Hello world.
Can you guys help me with these 2 questions? i don't need you to solve the questions or anything but just to please give me some hints on where to start would be greatly appreciated :)
1. an 80kg St Bernard dog leaps with an acceleration of 2ms^-2 from a stationary 40kg canoe to shore. What is the recoil acceleration of the canoe?
and
2. The Breaking strain on the cable holding the elevator in the eiffel tower is 30000N. The maximum number of people that can ride in the elevator at any one time is twenty. Given that the mass of each person is 70kg and the elevator has a mass of 400kg, what is the maximum upward acceleration that the elevator can have?
thankyou :)
Answer :
1) for the system acceleration of centre of mass is zero
hence, acm = m1 a1 + m2 a2 / m1 + m2 = 0 ie., a2 = - m1 a1 / m2 , where 'a2' is the acceleration of the canoe
hence, a2 = - 80 x 2 / 40 = - 4 m/sec^2 ( in opposite direction)
2) maximum upward accelration a = T / m - g , where 'm' is the total mass on the cable
hence, a = 30000/ 1800 - 9.8 = 6.87 m/sec^2 ( nearly)
Answer :
1.
By Newton's Third Law, the force on the canoe is the same as the force on the dog -- F1 = F2.
By Newton's Second Law, the force is the mass times the acceleration -- F = ma.
Since F1 = F2, just write F = ma. However, the masses are different: m1 = 80 kg, and m2 = 40 kg.
F = m1a = (80 kg)(2 m/s²) = 160 N.
F = m2a = (40 kg)(x m/s²) = 160 N.
x = 160/40 = 4 m/s².
2.
Total mass of people + elevator = (20)(70 kg) + 400 kg = 1800 kg.
Total weight = mass × g = (1800 kg)(9.81 m/s²) = 17 700 N (to 3 significant figures, although only 1 sig. fig. can be justified here).
Difference between strength of cable and maximum load = 30 000 N - 17 700 N = 12 300 N.
This is equivalent to a weight; find the acceleration by dividing by the mass:
(12 300 N) / (1800 kg) = 6.8 m/s².
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