An “extreme” pogo stick utilizes a spring whose uncompressed length is 36 cm and

Question

An “extreme” pogo stick utilizes a spring whose uncompressed length is 36 cm and whose force constant is 1.6×104 N/m. A 61-kg enthusiast is jumping on the pogo stick, compressing the spring to a length of only 9.0 cm at the bottom of her jump.

Part A

Calculate the net upward force on her at the moment the spring reaches its greatest compression.

Express your answer to two significant figures and include the appropriate units.

Part B

Calculate her upward acceleration, in g’s at that moment.

Express your answer using two significant figures.

Explanation / Answer

Given that,

uncompressed length = x1 = 36 cm = 0.36 m ; K = 1.6 x 104 N/m ; M = 61 kg ; x2 = 9 cm = 0.09 m

A)We need to find the upward force at the greatest compression of the spring, which will be given by:

Fu = K (x2 - x1) - mg

Fu =  1.6 x 104 N/m x (0.36-0.09) - 61 x 9.8 = 4320 - 597.8 = 3722.2 N

Hence, Upwards force = Fu = 3722.2 N

B) We know that, F = ma = Fu

a = Fu/m = 3722.2/61 = 61 m/s2 = 61/9.8 g = 6.23 g

Hence, acceleration = a = 6.23 g

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.