I've asked a similar qustion earlier and now I think I have drawn the correct free body diagram and go about solving the problem. The only thing is I do not know how to solve it.
a block (mass m1) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block (m2), which hangs vertically.
If m1 = 13.0 kg and m2 = 6.0 kg determine the acceleartion of each block. Ignore friction and the masses of the pulley and cord
ok well according to my free body diagram
acceleration of blcok one is equal to m1^-1 Ft = a
for block 2 acceleration = m2^-1(Ft + Fg)
I do not see how to solve for the acceleration of each block only knowing this and given only the masses of each block.
Please Help!
You have to use that the masses are connected by each other via a cord that has some fixed length. This means that the two accelerations are the same. The force exterted by the cord has an opposite sign in both cases, or you have to take the accelerations to be opposite to each other.
If you put:
Ft = m1 a
m2 a = m2 g - Ft
then you can solve for a.
What is the net pulling force? Answer m1(g-a).
What is the acceleration of the system? Answer: netforce/mass= (m1(g-a))/(m1+M2)
Observation: the acceleration each block is the same
ok how do I solve for a
m1 a - m2 g = m2 a
I got this
a = m2^-1 (m1 a) -g
i'm stuck from there
they cancle each other out look
(a = m2^-1 (m1 a) -g )a^-1 = 0 = m2^-1 m1 - g
0 = m2^-1 m1 - g
To solve for the acceleration of each block in this system, you need to apply Newton's second law of motion and consider the forces acting on each block.
Let's break down the problem step by step:
1. Identify the forces acting on each block:
- Block 1 (m1) on the smooth horizontal surface:
- Tension force (T) acting to the right because of the cord connected to block 2.
- (No other forces present because there is no friction and the block is on a smooth surface.)
- Block 2 (m2) hanging vertically:
- Tension force (T) acting upward because of the cord connected to block 1.
- Weight force (W) acting downward due to the gravitational force.
2. Write down the equations of motion for each block:
- Block 1 (m1):
- From Newton's second law: m1 * acceleration = T
- Block 2 (m2):
- From Newton's second law: m2 * acceleration = T + W
3. Substitute the known values:
- For Block 1 (m1):
- m1 = 13.0 kg
- acceleration = ?
- T = ?
- For Block 2 (m2):
- m2 = 6.0 kg
- acceleration = ?
- T = ?
- W = m2 * g, where g is the acceleration due to gravity (approximately 9.8 m/s^2).
4. Equate the tensions in the cord for both blocks:
- Since they are connected by a cord, the tension force in the cord connecting Block 1 and Block 2 is the same.
- Therefore, we can equate T for both block equations: T = T.
5. Now you have two equations with two unknowns (acceleration and tension):
- Block 1 equation: 13.0 kg * acceleration = T
- Block 2 equation: 6.0 kg * acceleration = T + (6.0 kg * 9.8 m/s^2)
6. Combine the two equations:
- 13.0 kg * acceleration = 6.0 kg * acceleration + (6.0 kg * 9.8 m/s^2)
7. Solve for acceleration:
- (13.0 kg - 6.0 kg) * acceleration = 6.0 kg * 9.8 m/s^2
- acceleration = (6.0 kg * 9.8 m/s^2) / (13.0 kg - 6.0 kg)
- acceleration = (58.8 N) / (7.0 kg)
- acceleration ≈ 8.4 m/s^2
So the acceleration of each block in this system is approximately 8.4 m/s^2.