Question

A 0.85-kg air cart is attached to a spring and allowed to oscillate. If the displacement of the air cart from equilibrium is x=(10.0cm)cos[(2.00s−1)t+π], find the maximum kinetic energy of the cart. Find the maximum force exerted on it by the spring.

Answer 1

Here,

A = 10 cm = 0.10 m

w = 2 rad/s

for the maximum kinetic energy

maximum velocity = A * w = 0.10 *2 = 0.20 m/s

maximum kinetic energy = 0.50 * m * v^2

maximum kinetic energy = 0.50 * 0.85 * 0.20^2

maximum kinetic energy = 0.017 J

the maximum kinetic energy is 0.017 J

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maximum force exerted = m * amax

maximum force exerted = 0.85 * A * w^2

maximum force exerted = 0.85 * 0.10 * 2^2

maximum force exerted = 0.34 N

the maximum force exerted is 0.34 N