A bb player crouches lowering center of gravity 0.3m. when he jumps, center of gravity reaches 0.9m above normal. A. Calculate velocity when feet left ground. B. Calculate acceleration produced to achieve velocity. C. What force exerted on floor if mass is 110 kg?
To solve these questions, we need to apply the principles of mechanics, specifically the laws of motion. Let's break down each part step by step.
A. Calculate velocity when feet leave the ground:
To find the velocity when the feet leave the ground, we can use the principle of conservation of mechanical energy. The potential energy at the highest point (when the center of gravity is 0.9m above the normal) is equal to the initial potential energy at the lowest point (when the center of gravity is lowered by 0.3m).
At the lowest point:
Potential Energy (PE) = mass (m) * acceleration due to gravity (g) * height (h)
PE_lowest = m * g * 0
At the highest point:
Potential Energy (PE) = mass (m) * acceleration due to gravity (g) * height (h)
PE_highest = m * g * 0.9
Since the potential energy is conserved, we can equate the two equations:
PE_lowest = PE_highest
m * g * 0 = m * g * 0.9
Canceling out the mass and the acceleration due to gravity, we have:
0 = 0.9g
To find the velocity, we can use the equation for free fall:
v^2 = u^2 + 2as
Since the initial velocity (u) is zero (from rest), the equation simplifies to:
v^2 = 2as
Since the object is moving vertically upwards, the acceleration (a) will be negative due to gravity (-9.8 m/s^2). The displacement (s) will be the difference in height from the lowest point to the highest point (0.9m - 0.3m = 0.6m).
Substituting the values into the equation:
v^2 = 2*(-9.8)*0.6
Simplifying:
v^2 = -11.76
Taking the square root of both sides:
v = √(-11.76)
Realizing that the velocity cannot be an imaginary number (since we only have real-life situations), we conclude that the velocity at the feet leaving the ground is zero (v = 0).
B. Calculate acceleration produced to achieve velocity:
Since the velocity is zero, the acceleration produced to achieve this velocity is also zero (a = 0). The player has reached the highest point and is momentarily at rest before coming back down due to the force of gravity.
C. What force is exerted on the floor if the mass is 110 kg:
To find the force exerted on the floor, we can use Newton's second law of motion:
Force (F) = mass (m) * acceleration (a)
In this case, the acceleration is due to gravity, so we can substitute -9.8 m/s^2 as the acceleration:
F = 110 kg * (-9.8 m/s^2)
Calculating:
F = -1078 N
The force exerted on the floor is -1078 Newtons, where the negative sign indicates that it is directed downward (opposite to the upward force exerted by the person).
Please note that in these calculations, we assumed that air resistance is negligible and that the motion is happening in a vacuum.