Answer:
a) 0.231 kg b)0.154 m (15.4cm) c) 5.58 m/s
Explanation:
The force constant of the spring = 303 N/m, displacement from the center = 0.13, speed at this point is 3 m/s, total energy at this point is 3.6 Joules
Using energy formula to calculate the mass of the toy
total energy = 1/2 mv² + 1/2kx²
substitute the values into the formula
3.6 = m (1/2 ×3²) + (1/2 ×303×0.13²)
3.6 = m(4.5) + 2.56
3.6 - 2.56 = 4.5 m
1.04 = 4.5 m
m = 0.231 kg
b) using the speed formula:
v = √ ((xo² - x²)K/m) where xo is the amplitude and x is the 0.13m displacement from equilibrium point.
square both side to remove the square root and substitute in the values
3² =(xo² - x²) 303/0.231 = (xo² - x²) 1311.7
9 = (xo² - x²) 1311.7
divide both side by 1311.7
9/1311.7 = (xo² - x²)
0.00686 = xo² - 0.13²
0.00686 + 0.0165 = xo²
xo² = 0.02376
take square root of both side
xo = √ 0.02376 = 0.154m = 15.4 cm
c) using maximum speed formula
Vmax = xo√(k/m)
substitute in the values
Vmax = 0.154 × √(k/m)
Vmax = 0.154 × √(303/0.231)
Vmax = 0.154× 36.22 = 5.58 m/s
