Step-by-step explanation:
To analyze the situation, we can use the concept of impulse and momentum. The impulse-momentum theorem states that the change in momentum of an object is equal to the impulse applied to it. Impulse is the product of the force applied to the object and the time over which the force is applied. Mathematically, it can be expressed as:
Impulse = Force × Time
Also, momentum (p) of an object is given by the product of its mass (m) and its velocity (v):
Momentum (p) = mass × velocity
Let's calculate the force applied to the object in both cases when it comes to rest in 0.03 seconds and 10 seconds.
1. When the object comes to rest in 0.03 seconds:
Initial momentum (p_initial) = mass × initial velocity
p_initial = 10 kg × 15 m/s = 150 kg m/s
Final momentum (p_final) = 0 (since the object comes to rest)
Change in momentum (Δp) = p_final - p_initial
Δp = 0 - 150 kg m/s = -150 kg m/s
Impulse (J) = Δp
J = -150 kg m/s
Impulse = Force × Time
-150 kg m/s = Force × 0.03 s
Now, calculate the force (F_1):
Force (F_1) = -150 kg m/s ÷ 0.03 s
F_1 ≈ -5000 N (the negative sign indicates that the force acts in the opposite direction of the initial motion)
2. When the object comes to rest in 10 seconds:
Initial momentum (p_initial) = 150 kg m/s (same as before)
Final momentum (p_final) = 0 (since the object comes to rest, same as before)
Change in momentum (Δp) = p_final - p_initial
Δp = 0 - 150 kg m/s = -150 kg m/s (same as before)
Impulse (J) = Δp
J = -150 kg m/s (same as before)
Impulse = Force × Time
-150 kg m/s = Force × 10 s
Now, calculate the force (F_2):
Force (F_2) = -150 kg m/s ÷ 10 s
F_2 = -15 N (the negative sign indicates that the force acts in the opposite direction of the initial motion)
So, when the object comes to rest within 0.03 seconds, the force applied is approximately -5000 N, and when it comes to rest within 10 seconds, the force applied is approximately -15 N. The negative sign indicates that the force acts in the opposite direction of the initial motion, which means the object experiences deceleration due to the collision with the wall.