Mass and weight

Question

A weight G = 10 N is subjected to a vertical upward pulling force F = 20 N. At the beginning, the weight is stationary. After some time, it is lifted up to 2 m, what is its velocity at this moment? Let the gravitational acceleration be g = 10 m/s²

Answer 1

This is a constant acceleration problem that you can use either kinematics or conservation of energy.

For kinematics the parameters are: Δy, v_i, v_f, a, Δt

Δy = the change in the objects position / displacement (is also Δx if horizontal change)

1. For this problem it is lifted up 2 m from initial to final position (Δy = +2 m)

v_i = initial object velocity before the force was applied (assumed to be 0 m/s)

v_f = the final object velocity, this is the unknown and it should be in the direction of net force

Δt = No time information is given, for kinematics you only need three parameters to solve for the others

a = the constant acceleration of the object between initial and final states

1. For this we must draw a free body diagram
2. For the FBD, an upward applied force is in the (+) y direction (F_app = 20N)
3. The only other force is that due to gravity assumed to be in the (-) y direction
4. G = mg (m = object mass ; g = gravitational acceleration ∼10 m/s²) (Solve for mass)
5. Thus the net force on the object will be F_y = F_app - G
6. Using Newton's Second Law of Motion we can find the acceleration:
7. F_y = F_app - G = ma --> a = (F_app - G)/m

We now know three kinematic parameters (Δy, v_i, and a) and solve for v_f or Δt

1. We want the kinematic equation without time since we not need it
2. v_f² = v_i² + 2aΔy --> Solve for v_f (take care of the exponent / square)

Answer should be between 5 and 7 m/s

Let me know if you or someone else would like the energy approach.