height

Work done by gravity = 3.8 * (Delta)height

Total work required to raise block 1m = Work done by friction + work done by gravity
= 7.6 * (Delta)height
When length is 2.5m height = 2.5*sin30 = 1.25m

Therefore work required to reach top of ramp = 7.6 * 1.25
= 9.5J
As 10.5J>9.5J The block will reach the top of the ramp.


Part B: If so, how much kinetic energy does it have there; if not, how close to the top, along the incline, does it get?

10.5J - 9.5J = 1J

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