A 0.54-kg air cart is attached to a spring and allowed to oscillate. If the disp

Question

A 0.54-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+pi], find the maximum KE of the cart.
Find the maximum force exerted on it by the spring. A 0.54-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+pi], find the maximum KE of the cart.
Find the maximum force exerted on it by the spring.
If the displacement of the air cart from equilibrium is x=(10.0cm)cos[2.00s^-1)t+pi], find the maximum KE of the cart.
Find the maximum force exerted on it by the spring.

Explanation / Answer

Given that

Mass of the air cart is (m) =0.54kg

The displacement of air cat is (x)=(10.0cm)cos[2.00s^-1)t+pi]

We know that x =Acos(wt+Pi)

From the above equation we get

A =10cm=0.1m

w =2s-1

Pi =Pi

Now speed v is given by v =dx/dt =-Awsin(wt+pi)

The maximum speed is given by Vmax =Aw =(0.1m)(2) =0.2m/s

Now the maximum kinetic energy is KEmax =0.5*(0.54)(0.2)2 =0.0108J

Then accelration is given by a =dv/dt =Aw2cos(wt+Pi)

Forthe maximum acceleration

amax =-Aw2 =0.4m/s2

The maximum force exerted on the spring is given by

Fmax= mamax =0.54kg*0.4=0.216N

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