A person doing a chin-up weighs 615.4 N,
disregarding the weight of the arms. During
the first 21.0 cm of the lift, each arm exerts
an upward force of 435 N on the torso.
The acceleration of gravity if 9.81 m/s
2
.
If the upward movement starts from rest,
what is the person’s speed at this point?
Answer in units of m/s.
To find the person's speed at this point, we can apply Newton's second law of motion which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = m * a).
Let's break down the forces acting on the person during the chin-up:
- The force exerted by each arm on the torso: 435 N (upward force)
- The weight of the person (force due to gravity): 615.4 N (downward force)
Since the arms are exerting an upward force, we can subtract this force from the person's weight to find the net force:
Net force = weight - force exerted by arms
Net force = 615.4 N - 435 N
Net force = 180.4 N (upward force)
Now, we can calculate the acceleration using Newton's second law:
F = m * a
180.4 N = m * 9.81 m/s^2
(multiplying both sides by 1/9.81)
m / 9.81 = 180.4 / 9.81
m = (180.4 / 9.81) kg
To find the speed at this point, we need to know the distance covered during the first 21.0 cm of the lift. Let's convert this distance to meters:
Distance = 21.0 cm = 0.21 m
Now we can use the equation for uniformly accelerated motion to find the speed:
v^2 = u^2 + 2as
Since the upward movement starts from rest, the initial velocity (u) is 0. The final velocity (v) is what we need to calculate. Plugging in the values, we have:
v^2 = 0 + 2 * a * s
v^2 = 2 * 180.4 / 9.81 * 0.21
v^2 = (2 * 180.4 * 0.21) / 9.81
v^2 = 7.224 m^2/s^2
Taking the square root of both sides to isolate v:
v = sqrt(7.224)
v ≈ 2.69 m/s
Therefore, the person's speed at this point is approximately 2.69 m/s.