A force of 5 N produces an acceleration of 8 ms 2 on a mass m, and an acceleration of 24 ms? on a mass m,. What acceleration (in ms 2) would the same force provide if both the masses are tied together?
1)12 2)9 3)10 4)6
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A force of 5 N produces an acceleration of 8 ms 2 on a mass m, and an acceleration of 24 ms? on a mass m,. What acceleration (in ms 2) would the same force provide if both the masses are tied together?
1)12 2)9 3)10 4)6
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Answer:
To find the acceleration when both masses are tied together, you can use the principle of conservation of momentum. The force applied will result in an acceleration that takes both masses into account.
The formula for acceleration is given by F = ma, where F is the force, m is the mass, and a is the acceleration.
For the first mass (m1) with an acceleration of 8 m/s^2:
F = 5 N
a1 = 8 m/s^2
m1 = F / a1
m1 = 5 N / 8 m/s^2
m1 = 5/8 kg
For the second mass (m2) with an acceleration of 24 m/s^2:
F = 5 N
a2 = 24 m/s^2
m2 = F / a2
m2 = 5 N / 24 m/s^2
m2 = 5/24 kg
Now, when both masses are tied together, the total mass (M) is the sum of m1 and m2:
M = m1 + m2
M = 5/8 kg + 5/24 kg
To add these fractions, find a common denominator, which is 24:
M = (15/24) kg + (5/24) kg
M = 20/24 kg
M = 5/6 kg
Now, you can find the acceleration (a_total) when the force of 5 N is applied to the combined mass (M) using the same force-acceleration relationship:
F = 5 N
M = 5/6 kg
a_total = F / M
a_total = 5 N / (5/6) kg
a_total = 5 N * (6/5) kg
a_total = 6 m/s^2
So, when both masses are tied together, the acceleration is 6 m/s^2. Therefore, the answer is option 4) 6.
Explanation:
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