A 40 kg child throws a 0.5 kg stone at a velocity of 5 m/s. To find the recoil, we apply the conservation of momentum formula: m1•v1 + m2•v2 = 0, where m1 is the mass of the child, and v1 is the child's recoil velocity. Applying the known values results in 40•v1 = -0.5 × 5, leading to v1 = -2.5 / 40, which simplifies to v1 = -0.0625 m/s. Thus, the child's recoil speed is 0.0625 m/s.
A tennis player recovering from an ankle injury, restricted from pivoting, can keep her cardiovascular fitness by using the rowing machine, pedaling on a stationary bike with one leg, or swimming. These exercises do not necessitate directional changes and are safe for her injury.
In the system analyzed, there is no heat transfer as the temperature remains constant at 25°C before and after the interaction. The heat exchange can be expressed by the equation Q = mCΔT, indicating that if ΔT equals zero, there is evidently no heat gain or loss. Considering the vacuum side of the tank, where m equals 0, we find Q equals 0 KJ, signifying that the system experienced no heat exchange.
Solution:
The kinetic energy of the clam at an elevation of 5.0 m is 5.19 J and the velocity of the clam at that height is 9.71 m/s.
Explanation:
Throughout its motion, mechanical energy remains constant. We understand that mechanical energy is the summation of potential energy and kinetic energy. Potential energy =
, Kinetic energy =
and Mechanical energy =
Initial kinetic energy is zero. At a height of 9.8 m, the mechanical energy of the clam with a mass of 0.11 kg and g=9.81
is calculated as follows: 0.11×9.81×9.8 = 10.58 J.
Mechanical energy of the clam at a height of 5.0 m =
=
. Given that mechanical energy is conserved, we can state that the mechanical energy of the clam at a height of 9.8 m is equal to that at 5.0 m. The representation is as follows:
10.58 =
10.58 – 5.39 =
5.19 =
the clam's kinetic energy measures 5.19 J.
Lastly, the speed of the clam at 5.0 m is computed; thus, 5.19 =
94.36 =
= 9.71 m/s. The clam's speed is determined to be 9.71 m/s.