A small robot (mass = 2kg) is hovering in the air when the wind pushes it towards a pole with a speed of 6 m/s. The robot rebounds with a speed of 1.5 m/s, and the collision lasts for 0.5 s. Determine the average force exerted by the pole on the robot when they collide.
momentum inbound = 2 * 6 = 12 kg m/s
momentum outbound = 2 * -1.5 = -3 kg m/s
change in momentum = -3 - 12 = -15 kg m/s
average force = rate of change of momentum = change in momentum / time
= -15 kg m /s / .5 s = -30 kg m/s^2 = -30 Newtons
Is the velocity always taken to be negative when we consider the rebound of the object?
I defined it going + direction to start. You can draw your coordinate system otherwise. However they asked for the force, not the magnitude of the force, so it has to have a direction (lousy problem statement)
To determine the average force exerted by the pole on the robot during the collision, we can use Newton's second law of motion, which states that force (F) is equal to the rate of change of momentum (p) of an object.
The formula for momentum is given by:
p = m * v
where:
p is momentum,
m is mass, and
v is velocity.
During the collision, the robot's velocity changes from 6 m/s to -1.5 m/s (rebound velocity). Since the velocity changes in direction, we will consider the negative value.
To find the change in momentum, we need to calculate the initial and final momenta of the robot.
Initial momentum (p_initial) = m * v_initial
p_initial = 2 kg * 6 m/s = 12 kg·m/s
Final momentum (p_final) = m * v_final
p_final = 2 kg * (-1.5 m/s) = -3 kg·m/s
Now, we can calculate the change in momentum:
Δp = p_final - p_initial
Δp = -3 kg·m/s - 12 kg·m/s
Δp = -15 kg·m/s
The collision lasts for 0.5 seconds, so we can determine the average force using the formula:
F = Δp / Δt
where:
F is average force,
Δp is change in momentum, and
Δt is time interval.
Substituting the known values:
F = (-15 kg·m/s) / (0.5 s)
F = -30 N
The negative sign indicates that the force exerted by the pole is in the opposite direction of the robot's velocity.
Therefore, the average force exerted by the pole on the robot during the collision is 30 Newtons (N).