a 65 kg male skater pushes a 45 kg female skater causing her to accelerate at a rate of 2.0 ms ^2 at what rate will the male skater accelerate? What is the rate of his acceleration?
Since they exert equal and opposite forces on each other,
M1*a1 = -M2*a2
a2 = -a1*(45/65)
= -1.38 m/s^2
Subscript 2 denotes male; 1 denotes female.
The minus sign means the accelerate in opposite directions.
To find the rate at which the male skater will accelerate, we need to use Newton's Third Law of Motion, which states that for every action, there is an equal and opposite reaction.
Since the female skater is accelerating, she is exerting a force on the male skater. According to Newton's Third Law, the male skater will exert an equal and opposite force on the female skater.
We can use the following formula to calculate the force experienced by the female skater:
Force = mass x acceleration
F = 45 kg x 2.0 m/s^2
F = 90 N
Since the force experienced by the female skater is exerted by the male skater in the opposite direction, the male skater will also experience a force of 90 N.
Now we can find the rate of acceleration of the male skater using the formula:
Force = mass x acceleration
90 N = 65 kg x acceleration
Solving for acceleration:
acceleration = 90 N / 65 kg
acceleration ≈ 1.38 m/s^2
Therefore, the rate of acceleration of the male skater is approximately 1.38 m/s^2.
To find the rate of acceleration of the male skater, we can use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration.
Let's denote the rate of acceleration for the male skater as 'a', and for the female skater as 'a1'. We know the following values:
- Mass of the male skater (m1) = 65 kg
- Mass of the female skater (m2) = 45 kg
- Acceleration of the female skater (a1) = 2.0 m/s^2
According to Newton's second law, the force acting on the male skater can be expressed as:
Force on male skater (F1) = m1 * a
The force exerted by the male skater on the female skater is equal in magnitude but opposite in direction. So:
Force on female skater (F2) = -m2 * a1
Since both skaters experience the same force, we can equate F1 and F2:
m1 * a = -m2 * a1
Now we can plug in the values and calculate the rate of acceleration for the male skater (a):
65 kg * a = -45 kg * 2.0 m/s^2
a = (-45 kg * 2.0 m/s^2) / 65 kg
a ≈ -1.38 m/s^2
Therefore, the rate of acceleration for the male skater is approximately -1.38 m/s^2.