A man (mass = 78.6 kg) is jogging through the woods and runs straight into a large oak tree at 6.1 m/s. Rebound speed is measured at 5.2 m/s in the opposite direction. If the time of contact with the tree is 0.041s, what is the magnitude of the force that the tree exerts on the man?
F•Δt = Δ(m•v) = m• Δv= m(v2-v1),
F = m(v2-v1)/Δt = 78.6(6.1 – (-5.2))/0.041= 21663 N
To find the magnitude of the force that the tree exerts on the man, we can use Newton's second law of motion, which states that the force acting on an object is equal to the rate of change of its momentum.
The momentum of an object is given by the product of its mass and velocity: p = m * v.
Initially, the man has a positive momentum (since he is moving forward) and after rebounding from the tree, his momentum becomes negative (as he moves in the opposite direction).
The change in momentum can be calculated using the equation: Δp = p_after - p_before.
Now, let's break down the problem to determine the magnitude of the force:
1. Calculate the initial momentum (p_before):
p_before = m * v_before
where m is the mass of the man (78.6 kg) and v_before is the velocity before the collision (6.1 m/s).
2. Calculate the final momentum (p_after):
p_after = m * v_after
where v_after is the velocity after the collision (5.2 m/s).
3. Calculate the change in momentum (Δp):
Δp = p_after - p_before
4. Calculate the force exerted by the tree:
F = Δp / Δt
where Δt is the time of contact with the tree (0.041 s).
Now, let's plug in the values and calculate the force:
Step 1:
m = 78.6 kg
v_before = 6.1 m/s
p_before = m * v_before
Step 2:
v_after = -5.2 m/s (opposite direction)
p_after = m * v_after
Step 3:
Δp = p_after - p_before
Step 4:
Δt = 0.041 s
F = Δp / Δt
By following these steps and substituting the values into the equations, you can calculate the magnitude of the force that the tree exerts on the man.