Final answer:
The acceleration of an ice skater with a mass of 49kg, being pushed with a force of 709N, and under the effect of a coefficient of kinetic friction of 0.38, is determined to be 10.74 m/s^2 after computing the net force and applying Newton's Second Law.
Step-by-step explanation:
To calculate the acceleration of the ice skater, we need to apply Newton's Second Law of Motion. First, we must determine the net force acting on the skater. The pushing force is given as 709N, but there is also a force of kinetic friction acting in the opposite direction that needs to be calculated. To find the force of kinetic friction , we multiply the mass of the skater (m) by the acceleration due to gravity (g) to get the normal force, and then multiply that by the coefficient of kinetic friction (μk).
The force of kinetic friction is calculated as m × g × μk. With a mass of 49kg, a gravitational acceleration of approximately 9.81 m/s2, and μk of 0.38, we have:
= 49kg × 9.81 m/s2 × 0.38 = 182.8N.
Now, the net force (Fnet) acting on the skater is the difference between the pushing force and the frictional force (Fnet = 709N - ):
Fnet = 709N - 182.8N = 526.2N.
Finally, we use Newton's Second Law to find the acceleration (a): Fnet = m × a, thus a = Fnet / m. Plugging in the net force and mass:
a = 526.2N / 49kg = 10.74 m/s2
The acceleration of the ice skater is therefore 10.74 m/s2.