A 10.6 N force is sufficient to keep a 15 kg mass moving in a circle. How much force in Newtons is needed to keep a 10.7 kg mass moving with the same speed in a circle of the same radius?
To find the force needed to keep a different mass moving with the same speed in a circle of the same radius, we can use the equation for centripetal force. The centripetal force (Fc) is equal to the mass (m) multiplied by the centripetal acceleration (ac).
In this case, we have the centripetal force (Fc) of 10.6 N and the mass (m) of 15 kg. We can use these values to find the centripetal acceleration (ac).
Fc = m * ac
10.6 N = 15 kg * ac
Now, we can solve for ac:
ac = 10.6 N / 15 kg
ac ≈ 0.707 m/s² (rounded to three decimal places)
Next, we can use the centripetal acceleration (ac) and the mass (m) of the second object to find the force needed to keep it moving with the same speed. Let's call this force F2.
F2 = m * ac
Substituting the given values:
F2 = 10.7 kg * 0.707 m/s²
F2 ≈ 7.5569 N (rounded to four decimal places)
Therefore, approximately 7.5569 Newtons of force is needed to keep a 10.7 kg mass moving with the same speed in a circle of the same radius.