Shawn ( m = 47.0 kg) rides his skateboard at a local skate park. He starts from

Question

Shawn (m = 47.0 kg) rides his skateboard at a local skate park. He starts from rest at the top of the track as seen in the figure below and begins a descent down the track, always maintaining contact with the surface. The mass of the skateboard is negligible, as is friction except where noted.

(a) What is Shawn's speed when he reaches the bottom of the initial dip, 12.0 m below the starting point?

(b) He then ascends the other side of the dip to the top of a hill, 8.0 m above the ground. What is his speed when he reaches this point?

(c) As he begins to descend again, down a straight, 18.0-m-long slope, he slows his skateboard down by using friction on the tail of the board. He is able to produce a friction force with a magnitude of 110.0 N. What is the change in thermal energy of the board-rider-track system as he descends the 18.0-m length of track?

(d) What is his speed when he reaches the bottom (the end of the 18.0-m length of track)?

Explanation / Answer

Here,

a) let the speed is v m/s

Using conservation of energy

0.5 * m * v^2 = m * g * 12

v = 15.34 m/s

the speed of shawn's board is 15.34 m/s

b)

at this point

Using conservation of energy

0.5 * m * v^2 = m * g * (12 - 8)

0.5 * m * v^2 = m * g * 4

v = 8.854 m/s

the speed of shawn's board is 8.854 m/s

c)

chnage in thermal energy = 110 * 18

chnage in thermal energy = 1980 J

the increase in thermal energy is 1980 J

d)

at the bottom of track

0.5 * 47 * v^2 = 47 * 9.8 * 12 - 1980

v = 12.3 m/s

the speed of board is 12.3 m/s

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