A skater with 60 kg mass pushes a skater of 80 kg with a 68 N force. What will be the magnitude and direction of force and acceleration of each skater?
To find the magnitude and direction of force and acceleration for each skater, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass.
Let's start with the first skater whose mass is 60 kg. We are given that a second skater with a mass of 80 kg is pushing this skater with a force of 68 N. Since the first skater is being pushed, the force acting on this skater is in the opposite direction to the force applied by the second skater.
To find the magnitude of the force acting on the first skater, we need to consider Newton's third law of motion which states that every action has an equal and opposite reaction. So, the magnitude of the force acting on the first skater is also 68 N, but in the opposite direction.
Next, let's calculate the acceleration of the first skater. We can use Newton's second law: F = m * a, where F is the net force applied, m is the mass of the object, and a is the acceleration.
Substituting the values we know:
68 N = 60 kg * a
We can rearrange the equation to solve for the acceleration:
a = 68 N / 60 kg
The acceleration of the first skater is approximately 1.13 m/s².
Moving on to the second skater with a mass of 80 kg, we know that the force applied by the second skater is 68 N. Since this skater is pushing, the force acting on this skater is in the same direction as the force applied.
As per Newton's third law of motion, the magnitude of the force acting on the second skater is also 68 N.
Now, let's calculate the acceleration of the second skater:
68 N = 80 kg * a
Again, rearranging the equation to solve for the acceleration:
a = 68 N / 80 kg
The acceleration of the second skater is approximately 0.85 m/s².
To summarize:
For Skater 1 (60 kg):
- Force magnitude: 68 N
- Force direction: Opposite to the direction of the applied force
- Acceleration magnitude: 1.13 m/s²
For Skater 2 (80 kg):
- Force magnitude: 68 N
- Force direction: Same as the direction of the applied force
- Acceleration magnitude: 0.85 m/s²
To solve this problem, we need to apply Newton's second law of motion, which states that the force exerted on an object is equal to the mass of the object multiplied by its acceleration.
Let's calculate the magnitude and direction of force and acceleration for each skater:
1. Skater with 60 kg mass:
Force: The skater exerts a force of 68 N in a certain direction (let's assume it is to the right).
Acceleration: We need to find the acceleration of the skater. Since the force and mass are given, we can use Newton's second law to find the acceleration:
Force = mass x acceleration
68 N = 60 kg x acceleration
acceleration = 68 N / 60 kg = 1.13 m/s²
Therefore, the magnitude of the force exerted by the skater with a mass of 60 kg is 68 N, and the magnitude of their acceleration is 1.13 m/s² to the right.
2. Skater with 80 kg mass:
Force: The skater experiences a force consequent to being pushed by the other skater. According to Newton's third law of motion, the force exerted by the first skater (68 N) will be equal in magnitude but opposite in direction to the force experienced by the second skater. So, the magnitude of the force experienced by the second skater is also 68 N.
Acceleration: To find the acceleration of the second skater, we use the same formula as before:
Force = mass x acceleration
68 N = 80 kg x acceleration
acceleration = 68 N / 80 kg = 0.85 m/s²
Therefore, the magnitude of the force exerted on the skater with a mass of 80 kg is 68 N, and the magnitude of their acceleration is 0.85 m/s² in the opposite direction of the force (to the left).
To summarize:
- Skater with 60 kg:
- Force: 68 N to the right
- Acceleration: 1.13 m/s² to the right
- Skater with 80 kg:
- Force: 68 N to the left
- Acceleration: 0.85 m/s² to the left