Final answer:
The acceleration of the cart with a total mass of 25 kg and two fans providing a total force of 8.0 N is 0.32 m/s². To give a second block with a mass of 6.0 kg the same acceleration, a force of 1.92 N is needed.
Step-by-step explanation:
To calculate the acceleration of the cart with the given parameters, we can use Newton's second law of motion, which is F = ma, where F is the net force applied to the object, m is the mass, and a is the acceleration. Given that each fan provides a force of 4.0 N and there are 2 fans, the total force provided by the fans is 2 fans × 4.0 N/fan = 8.0 N. The mass of the cart is 25 kg, so the acceleration (a) can be found by rearranging the formula to a = F/m.
Plugging in the values, the calculation becomes a = 8.0 N / 25 kg. After performing the division, we get the acceleration of the cart as 0.32 m/s².
(b) To give the second block, with a mass of 6.0 kg, the same acceleration, you would apply a force equal to the mass of the block times the acceleration. Therefore, the force needed would be F = ma which calculates to F = 6.0 kg × 0.32 m/s² = 1.92 N.