A ball whose mass is 0.4kg hits the floor with a speed of 7m/s and rebounds upward with a speed of 6m/s.
The correct answer and explanation is:
To solve this, we calculate the impulse imparted to the ball, which is the change in momentum.
Step-by-step Calculation
Given:
- Mass of the ball, m=0.4 kgm = 0.4 \, \text{kg}
- Velocity before hitting the floor (downward), vi=−7 m/sv_i = -7 \, \text{m/s}
- Velocity after rebounding (upward), vf=+6 m/sv_f = +6 \, \text{m/s}
Note: We take downward as negative and upward as positive to maintain a consistent direction.
Impulse JJ is given by: J=Δp=m(vf−vi)J = \Delta p = m(v_f – v_i) J=0.4×(6−(−7))=0.4×(13)=5.2 NsJ = 0.4 \times (6 – (-7)) = 0.4 \times (13) = 5.2 \, \text{Ns}
✅ Final Answer: Impulse = 5.2 Ns (Newton-seconds)
🧠 Explanation (≈300 words)
Impulse is a concept in physics that describes the effect of a force acting over time to change an object’s momentum. It’s defined as the product of force and the time interval during which the force acts, but it can also be calculated as the change in momentum of an object.
In this case, we have a ball with a mass of 0.4 kg falling to the ground at a speed of 7 m/s and then bouncing back upward at 6 m/s. Since velocity is a vector (has both magnitude and direction), we must assign opposite signs to the downward and upward motions. Assuming upward is positive, the downward velocity becomes -7 m/s, and the upward rebound is +6 m/s.
The change in momentum (also called impulse) is calculated by taking the difference between the final and initial momentum: Impulse=m(vf−vi)\text{Impulse} = m(v_f – v_i)
Substituting in the values, we get: Impulse=0.4×(6−(−7))=0.4×13=5.2 Ns\text{Impulse} = 0.4 \times (6 – (-7)) = 0.4 \times 13 = 5.2 \, \text{Ns}
This impulse is provided by the floor to reverse and reduce the ball’s velocity, essentially absorbing the incoming momentum and imparting upward momentum. This interaction is typically very brief but involves large forces, especially in rigid collisions.
Impulse also explains why the ball doesn’t rebound with the same speed—it loses energy due to deformation, heat, and sound. The difference in speeds before and after impact indicates some energy loss, though momentum change is still clearly defined.
In conclusion, the impulse experienced by the ball is 5.2 Ns, and it quantifies the total effect of the floor’s force during the collision.