CALC A Variable-Mass Raindrop. In a rocket-propulsion problem the mass is variable. Another such problem is a raindrop falling through a cloud of small water droplets. Some of these small droplets adhere to the raindrop, thereby increasing its mass as it falls. The force on the raindrop is F ext = d p d t = m d υ d t + υ d m d t Suppose the mass of the raindrop depends on the distance x that it has fallen. Then m = kx , where k is a constant, and dm/dt = kυ . This gives, since F ext = mg , m g = m d υ d t + υ ( k υ ) Or, dividing by k , x g = x d υ d t + υ 2 This is a differential equation that has a solution of the form υ = at , where a is the acceleration and is constant. Take the initial velocity of the raindrop to be zero, (a) Using the proposed solution for v , find the acceleration a . (b) Find the distance the rain-drop has fallen in t = 3.00 s. (c) Given that k = 2.00 g/m, find the mass of the raindrop at t = 3.00 s. (For many more intriguing aspects of this problem, see K. S. Krane, American Journal of Physics , Vol. 49 (1981), pp. 113–117.)
CALC A Variable-Mass Raindrop. In a rocket-propulsion problem the mass is variable. Another such problem is a raindrop falling through a cloud of small water droplets. Some of these small droplets adhere to the raindrop, thereby increasing its mass as it falls. The force on the raindrop is F ext = d p d t = m d υ d t + υ d m d t Suppose the mass of the raindrop depends on the distance x that it has fallen. Then m = kx , where k is a constant, and dm/dt = kυ . This gives, since F ext = mg , m g = m d υ d t + υ ( k υ ) Or, dividing by k , x g = x d υ d t + υ 2 This is a differential equation that has a solution of the form υ = at , where a is the acceleration and is constant. Take the initial velocity of the raindrop to be zero, (a) Using the proposed solution for v , find the acceleration a . (b) Find the distance the rain-drop has fallen in t = 3.00 s. (c) Given that k = 2.00 g/m, find the mass of the raindrop at t = 3.00 s. (For many more intriguing aspects of this problem, see K. S. Krane, American Journal of Physics , Vol. 49 (1981), pp. 113–117.)
CALC A Variable-Mass Raindrop. In a rocket-propulsion problem the mass is variable. Another such problem is a raindrop falling through a cloud of small water droplets. Some of these small droplets adhere to the raindrop, thereby increasing its mass as it falls. The force on the raindrop is
F
ext
=
d
p
d
t
=
m
d
υ
d
t
+
υ
d
m
d
t
Suppose the mass of the raindrop depends on the distance x that it has fallen. Then m = kx, where k is a constant, and dm/dt = kυ. This gives, since Fext = mg,
m
g
=
m
d
υ
d
t
+
υ
(
k
υ
)
Or, dividing by k,
x
g
=
x
d
υ
d
t
+
υ
2
This is a differential equation that has a solution of the form υ = at, where a is the acceleration and is constant. Take the initial velocity of the raindrop to be zero, (a) Using the proposed solution for v, find the acceleration a. (b) Find the distance the rain-drop has fallen in t = 3.00 s. (c) Given that k = 2.00 g/m, find the mass of the raindrop at t = 3.00 s. (For many more intriguing aspects of this problem, see K. S. Krane, American Journal of Physics, Vol. 49 (1981), pp. 113–117.)
A 1.2 kg ball is falling in the -y direction at a speed of 25 m/s. The ball strikes the floor and then rebounds with a speed of 10 m/s. If the ball is in contact with the floor for 0.02 seconds, what is the magnitude of the average force of the floor acting on the ball?
Group of answer choices
1500 N
900 N
600 N
2100 N
200 N
0 N
Ball A, with mass mA = 1.2 kg, is released from height h = 0.5 m and strikes block B, with mass mB = 2 kg, which is initially at rest on a horizontal surface. After impact, block B travels a distance d = 0.9 m along the horizontal surface, after which it stops. The coefficients of friction between block B and the horizontal surface are μs = 0.30 and μk = 0.20, respectively.
a. acceleration of block B as it moves along the horizontal surfaceb. speed of block B after impact with pendulum bob Ac. speed of pendulum bob A just before it hits block Bd. coefficient of restitution between pendulum bob A and block B
A space probe, initially at rest, undergoes an internal mechanical malfunction and breaks into three pieces. One piece of mass m1 = 48.0 kg travels in the positive x -direction at 12.0 m/s, and a second piece of mass m2 = 62.0 kg travels in the xy -plane at an angle of 105° at 15.0 m/s. The third piece has mass m3 = 112 kg. (a) Sketch a diagram of the situation, labeling the different masses and their velocities. (b) Write the general expression for conservation of momentum in the x and y -directions in terms of m1, m2, m3, v1, v2 and v3 and the sines and cosines of the angles, taking u to be the unknown angle. (c) Calculate the final x -components of the momenta of m1 and m2 . (d) Calculate the final y -components of the momenta of m1 and m2 . (e) Substitute the known momentum components into the general equations of momentum for the xand y -directions, along with the known mass m3, v3 cos0 and v3 sin0 , respectively, and use the identity cos0 + sin20 = 1 to obtain v3 . (g) Divide…
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.