A high jumper, falling at 3.8 m/s, lands on a foam pit and comes to rest compressing the pit 0.38 m. If the pit is able to exert an average force of 1100 N on the high jumper in breaking the fall, what is the jumper's mass?
dawd
Vf^2=Vi^2+2ad
but a= force/mass, negative here.
solve for mass
To find the mass of the high jumper, we can start by analyzing the forces acting on the jumper.
When the high jumper falls and lands on the foam pit, there are two forces at play: the force exerted by gravity (mg) pulling the jumper down and the force exerted by the foam pit pushing up on the jumper.
We can consider the foam pit as a spring, as it compresses under the weight of the jumper. According to Hooke's Law, the force exerted by a spring is proportional to its displacement: F = kx.
In this case, the average force exerted by the foam pit is given as 1100 N, and the compression of the pit is given as 0.38 m. Therefore, we have:
F = kx
1100 N = k × 0.38 m
To find the spring constant, k, we rearrange the equation:
k = 1100 N / 0.38 m
k ≈ 2894.74 N/m
Now, let's consider the force exerted by gravity. The weight of an object is given as the product of its mass (m) and the acceleration due to gravity (g). In this case, the force exerted by gravity is -mg, with a negative sign since it acts in the opposite direction to the force exerted by the foam pit.
The net force acting on the jumper can be obtained by subtracting the force exerted by the foam pit from the force exerted by gravity:
Net force = Force due to gravity - Force exerted by foam pit
Net force = -mg - F
Since the jumper comes to rest, we know that the net force is zero:
0 = -mg - F
Rearranging the equation, we have:
mg = - F
m = - F / g
Substituting the given values:
m = - 1100 N / (9.8 m/s²)
m ≈ - 112.24 kg
The negative sign indicates that the mass is in the opposite direction to the force exerted by gravity, which is expected since we are dealing with an upward force from the foam pit. Therefore, the magnitude of the mass is 112.24 kg.