The two ropes seen in (Figure 1) are used to lower a 255 kg piano exactly 8 m fr
ID: 1418679 • Letter: T
Question
The two ropes seen in (Figure 1) are used to lower a 255 kg piano exactly 8 m from a second-story window to the ground.
A) How much work is done by w? ?
B)How much work is done by T? 1?
C)How much work is done by T? 2?
question 2)
At what speed does a 1200 kg compact car have the same kinetic energy as a 20000 kg truck going 24 km/hr ?
Question 3)
A 19 g plastic ball is moving to the left at 15 m/s . How much work must be done on the ball to cause it to move to the right at 15 m/s ?
Question 4)
What is the kinetic energy of a 1800 kg car traveling at a speed of 30 m/s (?65 mph)?
Question 5)
From what height should the car be dropped to have this same amount of kinetic energy just before impact?
Figure 1 of 1 T1 1830 N | 60 71295 N 45Explanation / Answer
1. f you find the vertical components of the tensions in the ropes (1830 sin 60 and 1295 sin 45), you will see they equal the weight of the piano, so that the piano is being lowered at a constant speed (with no accleration)
the work done by a force is force in the direction of motion x displacement
so the work done by the ropes is - T sin(theta) x 5.9m
T sin(theta) is the vertical component of force, 5.9m is the distance, and the minus sign indicates that the force (due to the ropes) is opposite the direction of motion
the work done by gravity is simply 2500N x 5.9m and is positive since the force is in the direction of motion
W1 = - 1830 sin 60 x 5.9m
W2 = - 1295 sin 45 x 5.9m
W3 = 2500N x 5.9m
2.KE = (1/2)m*v^2
KE of the truck = KE of the car
(1/2)*12 x 10^4 * 24^2 = (1/2)*1200 * v^2
v(car) = 240 km/h
3. WD = loss of KE to bring the ball to a stop + extra KE to reach the ball's new velocity
v1 = +15 m/s, v2 = -15 m/s
WD = 0.5*m*v1^2 + 0.5*m*v2^2
WD = 2*0.5*0.019kg*(15m/s)^2 = 4.275 J
4. KE = 1/2 * m * v^2
1/2 * 1800 * 30^2 = 810,000 J
5. Height: v = a * t
t = (2 * h / a)^1/2
v = a * (2 * h / a)^1/2
Rearrange:
h = v^2 / (2 * a)
h = 30^2 / (2 * 9.8) = 45.92 m
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