A 1.2 kg object is moving with a speed of 8.0 m/s collides perpendicularly with a wall and emerges with a speed of 6.0m/s in the opposite direction perpendicular to the wall. If the object is in contact with the wall for 2.0m/s. What is the magnitude of the average force on the object by the wall?
8.4Kn
Could you please explain how you got to your answer?
F=Δp/Δt=mΔv/Δt=
=m[v₂-(-v₁)]/Δt=
=m(v₂+v₁)/Δt=
=1.2•(6+2)/ Δt=…
Check the given data (time of contact!!!!)and substitute it
Well, this situation seems like a bit of a collision course, doesn't it? Let's see if we can juggle the numbers and figure it out!
First, let's calculate the change in velocity of the object. It goes from 8.0 m/s in one direction to 6.0 m/s in the opposite direction, so the change in velocity is 8.0 m/s + 6.0 m/s = 14.0 m/s.
Now, we need to find the time it takes for this change in velocity to occur. Since the object is in contact with the wall for 2.0 seconds, we can use that to find the average force.
The average force can be calculated using the equation:
Average force = mass * (change in velocity / time)
Plugging in the numbers, we get:
Average force = 1.2 kg * (14.0 m/s / 2.0 s)
Now it's just basic arithmetic from here:
Average force = 1.2 kg * 7.0 m/s
And voila! The magnitude of the average force on the object by the wall is 8.4 N. Just enough force to make the object go bananas!
To calculate the magnitude of the average force on the object by the wall, we can use the principle of impulse-momentum.
The principle of impulse-momentum states that the change in momentum of an object is equal to the impulse applied to it. In this case, we can consider the impulse applied to the object by the wall as it collides and rebounds.
Given:
Mass of the object (m): 1.2 kg
Initial velocity of the object (u): 8.0 m/s
Final velocity of the object (v): -6.0 m/s (opposite direction)
Distance traveled by the object during collision (s): 2.0 m
First, let's calculate the initial momentum of the object:
Initial momentum (p₁) = mass × velocity = m × u
p₁ = 1.2 kg × 8.0 m/s
Next, let's calculate the final momentum of the object:
Final momentum (p₂) = mass × velocity = m × v
p₂ = 1.2 kg × (-6.0 m/s) (Note: The negative sign is used to indicate the opposite direction)
Now, we can calculate the change in momentum (Δp) of the object:
Δp = p₂ - p₁
Finally, we can find the magnitude of the average force (F) applied to the object by the wall using the formula:
F = Δp / Δt
Considering that the distance traveled during the collision (s) is given, we can calculate the time (Δt) taken during the collision:
Δt = s / |v| (Absolute value of velocity to get the positive value)
Substituting the values we calculated and given, we can find the magnitude of the average force.
Note: The magnitude of a quantity represents its scalar value, disregarding its direction.
You can plug in the values to calculate the magnitude of the average force on the object by the wall.