Download HW Set 14 - Rose

ES201 – HW Set 14
Problem 14.1 (10 points)
A train car filled with sand is traveling to the right with a constant velocity VTC = 20 mph. Suddenly
doors on the bottom of the train car open and sand falls through the opening as shown in the figure. The
The sand falls from the car at a mass flow rate of 600 lbm/s and a velocity measured with respect to the
moving train car of Vsand/TC. The direction of Vsand/TC depends on θ shown in the figure. The mass of the
empty train car is 26 tons (1 ton = 2000 lbm) and the initial mass of sand in the car is 50 tons.
Determine the magnitude and direction of
the force F required to keep VTC constant
immediately after the sand doors open if
VTC
(a) θ = 0o and |Vsand/TC|= 10 ft/s.
F
(b) θ = 60 and |Vsand/TC| = 20 ft/s
o
(c) θ = – 60o and |Vsand/TC| = 20 ft/s
θ
Problem 14.2 (10 points)
A tennis player practices hitting serves into a solid vertical barrier at her practice court. Measurements
have shown that the average force that the barrier exerts on the tennis ball as it hits and rebounds from
the barrier depends on the approach speed measured with respect to the barrier (Relative Approach
Speed).
Three measurements are shown in the table. The duration of the impact, the time the ball is in contact with the barrier, is estimated to be
0.02 seconds for all cases. The mass of the tennis ball is 58 grams.
Assume for modeling purposes that the incoming and leaving velocities are both horizontal, i.e. normal to the vertical barrier. When applying conservation of linear momentum to the tennis ball, you may find
the following relation useful:
t2
F
barrier
t1
dt  Fbarrier tcontact
average
Stationary Barrier
Case
Relative
Approach
Speed
Average
Barrier
Force
I
50 m/s
284 N
II
40 m/s
220 N
III
30 m/s
157 N
∆tcontact ≈ 0.02 seconds
Part A — As part of a physics experiment the player hits a horizontal 40 m/s serve towards a stationary
barrier. Determine the direction and magnitude of the return velocity of the tennis ball after it hits the
barrier. Use the information in the table to estimate the average barrier force. The contact time is still
0.02 seconds. [If careful you only need to set up the equations once to answer all parts of this problem.]
Part B —Repeat Part A only this time assume that the barrier is moving away from the player at 10 m/s.
In addition to the return velocity, determine the relative approach and return velocities measured with
respect to the barrier.
Part C — Repeat Part A only this time assume that the barrier is moving towards the player at 10 m/s.
In addition to the return velocity, determine the relative approach and return velocities measured with
respect to the barrier.
What if any conclusions can you draw from looking at these results? Does it make physical sense?