If you stand next to a wall on a frictionless skateboard and push the wall with a force of 40N, how hard does the wall push on you ? If your mass is 80kg show that your acceleration is 0.5m/s^2
Thw wall's force on the person pushing is the same (Newton's third law).
a = F/m = 40/80 = 0.5 m/s^2
To find how hard the wall pushes on you, we can use Newton's Third Law of Motion, which states that every action has an equal and opposite reaction. This means that the force you apply on the wall (40N) will result in the wall pushing back on you with an equal force.
So, the wall will push on you with a force of 40N in the opposite direction.
Now, let's calculate the acceleration. According to Newton's Second Law of Motion, the force acting on an object is equal to the mass of the object multiplied by its acceleration.
So, the force pushing you back (40N) is equal to your mass (80kg) multiplied by your acceleration (a), which we need to find.
We can rearrange the equation to solve for acceleration:
Force = mass * acceleration
40N = 80kg * a
Dividing both sides of the equation by 80kg:
a = 40N / 80kg
Simplifying:
a = 0.5m/s^2
Therefore, your acceleration is 0.5m/s^2.
To determine how hard the wall pushes on you, we can use Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. This means that the force with which you push the wall (40N) is the same magnitude as the force with which the wall pushes you. Therefore, the wall pushes back on you with a force of 40N.
Now, to show that your acceleration is 0.5 m/s^2, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a). Mathematically, it can be represented as F = m * a.
In this scenario, the force exerted on you by the wall (40N) is the same as the force acting on you (since the wall is the only force present). Therefore, we can set F equal to 40N. Given that your mass is 80kg, we can plug these values into the equation:
40N = 80kg * a.
Now, solving for acceleration (a), we divide both sides of the equation by 80kg:
40N / 80kg = a.
Simplifying the expression, we find:
0.5 m/s^2 = a.
Hence, we have shown that your acceleration in this scenario is 0.5 m/s^2.