Question

1. a 12 kg box sliding on a horizontal floor has an initial speed of 4.0 m/s. the coefficient of friction between the box and the floor is 0.20. the box moves a distance of 4.0 m in 2.0 s. the magnitude of the change in momentum of the box during this time is most nearly

a) 12 kg·m/s b) 48 kg·m/s c) 60 kg·m/s d) 96 kg·m/s

1. a mass m has speed v. it then collides with a stationary object of mass 2m. if both objects stick together in a perfectly inelastic collision, what is the final speed of the newly formed object?

(a) \\(\frac{v}{3}\\) (b) \\(\frac{v}{2}\\) (c) \\(\frac{2v}{3}\\) (d) \\(\frac{3v}{2}\\)

1. how does an air mattress protect a stunt person landing on the ground after a stunt?

(a) it reduces the kinetic energy loss of the stunt person.

Explanation:

Step1: Calculate initial momentum

Initial momentum $p_i = m \cdot v_i = 12 \, \text{kg} \times 4.0 \, \text{m/s} = 48 \, \text{kg·m/s}$

Step2: Calculate final velocity

Final velocity $v_f = \frac{d}{t} = \frac{4.0 \, \text{m}}{2.0 \, \text{s}} = 2.0 \, \text{m/s}$

Step3: Calculate final momentum

Final momentum $p_f = m \cdot v_f = 12 \, \text{kg} \times 2.0 \, \text{m/s} = 24 \, \text{kg·m/s}$

Step4: Calculate momentum change

Change in momentum $\Delta p = |p_f - p_i| = |24 - 48| = 24 \, \text{kg·m/s}$ (Note: No option matches? Wait, recheck question 5 options—wait original options for Q5: A)12, B)48, C)60, D)96. Wait maybe misread: friction force $F_f = \mu mg = 0.2×12×9.8≈23.52 \, N$. Impulse $\Delta p = F_f×t = 23.52×2≈47.04≈48 \, \text{kg·m/s}$. Oh right! Impulse equals momentum change, so $\Delta p = F_f t = \mu m g t$.
Recalculate: $\mu=0.2, m=12, g=9.8, t=2$. $\Delta p = 0.2×12×9.8×2≈47.04≈48$.

Step1: Apply conservation of momentum

Initial momentum: $m \cdot v + 2m \cdot 0 = mv$. Final momentum: $(m+2m)v_f = 3mv_f$. Set equal: $mv=3mv_f$.

Step2: Solve for final speed

Cancel $m$: $v=3v_f → v_f = \frac{v}{3}$.

An air mattress increases the collision time when landing, which reduces the impact force (by impulse-momentum theorem: $FΔt=Δp$). It also compresses to absorb kinetic energy, reducing the kinetic energy loss rate and peak force on the person.

Answer:

B) 48 kg·m/s